Gottfried Wilhelm Leibniz, his life and ideas. Gottfried Wilhelm Leibniz - biography, information, personal life

Surely many people remember from school that on the pages of algebra textbooks you can find the name of Leibniz, and sometimes his portrait. But not everyone knows that this man not only invented the integral sign and mathematical formulas, but also made discoveries in other scientific fields. Unfortunately, Leibniz did not receive due respect for his services during his lifetime, but his name became immortal, and the teachings of this philosopher became fundamental for future generations.

Childhood and youth

Gottfried Wilhelm Leibniz was born on June 21 (July 1), 1646, in the administrative center of Lower Saxony - Hanover. Gottfried grew up in the family of a professor of Serbian-Lusatian origin, who was not far from philosophical teaching: for 12 years the main breadwinner in the house taught a special form of knowledge of the world and positioned himself as a public professor of morality.

His third wife, Katerina Schmuck, the daughter of a high-ranking lawyer, is a purebred German by nationality. Gottfried was a child kissed by God: from early childhood the boy showed his genius, so the Leibniz tried to develop the curiosity of their little son. Even then there was no doubt that their offspring would become a great scientist who would give this world useful inventions.

The father of a gifted boy instilled in Gottfried a love of literature, so Leibniz devoured books one after another, reading historical stories about great kings and brave knights. Unfortunately, Leibniz the elder died when the boy was not even seven years old, but his parent left behind a large library, which became a favorite place for young Gottfried.

One day, the future philosopher and scientist came across two manuscripts that had once been left by a student. These were the works of the ancient Roman historian Livy and the chronological treasury of Calvisius. Young Leibniz read the latter author without difficulty, but understanding Livy turned out to be difficult for Gottfried, for the ancient book was written using sublime rhetoric and equipped with ancient engravings.

But Leibniz, not used to giving up, re-read the philosopher’s works until he understood the essence of what was written without using a dictionary. The young man also studied German and Latin, surpassing his peers in mental development. Leibniz's teacher noticed that his student did not follow the school curriculum, but ran ahead, adding to his knowledge the works of a writer whom he should have paid attention to as a high school student.

Therefore, the teacher, who believed that Gottfried should put Livy’s books away, argued to the young man’s educators that they needed to pay attention to Leibniz’s self-education and instill in the boy a love for the humanist Comenius and theologian. But, by a happy coincidence, a nobleman passing by heard this conversation and reproached the teacher for measuring everyone with the same standard.

Consequently, no one forbade Leibniz to independently replenish his knowledge, because a passer-by, a nobleman, who inquired about Leibniz’s genius, demanded that his parents give him the key to his father’s library. Thus, the young man, burning with impatience, touched the works of ancient scientists.

Leibniz studied at a prestigious educational institution - the Leipzig School of St. Thomas. There the young man demonstrated his mental abilities to the teachers. He quickly solved mathematical problems and even showed literary talent. On the Day of the Holy Trinity, the student who was supposed to read the holiday speech fell ill, so this duty was assigned to Leibniz.

Gottfried managed to compose a work in Latin overnight. Moreover, he was able to construct a poem from five dactyls, achieving the desired sound of the words. The teachers predicted a great future for the boy, who had just turned 13 years old.

Then 14 (15) year old Gottfried continued to gnaw on the granite of science, not at school, but at the University of Leipzig. There he was interested in philosophy - works and. Two years later, Leibniz transferred to the University of Jena, where he began to study mathematics in depth.

Among other things, the young man became interested in jurisprudence, because he believed that science, favored by the goddess Themis, would be useful in later life. In 1663, Leibniz received a bachelor's degree, and a year later - a master's degree in philosophy.

Teaching

Leibniz wrote his first treatise, On the Principle of Individuation, in 1663. Few people know, but after graduating from university, Gottfried became a hired alchemist. The fact is that Leibniz heard about the alchemical community in Nuremberg and decided to use cunning: he copied the most incomprehensible formulas from the books of famous alchemists and brought his work to the chairmen of the Rosicrucian Order.

Adherents of the mystical teaching were amazed at Gottfried’s knowledge and proclaimed him an adept. The scientist admitted that he was not tormented by remorse; the future mathematician took such a step because his unabating curiosity dictated it.

In 1667, the young Leibniz began to engage in journalistic activities and succeeded in philosophical and psychological teaching. It is worth saying that when talking about the unconscious comes up, many people remember, but it was Leibniz who put forward the concept of unconscious small perceptions, ahead of the German psychoanalyst by two hundred years. In 1705, “New Experiments on Human Understanding” were written, and five years later a philosophical work called “Monadology” (1710) was published.

The philosopher created his own synthetic system, believed that the entire diverse world consists of certain substances - monads, which exist separately from each other, and they, in turn, are the spiritual unit of being. Moreover, from his point of view, the world is not something inexplicable, because it is completely knowable, and the problem of truth requires a rational interpretation. According to Leibniz's teachings, the highest monad is the Creator who established a certain world order, and the criterion of truth was logical evidence.

Gottfried viewed existence as something harmonious, but he also tried to overcome the contradictions of good and evil. Leibniz's philosophical works influenced Schelling and, however, he considered his doctrine of the “Theodicy or Justification of God” (1710), which describes the three stages of evil, to be absurd.

Mathematics and Science

Because of his position in the service of the Elector of Mainz, Godfrey had to travel throughout Europe. During these travels, he met the Dutch inventor Christiaan Huygens, who agreed to teach him mathematics.

In 1666, Gottfried became the author of the essay “On the Art of Combinatorics,” and he also conceived a project on the mathematization of logic. We can say that Leibniz looked ahead again, because this scientist stood at the origins of computers and information science.

In 1673, he invented a desktop computer that automatically recorded processed numbers in the decimal system. This device is called the Leibniz adding machine (drawings of the adding machine are found in the manuscripts of Leonardo da Vinci). The fact is that Leibniz was annoyed that his friend Christian spent a lot of time adding numbers, while Gottfried himself believed that adding, subtracting, dividing and multiplying was the lot of slaves.

Leibniz's adding machine surpassed Pascal's calculating machine. It is noteworthy that one copy of the computing device fell into the hands of , who, surprised by the device, hastened to present this miracle device to the Chinese emperor.

The acquaintance of the king, who cut a window to Europe, and the German scientist occurred in 1697, and this meeting was accidental. After lengthy conversations, Leibniz received a monetary reward from Peter and the title of Privy Councilor of Justice. But earlier, after the defeat of the Russian army in the Battle of Narva, Leibniz composed an ode of praise to Charles XII, where he expressed the hope that Sweden would expand its borders from Moscow to the Amur.

But then he admitted that he had the good fortune to be a friend of the great Russian monarch, and thanks to Leibniz, Peter I approved the creation of the Academy of Sciences in St. Petersburg. From Gottfried's biography it is known that in 1708 he had a dispute with the author of the law of universal gravitation. Leibniz published his mathematical discovery about the differential calculus, but Newton, who became acquainted with this scientific work, accused his colleague of stealing ideas and plagiarism.

Isaac stated that he came to the same results 10 years ago, but did not make his work public. Leibniz did not deny that he had once studied Newton's manuscripts, but he came to the same results on his own. In addition, the German came up with more convenient symbolism, which mathematicians use to this day.

The controversy between Newton and Leibniz continued until 1713; this dispute became the seed at the beginning of the pan-European “priority war”, and anonymous brochures were found in cities defending the priority of one of the participants in the conflict. This confrontation became known as "the most shameful squabble in the entire history of mathematics."

Because of the enmity of the two scientists, the English mathematical school withered, and some of Newton's discoveries were ignored and became known to the public only many years later. In addition to mathematics, physics and psychology, Leibniz studied biology (the scientist put forward the idea of ​​​​organic systems as integrity), and also excelled in linguistics and jurisprudence.

Personal life

Leibniz is often called the all-encompassing mind of humanity, but Gottfried, full of ideas, did not always complete the work he started. It is difficult to judge the scientist’s character, since his contemporaries described the scientist’s portrait in different ways. Some said that he was a boring and unpleasant person, while others gave exclusively positive characteristics.

Gottfried, adhering to his own philosophy, was an optimist and a humanist, who, even during a conflict with Isaac Newton, did not say a bad word about his opponent. But Leibniz was quick-tempered and vulnerable, but he quickly came to his senses and often laughed, even if these were insincere emotions. However, the scientist also had a vice, which he himself admitted: sometimes the mathematician was stingy and self-interested.

Leibniz dressed neatly and wore a black wig, as the fashion of the time dictated. The scientist was not picky about food, and he rarely drank wine, often on holidays. But even in this strong drink made from grapes, Gottfried mixed sugar, as he adored sweets.

As for amorous relationships, there is little information about Gottfried’s novels, and some biographers are sure that there was only one woman in the scientist’s life – science. But he developed a warm friendship with the Prussian Queen Sophia Charlotte of Hanover, however, this relationship did not go beyond platonic. In 1705, Sophia died, and Leibniz could not come to terms with what had happened until the end of his life; after the death of his beloved, he did not find the young lady who would touch his heart.

Death

The last years of Leibniz’s life were tense, since his relationship with the current English king did not work out: the great scientist was looked at as a court historiographer, and the ruler, confident that he was spending extra money to pay for Leibniz’s work, constantly expressed his dissatisfaction. Therefore, the scientist was surrounded by intrigues from the courtiers and attacks from the church.

But, despite the futility of existence, Gottfried continued to engage in his favorite science. Due to a sedentary lifestyle, the scientist developed gout and rheumatism, but the genius did not trust his health to doctors, and used only one medicine, donated by a friend. In addition, Leibniz had problems with his eyesight, since the philosopher in his old age did not lose his love of reading.

On November 14, 1716, Leibniz did not calculate the dose of the medicinal drug and felt unwell. The arriving doctor, seeing the mathematician’s condition, went to the pharmacy himself, but did not have time - Gottfried Leibniz died. Behind the coffin of the sage, who gave the world unprecedented discoveries, there was only one person - his secretary.

Discoveries

• 1673 – adding machine
• 1686 – symbol for integral
• 1692 – concept and equation of the envelope of a one-parameter family of curves
• 1695 – exponential function in its most general form
• 1702 – method of decomposing rational fractions into the sum of simplest fractions

Gottfried Wilhelm Leibniz or German Gottfried Wilhelm von Leibniz

Saxon philosopher, logician, mathematician, mechanic, physicist, lawyer, historian, diplomat, inventor and linguist

Wilhelm Leibniz

short biography

German philosopher, mathematician, logician, physicist, inventor, theologian, historian, lawyer, linguist, diplomat, whose theoretical works and practical inventions greatly influenced modern philosophy and science. He founded the Berlin Academy of Sciences and was its first president.

Born in Leipzig in 1646, July 1. His father was a university professor, a famous lawyer, his mother was a professor's daughter, and in many ways this predetermined the future fate of their son. After his father, who died when Gottfried was 6 years old, there was left a huge library in which his son spent his days. His talent was visible from childhood. His mother sent him to the best school in the city, and at the age of 14 or 15 he was already a student at the University of Leipzig.

In terms of level of preparation, Leibniz was ahead of many senior students. He was not yet 18 when he was already a master of literature and philosophy. In 1663, Gottfried Wilhelm studied for a semester at the University of Jena. In the same year he received a bachelor's degree, and the next year he received a master's degree in philosophy. In November 1666, at Nuremberg, Altorf University, Leibniz successfully defended his doctoral dissertation and refused the offer to remain working at this educational institution.

In 1667, the young scientist moved to Mainz, where he met the elector, who highly appreciated Leibniz’s level and invited him to participate in the reform of legislation. For five years at court, the scientist occupied a prominent position; This was also a favorable period in his creative biography: a number of political and philosophical works appeared during these years.

From 1672 to 1676, Leibniz lived in Paris, going there as part of a diplomatic mission. His stay in the French capital made a huge contribution to his development as a scientist, in particular as a mathematician. So, in 1676 he developed the first foundations of the so-called. differential calculus, an outstanding mathematical method. At that time he gave preference to the exact sciences.

In 1676, Leibniz returned to Germany and entered the service of the Dukes of Hanover in order to receive a stable income. At first he was given the position of librarian, court adviser, and later Leibniz held the position of historiographer and privy councilor of justice. The scientist's duties included a wide variety of activities, from writing historical references to experiments in alchemy. During the 40 years spent in Hanover, Leibniz wrote a huge number of works in the field of sciences such as history, philosophy, mathematics, physics, law, and linguistics, which made him famous throughout Europe. The scientist initiated the creation of the Berlin Scientific Society and in 1700 became its first president.

There are also known facts from the biography of Gottfried Wilhelm Leibniz, such as his fruitful communication with Peter the Great. They met in 1711, 1712, 1716, the German scientist was the author of projects for reforming Russian education and government systems, and a project for the establishment of the St. Petersburg Academy of Sciences. Peter I was not the only famous foreigner with whom the famous German had established contacts; he corresponded with many of the greatest scientists, politicians, and philosophers of his time.

European fame did not brighten up the last years of Leibniz’s life; he had to endure a lot due to the unfavorability of the duke who did not like him, attacks from local clergy, and court intrigue. An assistant spy was assigned to him, who did not take his eyes off the scientist and from time to time made reports to his superiors, reporting on his decreased performance. He suffered not only morally, but also physically, because... he was tormented by illness. On November 14, 1716, Gottfried Wilhelm Leibniz died after taking an overdose of medicine. The death of the great scientist caused virtually no reaction from the ducal court and scientific communities; Only his personal secretary accompanied him on his final journey.

Biography from Wikipedia

Gottfried Wilhelm- Saxon philosopher, logician, mathematician, mechanic, physicist, lawyer, historian, diplomat, inventor and linguist. Founder and first president of the Berlin Academy of Sciences, foreign member of the French Academy of Sciences.

The most important scientific achievements:

• Leibniz, independently of Newton, created mathematical analysis - differential and integral calculus (see historical essay), based on infinitesimals.
• Leibniz created combinatorics as a science.
• He laid the foundations of mathematical logic.
• Described the binary number system with numbers 0 and 1.
• In mechanics, he introduced the concept of “living force” (the prototype of the modern concept of kinetic energy) and formulated the law of conservation of energy.
• In psychology, he put forward the concept of unconsciously “small perceptions” and developed the doctrine of unconscious mental life.

Leibniz is also the finalizer of the philosophy of the 17th century and the predecessor of German classical philosophy, the creator of a philosophical system called monadology. He developed the doctrine of analysis and synthesis, for the first time formulated the law of sufficient reason (to which, however, he gave not only a logical (relating to thinking) but also an ontological (relating to being) meaning: “... not a single phenomenon can turn out to be true or real, not a single statement is fair - without sufficient reason why exactly the situation is this way and not otherwise..."); Leibniz is also the author of the modern formulation of the law of identity; he coined the term “model” and wrote about the possibility of machine modeling of the functions of the human brain. Leibniz expressed the idea of ​​converting some types of energy into others, formulated one of the most important variational principles of physics - the “principle of least action” - and made a number of discoveries in special branches of physics.

He was the first to address the issue of the emergence of the Russian ruling dynasty, the first in German historiography to draw attention to the relationship of linguistic problems with genealogy, created a theory of the historical origin of languages ​​and gave their genealogical classification, and was one of the creators of the German philosophical and scientific lexicon.

Leibniz also introduced the idea of ​​the integrity of organic systems, the principle of the irreducibility of the organic to the mechanical, and expressed the idea of ​​the evolution of the Earth.

early years

Gottfried Wilhelm was born on July 1, 1646 in the family of Friedrich Leibnütz, a professor of moral philosophy (ethics) at the University of Leipzig (German: Friedrich Leibnütz or Leibniz; 1597-1652) and Katherine Schmuck (German: Catherina Schmuck), who was the daughter of an eminent professor of jurisprudence. Leibniz's father was of Serbian-Lusatian origin. On his mother's side, Gottfried Wilhelm Leibniz apparently had purely German ancestors.

Leibniz's father very early noticed the genius of his son and tried to develop curiosity in him, often telling him small episodes from sacred and secular history; According to Leibniz himself, these stories sank deeply into his soul and were the most powerful impressions of his early childhood. Leibniz was not even seven years old when he lost his father; his father died, leaving behind a large personal library. Leibniz said:

As I grew older, I began to derive extreme pleasure from reading all kinds of historical stories. I did not let go of the German books that came into my hands until I had read them to the end. At first I studied Latin only at school and, without a doubt, I would have progressed with the usual slowness if not for an incident that showed me a completely unique path. In the house where I lived, I came across two books left by a student. One of them was the work of Livy, the other was the chronological treasury of Calvisius. As soon as these books fell into my hands, I devoured them.

Leibniz understood Calvisius without difficulty, because he had a German book on general history, which said approximately the same thing, but when reading Livy he constantly found himself in a dead end. Leibniz had no idea either about the life of the ancients or about their manner of writing; also not accustomed to the sublime rhetoric of historiographers, which stands above ordinary understanding, Leibniz did not understand a single line, but this publication was old, with engravings, so he carefully examined the engravings, read the captions and, caring little about the dark places for him, simply skipped everything something I couldn't understand. He repeated this several times and leafed through the entire book; thus looking ahead, Leibniz began to understand the former a little better; delighted with his success, he moved on in this manner, without a dictionary, until at last most of what he read became quite clear to him.

Leibniz’s teacher soon noticed what his student was doing, and, without hesitation, he went to the persons to whom the boy was given for education, demanding that they pay attention to Leibniz’s “inappropriate and premature” activities; according to him, these classes were only a hindrance to Gottfried’s teaching. In his opinion, Livy was suitable for Leibniz, like a buskin for a pygmy; he believed that books suitable for older people should be taken away from the boy and given to him " Orbis pictus"Comenius and " Short Catechism» Luther. He would have convinced Leibniz’s educators of this if a scientist who lived in the neighborhood and a well-traveled nobleman, a friend of the owners of the house, had not accidentally witnessed this conversation; struck by the ill will and stupidity of the teacher, who measured everyone by the same standard, he began, on the contrary, to prove how absurd and inappropriate it would be if the first glimpses of a developing genius were suppressed by the severity and rudeness of the teacher. On the contrary, he believed that it was necessary to favor this boy, who promised something extraordinary, by all means; He immediately asked to send for Leibniz, and when, in response to his questions, Gottfried answered intelligently, he did not leave Leibniz’s relatives until he forced them to promise that Gottfried would be allowed into his father’s library, which had long been under lock and key. Leibniz wrote:

I triumphed as if I had found a treasure, because I was burning with impatience to see the ancients whom I knew only by name - Cicero and Quintilian, Seneca and Pliny, Herodotus, Xenophon and Plato, the writers of the Augustan century and many of the Latin and Greek fathers of the church. I began to read all this, depending on my inclination, and enjoyed the extraordinary variety of subjects. Thus, before I was twelve years old, I understood Latin fluently and began to understand Greek.

This story of Leibniz is confirmed by third-party evidence, proving that his outstanding abilities were noticed by both his comrades and the best teachers; Leibniz was especially friendly at school with the two Ittig brothers, who were much older than him and were considered among the best students, and their father was a physics teacher, and Leibniz loved him more than other teachers. Leibniz studied at the famous Leipzig School of St. Thomas.

His father's library allowed Leibniz to study a wide range of advanced philosophical and theological works that he would have only had access to as a student. At the age of 12, Leibniz was already an expert in Latin; at the age of 13 he showed a poetic talent that no one suspected in him. On the Day of the Holy Trinity, one student was supposed to read a festive speech in Latin, but he fell ill, and none of the students volunteered to replace him; Leibniz's friends knew that he was a master of writing poetry and turned to him. Leibniz got down to business and in one day composed three hundred hexameters of Latin verse for this event, and, just in case, he specially tried to avoid at least a single combination of vowels; his poem aroused the approval of his teachers, who recognized Leibniz as an outstanding poetic talent.

Various third-rate scientists intervened in the dispute between Leibniz and Newton, some of whom wrote libels against Leibniz, and others against Newton. From the summer of 1713, Europe was flooded with anonymous pamphlets that defended Leibniz's priority and argued that "Newton arrogates to himself the honor that belongs to another"; the pamphlets also accused Newton of stealing the results of Hooke and Flamsteed. Newton's friends, for their part, accused Leibniz himself of plagiarism; According to their version, during his stay in London (1676), Leibniz at the Royal Society became acquainted with Newton’s unpublished works and letters, after which Leibniz published the ideas expressed there and passed them off as his own.

The dispute between Leibniz and Newton over scientific priority became known as "the most shameful squabble in the entire history of mathematics." This quarrel between two geniuses cost science dearly: the English mathematical school soon withered for a whole century, and the European one ignored many of Newton’s outstanding ideas, rediscovering them much later.

Last years

The last years of Leibniz's life were sad and restless. Ernst August's son, Georg Ludwig, who succeeded his father in 1698, did not like Leibniz. He looked upon him only as his court historiographer, who cost him a lot of extra money. Their relationship cooled even more when Georg Ludwig, under the name of George I, ascended to the English throne. Leibniz wanted to be invited to the London court, but he met with stubborn resistance from English scientists, since the notorious dispute that he had with Newton greatly damaged him in the eyes of the English; Leibniz tried unsuccessfully to reconcile with the king and win him over to his side. George I constantly reprimanded Leibniz for his sloppy history of his dynasty; this king immortalized himself with a rescript addressed to the Hanoverian government, where Leibniz was officially condemned, and the famous scientist was publicly named as a person who should not be trusted. Leibniz responded to this rescript with a dignified letter in which he wrote:

I never thought that my first act upon Your Majesty’s accession to the throne of England would be an apologia.

Leibniz wrote nine-tenths of the entire work; he worked very hard, and his eyesight suffered from archival studies that were beyond his age. However, the king argued that Leibniz was doing nothing and forgetting his promises: he was annoyed that history had not been brought to his own prosperous reign.

Gottfried Wilhelm Leibniz was surrounded by court intrigues; he was irritated by the attacks of the Hanoverian clergy. The last two years of his life in Hanover were especially difficult for Leibniz; he was in constant physical suffering; “Hannover is my prison,” he once said. The assistant assigned to Leibniz, Georg Eckhardt, on occasion followed Leibniz as a spy, reporting to the king and his minister Bernstorff that Leibniz was not working enough due to his decrepitude. When Leibniz fell ill with a long illness, Eckhardt wrote: “Nothing else will put him on his feet, but if the king and a dozen other monarchs give him hope for new pensions, then he will immediately begin to walk.”

• 1716: At the beginning of August of this year, Leibniz felt better and decided to finally finish the Brunswick story. However, he caught a cold, had an attack of gout and rheumatic pains in the shoulders; Of all the medicines, Leibniz trusted only one, which was once given to him by a friend, a Jesuit. But this time Leibniz took too large a dose and felt unwell; the arriving doctor found the situation so dangerous that he himself went to the pharmacy for medicine, but during his absence Gottfried Wilhelm died.

None of the retinue of the Duke of Hanover accompanied Leibniz on his last journey; only his personal secretary followed the coffin. The Berlin Academy of Sciences, of which he was the founder and first president, did not pay attention to his death, but a year later B. Fontenelle made a famous speech in his memory to members of the Paris Academy of Sciences.

Ratings

In a famous speech given in memory of Leibniz to members of the Paris Academy of Sciences, Bernard Le Beauvier de Fontenelle recognized him as one of the greatest scientists and philosophers of all time.

« He loved to watch how plants, the seeds of which he himself provided, bloom in someone else's garden"(Fontenelle).

Later generations of English philosophers and mathematicians paid tribute to Leibniz's achievements, thereby compensating for the deliberate neglect of his death on the part of the Royal Society.

Denis Diderot noted in his Encyclopedia that Leibniz was to Germany what Plato, Aristotle and Archimedes combined were to Ancient Greece. Norbert Wiener said that if he were asked to choose a patron saint of cybernetics, he would choose Leibniz.

Personal qualities

Mental capacity

What distinguished Leibniz from his earliest years was his genius, which did not fit into traditional educational schemes. Difficult books seemed easy to him, and easy books difficult; if the depth of the material being studied was insufficient, then Leibniz’s thought worked in vain, leading to ineffective waste of intelligence. Remembering the school, Gottfried Wilhelm Leibniz wrote mainly about what he learned not in it, but outside its walls. He wrote:

Two things have brought me great benefit, although they usually do harm. Firstly, I was, strictly speaking, self-taught, secondly, in any science, as soon as I acquired the first concepts about it, I always looked for something new, often simply because I did not have time to sufficiently assimilate the ordinary...

Leibniz is considered one of the most comprehensive geniuses in all of human history. His thought introduced new things into many branches of knowledge that existed under him. It is believed that the list of Leibniz's significant achievements is almost as long as the list of his activities. However, Leibniz's versatility was also the source of the shortcomings of his work: it was to some extent fragmentary; he discovered new paths much more often than he followed them to the end; The courage and richness of his plans were not always met by their execution in detail. Leibniz's contemporaries were amazed by his fantastic erudition, almost supernatural memory and amazing capacity for work. He mastered foreign languages ​​with extraordinary ease. The influence of heredity on Leibniz's mental abilities can be traced quite deeply: on both sides - both his father's and his mother's - he had ancestors who were more or less outstanding in their mental development.

Character traits

According to Bertrand Russell, Leibniz "was one of the greatest minds of all time, but he was an unpleasant man." Russell also wrote that "Leibniz is a dull writer, and his influence on German philosophy has made it pedantic and dry." However, according to the characterization of L.A. Petrushenko, Leibniz made a generally pleasant impression, being by nature a peace-loving, humane, gentle, generous, democratic and benevolent person; He spoke only good things about all people and even spared his enemies.

Leibniz's spiritual mood was in complete harmony with his philosophical optimism: he was almost always cheerful and lively; He spoke well of everyone, even of Isaac Newton before his final quarrel with him. According to Leibniz himself, he had a lack of “censorship spirit”: he liked almost any book, he looked for and remembered only the best in it. Leibniz had charm, good manners, a sense of humor and imagination. He laughed often, even when, as he said, it was only external and not internal laughter; he was touchy, but not vindictive, and it was easy to arouse in him a feeling of compassion.

Leibniz was quick-tempered, but his anger was easily stopped, he loved a cheerful conversation, willingly traveled, loved and knew how to talk with people of all ranks and professions, loved children, sought the company of women, but did not think about marriage. In 1696, Leibniz proposed to a girl, but she asked for time to think. Meanwhile, 50-year-old Leibniz changed his mind about getting married and said: “Until now I imagined that I would always be on time, but now it turns out that I am late.”

Gottfried Leibniz was a man of versatile talents and tireless energy; he was very far from the type of solitary thinker that Descartes and Spinoza represented. In terms of his personality, he was closer to the English Lord Chancellor Francis Bacon - a diplomat, politician and socialite.

Even at the age of twelve, Gottfried Wilhelm Leibniz loved to look for “unity and harmony” in everything; he realized that the goal of all sciences is the same and that science exists for man, and not man for science; he came to the idea that what should seem best to an individual is what is most fruitful for the universal.

According to many biographers, Leibniz was stingy, although he himself denied self-interest. When a lady-in-waiting of the Hanoverian court got married, Leibniz usually presented her with what he called a “wedding gift,” consisting of useful rules, ending with the advice not to give up washing now that she had a husband.

Appearance, health, habits and lifestyle

At first glance, Leibniz gave the impression of a rather plain-looking person. He was thin, of average height, with a pale face. His complexion seemed even paler in contrast to the huge black wig he wore according to the custom of the time.

Until the age of 50, Leibniz was rarely ill. By this time, due to a sedentary lifestyle and poor nutrition, he had developed gout. He respected medicine in principle, but he valued the medical art of that time low; in one of his letters, after reading the book by doctor Behrens, “ On the reliability and difficulty of the art of medicine“said: “God grant that the certainty be as great as the difficulty.”

Leibniz was very fond of sweets, he even mixed sugar into his wine, but in general he drank little wine. He ate with great appetite, without much discernment; he could be equally content with the bad dinner that was brought to him from the hotel, and with the exquisite court dishes, and he did not eat at any particular time, but when he had to, and he also slept as he had to. He usually went to bed no earlier than one in the morning and got up no later than seven in the morning; Leibniz led such a lifestyle until he was very old, and it often happened that he fell asleep in his work chair from overwork and slept like that until the morning. Gottfried Wilhelm Leibniz was a man capable of both thinking for several days while sitting in the same chair, and thinking while traveling along the roads of Europe in summer and winter. As G. Kruger wrote, Leibniz’s life was spent in tireless activity, but this activity was not purposeful, and his life was “monadic,” solitary, outside the established circle of professors, but Gottfried Wilhelm was always associated with many researchers. Leibniz wrote his works only for a specific reason; these were a few summary sketches and countless letters.

Leibniz's philosophy

In philosophy, Leibniz made a large-scale and fruitful attempt at a “synthesis” of ancient, scholastic and Cartesian ideas based on the method of comprehensiveness and rigor of reasoning. In a letter to Thomasius, Leibniz wrote: “... I am not afraid to say that I find much more merit in the books of Aristotle’s Physics than in the thoughts of Descartes... I would even dare to add that it is possible to preserve all eight books of Aristotle’s physics without prejudice to modern philosophy ..."; he also wrote that “most of what Aristotle says about matter, form, ... nature, place, infinity, time, motion, is completely reliable and proven...”.

Leibniz's philosophy completed the philosophy of the 17th century and preceded German classical philosophy. In the process, Leibniz subjected a critical rethinking of the views of Democritus, Plato, Augustine, Descartes, Hobbes, Spinoza and others; the formation of his philosophical system was completed by 1685 after twenty years of development. Although Leibniz admired Spinoza's intellect, he was also openly alarmed by his conclusions. According to Leibniz himself, he accepted much of what he read, which, according to modern researchers, confirms Leibniz’s ability to synthesize various ideas in creating his own metaphysics. This approach distinguishes Leibniz from Descartes: the German scientist did not abandon scholasticism, but, on the contrary, tried to combine medieval interpretations of Platonism and Aristotelianism with new scientific methods - physics, astronomy, geometry, biology. Plato, Aristotle, Plotinus, Augustine, Thomas Aquinas and other thinkers were no less important for Leibniz than Galileo, Kepler, Cavalieri, Wallis, Huygens, Leeuwenhoek, Malpighi and Swammerdam. Leibniz's philosophical views underwent changes more than once, but at the same time they moved towards the creation of a complete system that reconciled contradictions and sought to take into account all the details of reality.

Leibniz was a man interested in Chinese philosophy; Leibniz's interest in Chinese philosophy was due to the fact that it was similar to his own. Historian R. Hughes believes that Leibniz's ideas about "simple substance" and "pre-established harmony" arose directly under the influence of Confucianism; this is indicated by the fact that they arose during the period when he read " Confucius Sinicus Philosophus».

Philosophical principles

Leibniz considered the Cartesian approach to truth to be too psychological, and therefore overly subjective - the principle of evidence, clarity and definiteness of ideas. Instead of Descartes' evidence, he proposed using logical proof as a criterion of truth and objectivity. According to Leibniz, “the criteria for the truth of judgments... are the rules of ordinary logic, which geometers also use: for example, the injunction to accept as reliable only what is confirmed by reliable experience or strict proof.” Setting objective truth as his goal, Leibniz partially accepted the principle of evidence, however, unlike Descartes, he started not from the human Self, but from God.

The most important requirements of the methodology proposed by Leibniz were the universality and rigor of philosophical reasoning; According to Leibniz, the feasibility of these requirements is ensured by the presence of “a priori” principles of being, independent of experience, to which Leibniz attributed:

• the consistency of every possible or conceivable being (the law of contradiction);
• logical primacy of the possible over the actual (existing); the possibility of an infinite number of consistent “worlds”;
• sufficient justification for the fact that this particular world exists, and not any other possible one, that this particular event occurs, and not another (the law of sufficient reason, see the principle of sufficient reason);
• the optimality (perfection) of a given world as a sufficient basis for its existence.

According to Leibniz, the diversity of existing things and actions of nature optimally correlates with their order, and this is the reason for the perfection of the real world, which lies in the “harmony of essence and existence.” The ontological principle of “minimum means with maximum result” entails as a consequence a number of other principles: uniformity of the laws of nature (universal interconnection), the law of continuity, the principle of the identity of indistinguishables, in addition, the principles of universal change and development, simplicity and completeness. According to Leibniz, the existing world was created by God as “the best of all possible worlds.”

Monadology

Leibniz is one of the most important representatives of modern European metaphysics, the focus of which is the question of what substance is. Leibniz develops a system called substantial pluralism, or monadology. According to Leibniz, the foundations of existing phenomena, or phenomena, are simple substances, or monads (Greek μονάδα from ancient Greek μονάς, μονάδος - “unit”, “simple essence”). All monads are simple and do not contain parts. There are infinitely many of them. Monads have qualities that distinguish one monad from another; no two monads are absolutely identical. This provides an infinite variety of the world of phenomena. Leibniz formulated the idea that there are no absolutely similar monads or two completely identical things in the world as the principle of “universal difference” and at the same time as the identity of the “indistinguishable,” thereby putting forward a deeply dialectical idea. According to Leibniz, monads, self-developing all their contents thanks to self-consciousness, are independent and self-active forces that bring all material things into a state of motion. According to Leibniz, monads form an intelligible world, from which the phenomenal world (physical cosmos) is a derivative.

Simple substances are created by God at once, and each of them can only be destroyed all at once, in one moment, that is, simple substances can get a beginning only through creation and perish only through destruction, while what is complex begins or ends by parts. Monads cannot undergo changes in their internal state from the action of any external causes other than God. Leibniz, in one of his final works, Monadology (1714), uses the following metaphorical definition of the autonomy of the existence of simple substances: “Monads have no windows or doors through which anything could enter or exit.” The monad is capable of changing its state, and all natural changes of the monad proceed from its internal principle. The activity of the inner principle which produces a change in the inner life of the monad is called aspiration.

All monads are capable of perception or perception of their inner life. Some monads, in the course of their internal development, reach the level of conscious perception, or apperception.

For simple substances having only perception and aspiration, the general name of monad or entelechy is sufficient. Leibniz calls monads that have more distinct perceptions, accompanied by memory, souls. Moreover, according to Leibniz, there is no completely inanimate nature. Since no substance can perish, it cannot completely lose any inner life. Leibniz says that the monads that ground the phenomena of “inanimate” nature are actually in a state of deep sleep. Minerals and plants are like sleeping monads with unconscious ideas.

Rational souls, constituting a special Kingdom of the Spirit, are in a special position. The endless progress of the entire set of monads is, as it were, presented in two aspects. The first is the development of the kingdom of nature, where mechanical necessity predominates. The second is the development of the kingdom of the spirit, where the main law is freedom. By the latter, Leibniz understands, in the spirit of modern European rationalism, the knowledge of eternal truths. Souls in Leibniz's system represent, in his own words, “living mirrors of the Universe.” However, rational souls are at the same time reflections of the Divinity itself, or the Creator of nature itself.

In each monad, the entire Universe is potentially folded. Leibniz whimsically combines the atomism of Democritus with the distinction between the actual and the potential in Aristotle. Life appears when atoms are awakening. These same monads can reach the level of self-consciousness (apperception). The human mind is also a monad, and habitual atoms are sleeping monads. The Monad has two characteristics - aspiration and perception.

Leibniz makes the statement that space and time are subjective - they are modes of perception characteristic of monads. In this, Leibniz influenced Immanuel Kant, in whose philosophical system time is viewed as an a priori, that is, pre-experimental form of sensory intuition. Kant wrote: “Time is not an empirical concept derived from any experience... Time is the pure form of sensory intuition... Time is nothing more than the form of internal feeling, that is, contemplation of ourselves and our internal state... Time is an a priori formal condition of all phenomena in general... Space and time taken together are the pure forms of all sensory intuition, and it is precisely because of this that a priori synthetic propositions are possible.”

Leibniz, revealing the content of the concept of time, used the term “phenomenon”; he explained that space and time are not realities existing in themselves, but phenomena resulting from the existence of other realities; according to Leibniz, space represents the order in which bodies are placed, through which they, coexisting, acquire a certain location relative to each other; time is an analogous order, which relates already to the succession of bodies, and that if there were no living creatures, space and time would remain only in the ideas of God. This concept was especially clearly expressed in Leibniz's letters to the Newtonian S. Clarke. Yu. B. Molchanov proposed calling this concept relational.

In Leibniz's concept of time, a certain role is played by small perceptions characteristic of a single monad. Leibniz wrote:

...the effect of...small perceptions is much more significant than is thought. It is they who form those indefinable tastes, those images of sensual qualities, clear in the aggregate, but not distinct in their parts, those impressions that the bodies around us make on us and which contain infinity - the connection in which every being with the rest of the universe. One might even say that by virtue of these small perceptions the present is fraught with the future and burdened with the past, that everything is in mutual agreement... and that in the most insignificant of substances a gaze as penetrating as the gaze of a deity could read the entire history of the Universe...

Leibniz's Monadology was not published during his lifetime. Since there was no title in the author's text of the work, there are publications with different titles. This work was first published in German in a translation by G. Köhler: “ Lehrsätze über die Monadologie…", Frankf.-Lpz., 1720, and reprinted in 1740. Then a Latin translation came out called " Principia philosophiae…" V " Acta eruditorum Lipsiae publicantur" Supplemente, t. 7, sect. 11, 1721. The French original of the work was published by Erdmann together with “New Experiments” only in 1840 (“ Opera philosophica…", Bd. 1-2, V.). The best editions of the original belong to Guyot (1904) and Robinet (1954). The best German edition is considered to be the 1956 edition.

Title page of Leibniz's work " Experiments in theodicy", 1734 version

Experiments in theodicy

Job " Experiments in theodicy"(the word "theodicy" (Novolat. theodicea) means "justification by God") was Leibniz's attempt to reconcile his personal philosophical system with his interpretation of the dogmas of Christianity. The purpose of this work was to show that the evil in the world is not contrary to the goodness of God, and that, indeed, despite many evils, this world is the best of all possible worlds.

In his work " Experiments in theodicy Leibniz pointed out the following:

Time will consist in the totality of points of view of each monad on itself, like space - in the totality of points of view of all monads on God. Harmony produces a connection between both the future and the past, and the present with the absent. The first type of connection unites times, and the second - places. This second connection is found in the unity of the soul with the body, and in general in the connection of true substances with each other. But the first connection takes place in the preformation of organic bodies, or, better of all bodies...

Leibniz wrote that evil can be understood metaphysically, physically and morally; According to Leibniz, metaphysical evil consists of simple imperfection, physical evil consists of suffering, and moral evil consists of sin. Leibniz pointed out that God first of all desires the good, and then the best; in relation to the essence of evil, God does not desire moral evil at all and does not desire physical evil or suffering at all. God often desires physical evil only as a due punishment for guilt, and also often to prevent greater evils and to achieve the greatest benefits. Leibniz wrote that “punishment serves equally as an example and as a deterrent, and evil often leads to a greater sense of goodness and sometimes also leads to greater perfection of the one who creates it, just as a sown seed undergoes some kind of corruption when it germinates.” " As for moral evil or sin, it very often happens that it can serve as a means for acquiring a good or for stopping another evil, but this, however, does not make it a satisfactory object of the divine will; it is permissible or permissible only for the reason that a person who does not want to allow anyone else to sin can prevent this by committing a moral evil himself, just as an officer obliged to guard an important post leaves him to stop a quarrel in the city between two garrison soldiers ready to kill each other. In other words, in his work, Leibniz pointed out that, despite the ideal divine foresight of everything that happens, absolute free will dominates in the world, which is why evil is possible. At the same time, according to Leibniz, God predetermined all the laws of the world, initially established the necessary and universal correspondence of souls and bodies, freedom and necessity, for example, allowed evil to express good, and thus created “the most perfect of all possible worlds” . This attempt by Leibniz to reconcile fatalism with the recognition of free will, to explain the existence of evil and to justify it in a spirit of optimism, was sarcastically criticized by Voltaire in his Candide.

Leibniz interpreted nature as the habit of God. In Leibniz's understanding, God is, as it were, the actual infinity of the human spirit, the complete realization of pure knowledge, which is not feasible for man. God is a creative monad, possessing the property of actual absolute thinking. God is the first monad, all other monads are its emanations. God is free from passive, that is, unconscious, states; it is the source of eternal truths and pre-established world harmony, the guarantee of the perfection of the universe. Pre-established harmony, as a one-to-one correspondence between monads, was originally established by God when he chose the “best possible world” to exist. Due to the pre-established harmony, although no one monad can influence the others, since monads as substances do not depend on each other, nevertheless, the development of each of them is in full accordance with the development of others and the whole world as a whole. This happens due to the God-given ability of monads to represent all other monads and the whole world.

With the help of the concept of pre-established harmony, Leibniz, in the spirit of occasionalism, solves the problem of the connection between soul and body, so difficult for the rationalism of the 17th century, which goes back to the teachings of Descartes. As a theist, Gottfried Wilhelm Leibniz allowed the constant influence of God on the course of world processes, but rejected his influence on changes in created monads and, in the spirit of deism, brought together the “Creator God” with the “created world”, denied a personal humanoid God. According to Leibniz, the highest monad, God, should not be overly likened to the lower one, the spirit of man.

Criticism of Locke's doctrine of the soul as a “blank slate”

In the theory of knowledge and psychology, the rationalist Leibniz criticized the teaching of the representative of empiricism, John Locke, about the soul as a “blank slate” (lat. tabula rasa), on which only experience writes its own writings. Leibniz tried to find a compromise position between Cartesian rationalism and Lockean empiricism and sensationalism. In accordance with Leibniz’s ideas, the soul, even before any real experience, has its own individual characteristics, predispositions, on which the reception of external impressions depends. The thesis of empiricism, according to which there is nothing in the mind that was not previously in the feelings (« nihil est in intellectu, quod non fuerit in sensu"), he countered with the statement: there is nothing in the mind that was not previously in the senses, except the mind itself. Leibniz believed that the mind has an innate ability to understand certain fundamental principles, however, unlike Descartes’ “innate ideas,” this ability is not given in ready-made form, but is only a predisposition, a “predisposition.” The subject of such knowledge in the field of ideas is the highest existential categories, such as “I”, “identity”, “being”, “perception”, in the sphere of truths - universal and necessary logical and mathematical truths.

Perception of Leibniz's ideas

Gottfried Wilhelm Leibniz was the most important authority in German philosophy of the pre-Kantian period. Leibniz's student Christian von Wolff and his school owe much credit for the systematization and popularization of Leibniz's philosophical ideas in Germany. Many of these ideas received their reception in German classical philosophy. In the work of a number of idealist philosophers of the 20th century, belonging to personalism, as well as some other schools (Edmund Husserl, Alfred North Whitehead), the principles of “monadology” developed.

Leibniz's ideas were reflected in the worldview of the poets of Sturm and Drang, in the aesthetic views of Lessing, and in the worldview of Goethe and Schiller. Leibniz's teaching about the organic unity of all things in the world and their development was accepted by Schelling and found expression in his natural philosophy. The essential features of Leibniz's idealism were revived in Hegel's objective idealism (Leibniz's active, spiritual monad is the prototype of Hegel's self-developing idea). Under the influence of Leibniz's ideas, the teachings of Herbart, Benecke, Lotze, Teichmüller, Wundt and Renouvier were also formed. Feuerbach highly valued Leibniz's teaching on the active force of self-motion as the basic and most essential definition of substance, and at the same time noted that theology distorts his best thoughts. Leibniz was highly regarded as an outstanding thinker by Lomonosov, who, however, sharply criticized his monadology as a “mystical teaching.” Leibniz's metaphysics was revived in Russia in the teachings of A. A. Kozlov, S. A. Askoldov, L. M. Lopatin, N. O. Lossky and S. A. Levitsky

Scientific activity

Logics

In the field of logic, Godfried Wilhelm Leibniz developed the doctrine of analysis and synthesis. He understood logic as the science of all possible worlds. Leibniz is the first in history to formulate the law of sufficient reason; he is also the author of the form of expression of the law of identity accepted in modern logic. He considered the law of identity to be the highest principle of logic. “The nature of truth in general is that it is something identical.”

The law of identity formulated by Leibniz is currently used in most modern logical-mathematical calculus. Associated with the law of identity is the principle of substitution of equivalents: “If A is B and B is A, then A and B are called “ the same thing“. Or: A and B are the same if they can be substituted for one another.”

For Leibniz, the principles of identity, substitution of equivalents, and contradiction are the fundamental means of any deductive proof; Based on them, Leibniz attempted to prove some so-called axioms. He believed that axioms are unprovable propositions that represent identities, but in mathematics, not all provisions passed off as axioms are identities, and therefore, from Leibniz’s point of view, they need to be proven. The criterion of identification and distinction of names introduced by Leibniz corresponds to a certain extent to the modern distinction between the meaning and meaning of names and expressions, for example, the well-known example of the equivalence of the expressions “Sir Walter Scott” and “the author of Waverley,” going back to Russell, literally repeats this thought of Leibniz.

Leibniz did not develop a unified notation system; he most developed the “plus-minus” calculus. The representation of judgments by means of parallel segments or circles (“An Experience in Demonstrative Syllogistics” in the book “Opuscules et fragments inédits de Leibniz”), proposed by Leibniz for deriving the correct modes of syllogisms, turned out to be successful. Leibniz's defense of the object and method of formal logic occupied an important place. He wrote to G. Wagner the following:

... although Mr. Arnaud, in his art of thinking, asserted that people rarely make mistakes in form, but almost exclusively in essence, in reality the situation is completely different, and Mr. Huygens, together with me, has already noticed that usually mathematical errors, called paralogisms, caused by sloppy form. And, of course, it is not a trifle that Aristotle derived strict laws for these forms and thereby turned out to be the first to write mathematically outside of mathematics.

Leibniz was the creator of the most complete classification of definitions for his time; in addition, he developed the theory of genetic definitions. In his work " About the art of combinatorics", written in 1666, Leibniz anticipated some aspects of modern mathematical logic. Leibniz called combinatorics the idea of ​​the “great art” of discovery, developed by him under the influence of R. Lull, which, based on obvious “first truths,” would make it possible to logically deduce the entire system of knowledge from them. This topic became one of Leibniz’s key ones, and throughout his life he developed the principles of “universal science,” on which, in his words, “the well-being of mankind largely depends.”

Gottfried Wilhelm Leibniz is the author of the idea of ​​using mathematical symbols in logic and constructing logical calculus. He put forward the task of basing mathematical truths on general logical principles, and also proposed using a binary, that is, binary, number system for the purposes of computational mathematics. Leibniz substantiated the importance of rational symbolism for logic and for heuristic conclusions; he argued that knowledge comes down to proof of statements, and it is necessary to find evidence using a certain method. According to Leibniz, the mathematical method itself is not sufficient to discover everything we are looking for, but it protects against mistakes. The latter is explained by the fact that in mathematics, statements are formulated using certain signs and operate according to certain rules, and verification, possible at each stage, requires “only paper and ink.” Leibniz was also the first to express the idea of ​​​​the possibility of machine modeling of human functions, and the term “model” itself belongs to him.

Leibniz made a major contribution to the development of the concept of “necessity”. He understood necessity as something that must be obligatory. According to Leibniz, the very first necessity is metaphysical, absolute, as well as logical and geometric necessity. It is based on the laws of identity and contradiction, therefore it allows for the only possibility of events. Leibniz noted other features of necessity. He contrasted necessity with chance, understanding it not as a subjective appearance, but as such an objective connection of phenomena that depends on free decisions and on the course of processes in the Universe. He understood it as a relative accident, objective in nature and arising at the intersection of certain necessary processes.

In New Experiments (Book 4), Leibniz gave a deductive analysis of traditional logic, showing that the 2nd and 3rd figures of a syllogism can be obtained as a consequence of the mode Barbara using the law of contradiction, and the 4th figure - using the law of circulation; here he gave a new classification of the modes of syllogism.

Leibniz's original logical ideas, most valued today, became known only in the 20th century. Leibniz's results had to be rediscovered because his own work was buried in piles of manuscripts in the royal library in Hanover.

Mathematics

A number of techniques for solving problems of drawing tangents, finding extrema and calculating quadratures were created even before Leibniz, but in the works of his predecessors there was no general method that would allow the extension of research, limited primarily to entire algebraic functions, to any fractional and irrational and especially to transcendental functions. In these works, the basic concepts of analysis were not clearly identified, and their relationships were not established; there was no developed and unified symbolism. Gottfried Leibniz brought together particular and disparate techniques into a single system of mutually related concepts of analysis, expressed in notations that allow operations with infinitesimals according to the rules of a certain algorithm.

• 1675: Leibniz created differential and integral calculus and subsequently published the main results of his discovery, ahead of Newton, who had come to similar results even earlier than Leibniz, but had not yet published them at that time, although Leibniz knew some of them privately.
• 1684: Leibniz published the world's first major work on differential calculus: “The New Method of Maximums and Minimums,” without even mentioning Newton's name in the first part, and in the second part Newton's achievements are not entirely clearly described. Newton did not pay attention to this then. His works on analysis began to be published only in 1704. Subsequently, a long-term dispute arose on this topic between Newton and Leibniz about the priority of the discovery of differential calculus.

Leibniz's work sets out the foundations of differential calculus and the rules for differentiating expressions. Using a geometric interpretation of the relationship dy/dx, he briefly explains the signs of increasing and decreasing, maximum and minimum, convexity and concavity (hence, sufficient conditions for an extremum for the simplest case), as well as inflection points. Along the way, without any explanation, “differences of differences” (multiple differentials) are introduced, denoted ddv. Leibniz wrote:

What a person versed in this calculus can obtain directly in three lines, other learned men were forced to look for by following complex detours.

• 1686 For the first time in print, he introduced the symbol ∫ for the integral (and indicated that this operation is the inverse of differentiation).
• 1692: the general concept of the envelope of a one-parameter family of curves is introduced, its equation is derived. Leibniz developed the theory of envelopes of a family of curves simultaneously with H. Huygens in 1692-1694.
• 1693: Leibniz considered the question of the solvability of linear systems; his result actually introduced the concept of a determinant. But this discovery did not arouse interest then, and linear algebra arose only half a century later.
• 1695: Leibniz introduced the exponential function in its most general form: u^(v). Later, in 1697, Johann Bernoulli studied the calculus of exponential functions.
• 1702: Together with Johann Bernoulli, Leibniz discovered the method of decomposing rational fractions into the sum of simple fractions. This solved many problems of integrating rational fractions.

There were some peculiarities in Leibniz's approach to mathematical analysis. Leibniz thought of higher analysis not kinematically, like Newton, but algebraically. In his early works he seemed to understand infinitesimals as actual objects, comparable to each other only if they were of the same order. Perhaps he hoped to establish their connection with his concept of monads. At the end of his life, he spoke out rather in favor of potentially infinitesimal, that is, variable quantities, although he did not explain what he meant by this. In general philosophical terms, he considered infinitesimals as the support of continuity in nature. Leibniz's attempts to give a strict substantiation of analysis were not crowned with success; he hesitated between different interpretations of infinitesimals, and sometimes tried to resort to unspecified ideas of limit and continuity. Leibniz's views on the nature of infinitesimals and on the justification of operations on them aroused criticism during his lifetime, and a justification for the analysis that satisfied modern scientific requirements could only be given in the 19th century.

Leibniz's binary number system. Page from

Gottfried Wilhelm Leibniz showed the power of his general methods by solving a number of difficult problems with their help. For example, in 1691, he established that a heavy flexible homogeneous thread suspended at two ends has the shape of a chain line, and, along with Isaac Newton, Jacob and Johann Bernoulli, as well as L'Hopital, in 1696 he solved the problem of the brachistochrone.

His extensive correspondence played a major role in the dissemination of Leibniz's ideas. Some discoveries were outlined by Leibniz only in letters: the beginnings of the theory of determinants in 1693, the generalization of the concept of differential to negative and fractional exponents in 1695, the test for the convergence of an alternating series (Leibniz test, 1682), methods for solving various types of ordinary differential equations in quadratures.

Leibniz introduced the following terms: “differential”, “differential calculus”, “differential equation”, “function”, “variable”, “constant”, “coordinates”, “abscissa”, “algebraic and transcendental curves”, “algorithm” ( in a sense close to modern). Although the mathematical concept of function was implicit in the trigonometric and logarithmic tables that existed in his time, Leibniz was the first to use it explicitly to refer to any of several geometric concepts derived from the curve, such as abscissa, ordinate, tangent, chord, and normal.

Leibniz formulated the concepts of a differential as an infinitesimal difference between two infinitely close values ​​of a variable and an integral as the sum of an infinite number of differentials and gave the simplest rules of differentiation and integration already in his Parisian handwritten notes dating back to October and November 1675; here Leibniz first encounters modern differential signs d and integral ∫ . The definition and sign of the differential were given by Leibniz in his first memoir on differential calculus, “The New Method of Maxima and Minima...”, published in 1684. In the same work, the rules for differentiating a sum, difference, product, quotient, any constant degree, function of a function (invariance of the first differential), as well as rules for finding and distinguishing (using the second differential) maxima and minima and finding inflection points were given without proof . The differential of a function was defined as the ratio of the ordinate to the subtangent multiplied by the differential of the argument, the value of which can be taken arbitrarily; at the same time, Leibniz pointed out that differentials are proportional to infinitesimal increments of magnitude and that on the basis of this it is easy to obtain proof of his rules.

The work of 1684 was followed by a number of other works by Leibniz, which together covered all the basic branches of differential and integral calculus. In these works, Gottfried Wilhelm Leibniz gave the definition and sign of the integral (1686), emphasizing the mutually inverse nature of both main operations of analysis, indicated the rules for differentiation of the general exponential function and multiple differentiation of the product (Leibniz formula, 1695), and also laid the foundation for the integration of rational fractions (1702 -1703). In addition, Leibniz attached fundamental importance to the use of infinite power series for the study of functions and the solution of differential equations (1693).

Due not only to earlier publications, but also to significantly more convenient and transparent notations, Leibniz's writings on differential and integral calculus had a much greater influence on his contemporaries than Newton's theory. Even Newton's compatriots, who had long preferred the fluxion method, gradually adopted Leibniz's more convenient notation.

Leibniz also described the binary number system with the digits 0 and 1. The modern binary system was fully described by him in his work Explication de l'Arithmétique Binaire. As a person interested in Chinese culture, Leibniz knew about the Book of Changes and noticed that hexagrams correspond to binary numbers from 0 to 111111; he admired how this mapping was evidence of major Chinese achievements in philosophical mathematics at the time. Leibniz may have been the first computer programmer and information theorist. He discovered that if certain groups of binary numbers were written one below the other, the zeros and ones in the vertical columns would repeat regularly, and this discovery led him to believe that there were entirely new laws of mathematics. Leibniz realized that binary code was optimal for a system of mechanics that could operate on the basis of alternating active and passive simple cycles. He tried to apply binary code in mechanics and even made a drawing of a computer that worked on the basis of his new mathematics, but he soon realized that the technological capabilities of his time did not allow him to create such a machine. The design of a computer operating in a binary system, which used a prototype of a punched card, was outlined by Leibniz in a work written back in 1679 (before he described binary arithmetic in detail in a treatise of 1703 Explication de l'Arithmétique Binaire). The ones and zeros in the imaginary machine were represented by open or closed holes, respectively, in a moving jar through which balls were supposed to pass and fall into the grooves below. Leibniz also wrote about the possibility of machine modeling of the functions of the human brain.

Mechanics and physics

In the field of physics, Leibniz developed the doctrine that space, time and motion are relative in nature. His merit is the introduction into mechanics of a quantitative measure of motion - the product of body mass and the square of velocity. This quantity, which he called “living force,” in contrast to the approach of R. Descartes, who considered the measure of motion to be the product of mass and speed (“dead force,” according to Leibniz’s definition), later received the name kinetic energy. An important example of Leibniz's mature physical views is his essay "Essay on Dynamics" ("Specimen Dynamicum"), 1695.

Partially using the results of H. Huygens, Leibniz discovered the law of conservation of “living forces”, thus giving the first formulation of the law of conservation of energy. In addition, he came up with the idea of ​​converting some types of energy into others.

Taking as a basis the philosophical principle of the optimality of all actions of nature, Gottfried Wilhelm Leibniz formulated one of the most important variational principles of physics - the “principle of least action”, later called the “Maupertuis principle”. Leibniz also made a number of discoveries in special branches of physics: in the theory of elasticity, the theory of vibrations, in particular, he derived a formula for calculating the strength of beams (Leibniz formula).

Like the atomists and Cartesians, Leibniz did not accept Isaac Newton's idea of ​​universal gravitation. According to Leibniz, “the actual attraction of bodies is a miracle for the mind, since it is inexplicable by their nature”; in accordance with Leibniz’s ideas, any change in the state of bodies, that is, their transition from a state of motion to a state of rest and vice versa, must be due to the influence of others bodies directly in contact or colliding with a given body. Leibniz said the following:

It would be a strange delusion if all matter were given gravity and considered to be effective in relation to all other matter, as if all bodies were mutually attracted in accordance with their masses and distances, that is, they had attractions in the proper sense, which cannot be reduce to the results of a hidden push of the body. The gravitation of sensory bodies towards the center of the Earth presupposes, on the contrary, the movement of some medium as the cause. The same applies to other types of gravity, for example, to the gravitation of planets towards the Sun and towards each other. A body cannot naturally be set in motion except by another body touching it and thus causing it to move, and after that it continues its motion until contact with another body prevents it. Any other effect on bodies should be considered either as a miracle or as pure imagination.

Gottfried Wilhelm Leibniz explained the gravity of earthly bodies and the gravitation of heavenly bodies using the movement of the medium, in particular the ethereal one, following in this regard the concept of Descartes' vortices. Leibniz qualified Newton's principle of gravitation as the action of bodies at a distance as a miracle or "an absurdity like the occult qualities of the scholastics, which are now again presented to us under the specious name of forces, but which lead us back to the kingdom of darkness."

Story

Gottfried Wilhelm Leibniz was the first to address the issue of the emergence of the Russian ruling dynasty, which was associated primarily with the problem of the formation of the Old Russian state. Leibniz began his work with questions about the origin of genealogies.

First of all, Leibniz was interested in the roots of the Russian royal family, and he understood that these roots go back to ancient times. On July 26, 1697, Leibniz wrote to Count Palmieri:

... I would like to know various details both about the genealogical origin of the king, about which I have a table, and about the ethnographic differences of the peoples under his control. The family tree of which I speak shows how Mikhail Fedorovich, the first great tsar of the now reigning branch, descends in the direct male line from the same ancestor from whom descended the now ceased branch of tsars.

The question of the roots of the Russian ruling dynasty in the minds of that time was directly related to the question of the ethnic origin of Rurik. Gottfried Wilhelm Leibniz collected and systematized a large amount of materials on ancient Russian history for this purpose, leaving interesting correspondence. In his letter dated April 15, 1710 to La Croze, Leibniz wrote that he considered the Varangian region to be the Vagria region in the vicinity of Lübeck. This area was later conquered by the Normans and Danes. According to Leibniz, the word “Varangian” itself is a distorted derivative of the name Vagria.

Despite the fact that Leibniz derived Rurik from the region of Vagria, he called him a “noble Danish lord” on the grounds that the name Rurik “is often used among the Danes and other northern Germans.” This proof from a modern point of view does not seem so impeccable, because, judging by the names, the majority of the current population of Russia are Greeks and Jews, which is not true, but in the 18th century they treated antiquity differently.

Leibniz may have suspected the existence of some ancient genealogies that presented Rurik in a different light. At one time he corresponded with Baron von Urbig, when he was the Russian ambassador in Vienna from 1707 to 1712; Through Urbich, Leibniz made inquiries in the Bavarian archives to research the history of the House of Brunswick, but all his attempts only aroused suspicion in Vienna, since at that time Bavaria was ruled by an Austrian governor.

Interest in the question of the origin of the Varangians fit well into the general direction of Leibniz’s scientific interests. Leibniz, studying the works of Greek and Latin authors, formulated the task of finding “ origines populorum"(beginning of nations); he understood ethnogenesis as the process of language formation, therefore for him the genealogical scheme of language development was fully consistent with the scheme of ethnic development. Leibniz wrote about the Wends who inhabited Northern Germany in a letter to General Bruce dated November 23, 1712.

The undoubted merit of Gottfried Wilhelm Leibniz was that he was the first in German historiography to draw attention to the relationship between linguistic problems and genealogy. However, this idea of ​​Leibniz did not immediately receive proper development.

After the marriage of Tsarevich Alexei to the Brunswick-Lüneburg princess, the German historian I. G. Eckhart began to trace genealogies to the Byzantine Emperor Constantine Porphyrogenitus. Eckhart was Leibniz's collaborator and assistant. In general, ideas about “sustainable friendship” between the Russian and German empires were later developed in the work of S. Treuer. In 1734, his publication was republished at the St. Petersburg Academy of Sciences. Following Leibniz, he assumed that Rurik originated from Holstein Vagria.

Aesthetics

G. Leibniz stood at the origins of philosophical aesthetics and influenced the aesthetics of the German Enlightenment (Baumgarten and others). In his teaching, the meaning of “symbol” and “symbolic”, characteristic of German rationalist philosophy and aesthetics of the pre-Kantian period, took shape.

Two of his key ideas played a particularly important role: first, the characterization of sensory perception as clear; but it is not as clear as the distinct perception of things which can, in principle, be perceived by the intellect. And secondly, this is a characteristic of pleasure as a sensory perception of the perfection of things. Leibniz's concept of sense perception was presented in his 1684 work, Meditations on Knowledge, Truth and Ideas. There Leibniz states that “knowledge is clear when I have something by which I can recognize the object being represented”, but it “vaguely, if I cannot separately list the signs sufficient to distinguish this object from another, although this object really has such signs and details into which its concept can be decomposed”. And vice versa, knowledge is both clear and distinct when it is possible not only to distinguish its object from others, but also to list its “signs” or qualities on which the difference is based. Leibniz then says that sense perception is clear but indistinct or vague knowledge, and illustrates his main thesis about the sense of perception with a remark about the perception of art and the judgment of it: “In the same way, painters and other creators of art know very well what has been done well and what has been done poorly, but they are often unable to give the basis for their judgment, and when asked, they answer that there is something missing in the subject they do not like.” enough."

The second idea that influenced the further development of aesthetics (Wolf et al.) is the idea that pleasure itself is a sensory perception of the perfection existing in an object. For Leibniz and his followers, there is only one sense in which all properties of actually existing objects can be regarded as perfections, since they believed that the real world is the only one chosen by God to exist among all possible worlds precisely because it is the most perfect; and therefore every object and all its properties must in some sense contribute to the perfection of the world. But they also used the concept of perfection in the more familiar sense, in which some real objects have special perfections that others do not, and this is precisely the sense of perfection that Leibniz is talking about when he argues that pleasure is the feeling of being flawless or perfect, whatever. , whether in yourself or in something else. To call "perfection" in another being something like understanding, courage, or especially beauty in a person, or in an animal, or even in a lifeless creation, a painting, or a work of art, is acceptable.

Leibniz also believed that the perfection we perceive in other objects is in some sense related to us, although he does not say that our pleasure in perceiving perfection is actually aimed at self-improvement.

Linguistics

Gottfried Wilhelm Leibniz's contribution to linguistics was the theory of the historical origin of languages ​​and their genealogical classification, as well as the development of the doctrine of the origin of names. Leibniz rejected the prevailing “biblical” view of linguistic diversity at that time, according to which all dialects go back to the Hebrew language, in addition, he drew attention to the historical proximity between some languages ​​(such as Germanic and Slavic, Finnish and Hungarian, Turkic languages) .

Leibniz is rightfully considered one of the creators of the German philosophical and scientific lexicon. Gottfried Wilhelm Leibniz wrote in various languages, most notably Latin (~40%), French (~30%) and German (~15%).

Biology

In the field of biology, Leibniz put forward the idea of ​​organic systems as wholes, in addition, he introduced the principle of the irreducibility of the organic to the mechanical.

When a huge prehistoric skeleton was found in a quarry near Tiede in June 1692, Leibniz established from the tooth that it was the skeleton of a mammoth or elephant seal.

Gottfried Wilhelm Leibniz summarized the accumulated material in the field of paleontology in his work “Protogea” (1693), unpublished during his lifetime, in which he also expressed a thesis about the evolution of the Earth. The evolutionary doctrine defended by Leibniz was interpreted by him, however, in a mechanistic manner, evolution was understood as the continuous development of preformed embryos. Based on the principle of continuity, Leibniz gave one of the first formulations in new philosophy of the idea of ​​the universal connection of existence: “Everything in the universe is in such a connection that the present always hides the future in its depths, and any given state can be explained in a natural way only from what immediately preceded it.” Based on this position, Leibniz came to the conclusion about the organic kinship of all living beings and their connection with inorganic nature. With this formulation of the question, Leibniz, despite the fallacy of the idea of ​​​​the existence of zoophytes, that is, animal-plants, took a step towards a dialectical understanding of nature, however, his concept of development was metaphysical in the sense that it denied spasmodicity and absolutized the principle of continuity. According to Leibniz, development occurs only from initial forms in the “small perceptions” of the monad through infinitesimal changes. Gottfried Wilhelm put forward the preformationist doctrine of the gradual development of living nature from eternally existing embryos and denied the presence of leaps in its evolution. He wrote the following: “We recognize that through displacement alone one can explain all other material phenomena.”

Psychology

In the field of psychology, Gottfried Wilhelm Leibniz's contribution was the introduction of the concept of unconscious "small perceptions" ("small perceptions") and the development of the doctrine of unconscious mental life. In the concept of “small perceptions” he developed, he separated the concepts of psyche and consciousness, recognizing that there are vaguely conscious and completely unconscious mental processes. According to Leibniz, unconscious “small perceptions” are like a differential: only an infinitely larger number of them, when summed, gives a finite, that is, distinguishable by us, value, while each small perception, taken separately, does not reach the threshold of consciousness. By creating the doctrine of the unconscious activity of the soul, including the rational soul, Gottfried Wilhelm tried to solve the problem that arises with the assumption of some semblance of souls also in inanimate nature. The theory of unconscious perceptions and drives influenced the further development of philosophical thought - from Schelling to Schopenhauer, Eduard Hartmann and Sigmund Freud. Leibniz also introduced into psychology the concept of apperception, by which he understood a form of activity of the soul that manifests itself already in the process of elementary sensations.

Leibniz as diplomat and lawyer

Gottfried Wilhelm Leibniz was a prominent public figure in Germany who reflected the views of the progressive but indecisive German bourgeoisie, which acted in conditions of feudal fragmentation through a compromise with the “enlightened” absolutism of the German princes. As a diplomat and lawyer, Leibniz defended the principles of national unity of the German states and the principles of natural law. Gottfried tried to connect together the legal and police state, the ideas of democracy and absolutism. According to Leibniz, the state is formed through a social contract. In this case, the subject of power is the state itself, and not the personality of the ruler. Leibniz came close to the idea of ​​popular sovereignty. He distinguishes three stages of natural law or justice: strict law, equality, piety and righteousness.

Leibniz, dealing with social issues, drew up proposals for the reform of the tax system, the abolition of corvee, serfdom and the introduction of communal self-government. As a thinker, he tended to compromise with official religious ideology, while simultaneously speaking out against theological orthodoxy, and against materialism and atheism. Lenin noted in Leibniz “...conciliatory aspirations in politics and religion.” Leibniz sought to reconcile the warring electors and courts, the Catholic and Protestant churches, religion and natural science, idealism and materialism (on the basis of objective idealism), as well as apriorism with empiricism.

Inventions

In 1673, after meeting Christiaan Huygens, Leibniz created a mechanical calculator (arithmometer) that performed addition, subtraction, multiplication and division of numbers, as well as taking roots and exponentiation. The machine was demonstrated at the French Academy of Sciences and the Royal Society of London.

Leibniz suggested to Denis Papin the design of a steam engine (cylinder and piston). Gottfried Leibniz himself tried, with varying degrees of success, to create a steam pump at the turn of the 17th and 18th centuries, along with Christian Huygens.

Leibniz could come up with half a dozen brilliant ideas in a week: from a submarine to a completely new form of clock, from an innovative model of a flashlight to a cart that could move at the same speed as modern cars (even in times when roads were rutted tracks) , however, none of these inventions were ever completed. As an engineer, Leibniz worked on computers, clocks, and even mining equipment. As a librarian, he more or less invented the modern idea of ​​cataloging.

Among Leibniz's inventions one can also note:

• design of optical instruments and hydraulic machines;
• work on the creation of a “pneumatic engine”.

Honors

Leibniz became the first German civilian to have a monument erected to him.

Statues of Gottfried Wilhelm Leibniz:

Leibniz statue in Göttingen

Leibniz statue in London

Statue of Leibniz at the Natural History Museum, Oxford University

Coins depicting Gottfried Wilhelm Leibniz:

In honor of Leibniz they received the name:

Theorems

• Leibniz's theorem (geometry) - about medians;
• Leibniz's theorem on the convergence of alternating series.

Formulas

• The Newton-Leibniz formula is the basic formula (theorem) of mathematical analysis;
• Leibniz formula for differentiating an integral with variable limits;
• Leibniz's formula for multiple differentiation of the product of two functions;
• Leibniz formula for the median of a tetrahedron;
• Leibniz's formula for determinants.

Objects

• Crater on the Moon;
• Minor planet (5149) Leibniz;
• University of Hannover in Hannover.

Other

• Leibniz cookies;
• Leibniz algebra;
• Leibniz notation;
• Leibniz operator;
• Leibniz Prize;
• Leibniz series for pi;
• Leibniz identity for differential operators;
• Leibniz Association;
• Genus of plants Leibnitzia (lat. Leibnitzia) of the Asteraceae family.

Essays

Major philosophical works

• "Discourse on Metaphysics" ( Discours de metaphysique), 1685 or 1686, edition 1846.
• "A new system of nature and communication between substances, as well as the connection existing between soul and body" (Système nouveau de la nature et de la communication des substances, aussi bien que de l’union qu’il y a entre l" âme et le corps), 1695.
• "New Experiments on the Human Mind" (Nouveaux essais sur l'entendement humain par l'auteur du système de l'harmonie préetablie), 1704, edition 1765.
• “Experiments in theodicy about the goodness of God, human freedom and the beginning of evil” (Essais de théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal), 1710.
• "Monadology" (La Monadologie), 1714, edition 1720.

Basic mathematical essays

• "On the true relation of the circle to the square" (1682).
• "The New Method of Highs and Lows" (1684).
• “On hidden geometry and analysis of indivisibles...” (1686).

Basic works on physics

• "New physical hypothesis" (1671).
• "Proof of Descartes' Memorable Error" (1686).
• "Essay on Dynamics" (1695).

Political and legal writings

• "Treatise on Law..." (1667).
• "Most Christian Mars..." (1680).
• "Code of International Diplomatic Law" (1693).

Other writings

• "On the art of combinatorics" (1666).
• "Protogaea" (Protogaea), OK. 1693, edition 1748.

Translations of essays into Russian

• Leibniz G.V. Works, in four volumes. Series: Philosophical Heritage. M.: Thought.
  • Volume 1. Metaphysics. "Monadology". 1982. - 636 pp.
  • Volume 2. “New experiments on human understanding.” 1983. - 686 pp.
  • Volume 3. Theory of knowledge, methodology, logic and general theory of science. 1984. - 734 pp.
  • Volume 4. “Experiments in theodicy about the goodness of God, human freedom and the beginning of evil.” 1989. - 560 pp.
  • Leibniz G.V. On freedom from the need to choose. Translation and notes by O. M. Bashkina, edited by V. L. Ivanov // EINAI: Problems of Philosophy and Theology." Volume 3, No. 1/2 (5/6) 2014
  • Leibniz, G.W. Confession of Nature against Atheists, 1668. Translation from it. edited by Vasily Preobrazhensky, 1892 / Cm.: Luther, Martin. About the freedom of a Christian. [Collection]. Ufa: ARC, 2013. pp. 193-203.
• Leibniz G.V. Mathematical works translated by A. P. Yushkevich // Uspekhi Mat. Sciences, vol. 3, v. 1 (23).
• On the enhancement of sciences (archive) (from 13-05-2013 - story).
• Leibniz G.V. Letters and essays on Chinese philosophy and the binary system. Preface, translations and notes by V. M. Yakovlev. M., 2005. - 404 p.
› Wilhelm Leibniz

Gottfried Wilhelm Leibniz was a German philosopher, mathematician, logician, physicist, inventor, theologian, historian, lawyer, linguist, diplomat, whose theoretical works and practical inventions greatly influenced modern philosophy and science. He founded the Berlin Academy of Sciences and was its first president.

Born in Leipzig in 1646, July 11. His father was a university professor, a famous lawyer, his mother was a professor's daughter, and in many ways this predetermined the future fate of their son. After his father, who died when Gottfried was 6 years old, there was left a huge library in which his son spent his days. His talent was visible from childhood. His mother sent him to the best school in the city, and at the age of 14 or 15 he was already a student at the University of Leipzig.

In terms of level of preparation, Leibniz was ahead of many senior students. He was not yet 18 when he was already a master of literature and philosophy. In 1663, Gottfried Wilhelm studied for a semester at the University of Jena. In the same year he received a bachelor's degree, and the next year he received a master's degree in philosophy. In November 1666, at Nuremberg, Altorf University, Leibniz successfully defended his doctoral dissertation and refused the offer to remain working at this educational institution.

In 1667, the young scientist moved to Mainz, where he met the elector, who highly appreciated Leibniz’s level and invited him to participate in the reform of legislation. For five years at court, the scientist occupied a prominent position; This was also a favorable period in his creative biography: a number of political and philosophical works appeared during these years.

From 1672 to 1676, Leibniz lived in Paris, going there as part of a diplomatic mission. His stay in the French capital made a huge contribution to his development as a scientist, in particular as a mathematician. So, in 1676 he developed the first foundations of the so-called. differential calculus, an outstanding mathematical method. At that time he gave preference to the exact sciences.

In 1676, Leibniz returned to Germany and entered the service of the Dukes of Hanover in order to receive a stable income. At first he was given the position of librarian, court adviser, and later Leibniz held the position of historiographer and privy councilor of justice. The scientist's duties included a wide variety of activities, from writing historical references to experiments in alchemy. During the 40 years spent in Hanover, Leibniz wrote a huge number of works in the field of sciences such as history, philosophy, mathematics, physics, law, and linguistics, which made him famous throughout Europe. The scientist initiated the creation of the Berlin Scientific Society and in 1700 became its first president.

There are also known facts from the biography of Gottfried Wilhelm Leibniz, such as his fruitful communication with Peter the Great. They met in 1711, 1712, 1716, the German scientist was the author of projects for reforming Russian education and government systems, and a project for the establishment of the St. Petersburg Academy of Sciences. Peter I was not the only famous foreigner with whom the famous German had established contacts; he corresponded with many of the greatest scientists, politicians, and philosophers of his time.

European fame did not brighten up the last years of Leibniz’s life; he had to endure a lot due to the unfavorability of the duke who did not like him, attacks from local clergy, and court intrigue. An assistant spy was assigned to him, who did not take his eyes off the scientist and from time to time made reports to his superiors, reporting on his decreased performance. He suffered not only morally, but also physically, because... he was tormented by illness. On November 14, 1716, Gottfried Wilhelm Leibniz died after taking an overdose of medicine. The death of the great scientist caused virtually no reaction from the ducal court and scientific communities; Only his personal secretary accompanied him on his final journey.

Gottfried Wilhelm Leibniz(German) Gottfried Wilhelm Leibniz or German Gottfried Wilhelm von Leibniz, IPA (German): or; June 21 (July 1) 1646 - November 14, 1716) - German philosopher, logician, mathematician, mechanic, physicist, lawyer, historian, diplomat, inventor and linguist. Founder and first president of the Berlin Academy of Sciences, foreign member of the French Academy of Sciences.

The most important scientific achievements:

Leibniz, independently of Newton, created mathematical analysis - differential and integral calculus (see historical essay), based on infinitesimals.

Leibniz created combinatorics as a science; Only in the entire history of mathematics he worked equally freely with both continuous and discrete.

He laid the foundations of mathematical logic.

He described the binary number system with the numbers 0 and 1, on which modern computer technology is based.

In mechanics, he introduced the concept of “living force” (the prototype of the modern concept of kinetic energy) and formulated the law of conservation of energy.

In psychology, he put forward the concept of unconsciously “small perceptions” and developed the doctrine of unconscious mental life.

Leibniz is also the finalizer of the philosophy of the 17th century and the predecessor of German classical philosophy, the creator of a philosophical system called monadology. He developed the doctrine of analysis and synthesis, for the first time formulated the law of sufficient reason (to which, however, he gave not only a logical (relating to thinking) but also an ontological (relating to being) meaning: “... not a single phenomenon can turn out to be true or real, not a single statement is fair - without sufficient reason why exactly the situation is this way and not otherwise..."); Leibniz is also the author of the modern formulation of the law of identity; he coined the term “model” and wrote about the possibility of machine modeling of the functions of the human brain. Leibniz expressed the idea of ​​converting some types of energy into others, formulated one of the most important variational principles of physics - the “principle of least action” - and made a number of discoveries in special branches of physics.

He was the first to address the issue of the emergence of the Russian ruling dynasty, the first in German historiography to draw attention to the relationship of linguistic problems with genealogy, created a theory of the historical origin of languages ​​and gave their genealogical classification, and was one of the creators of the German philosophical and scientific lexicon.

Leibniz also introduced the idea of ​​the integrity of organic systems, the principle of the irreducibility of the organic to the mechanical, and expressed the idea of ​​the evolution of the Earth.

early years

Gottfried Wilhelm was born on July 1, 1646 in the family of Friedrich Leibnütz, a professor of moral philosophy (ethics) at the University of Leipzig (German). Friedrich Leibnütz or German Friedrich Leibniz) and Katerina Schmuck (German) Catherine Schmuck), who was the daughter of an eminent law professor. Leibniz's father was of Serbian-Lusatian origin. On his mother's side, Gottfried Wilhelm Leibniz apparently had purely German ancestors.

Leibniz's father very early noticed the genius of his son and tried to develop curiosity in him, often telling him small episodes from sacred and secular history; According to Leibniz himself, these stories sank deeply into his soul and were the most powerful impression of his early childhood. Leibniz was not even seven years old when he lost his father; his father died, leaving behind a large personal library. Leibniz said:

As I grew older, I began to derive extreme pleasure from reading all kinds of historical stories. I did not let go of the German books that came into my hands until I had read them to the end. At first I studied Latin only at school and, without a doubt, I would have progressed with the usual slowness if not for an incident that showed me a completely unique path. In the house where I lived, I came across two books left by a student. One of them was the works of Livy, the other was the chronological treasury of Calvisius. As soon as these books fell into my hands, I devoured them.

Leibniz understood Calvisius without difficulty, because he had a German book on general history, which said approximately the same thing, but when reading Livy he constantly found himself in a dead end. Leibniz had no idea either about the life of the ancients or about their manner of writing; also not accustomed to the sublime rhetoric of historiographers, which stands above ordinary understanding, Leibniz did not understand a single line, but this publication was old, with engravings, so he carefully examined the engravings, read the captions and, caring little about the dark places for him, simply skipped everything something I couldn't understand. He repeated this several times and leafed through the entire book; thus looking ahead, Leibniz began to understand the former a little better; delighted with his success, he moved on in this manner, without a dictionary, until at last most of what he read became quite clear to him.

Leibniz’s teacher soon noticed what his student was doing, and, without hesitation, he went to the persons to whom the boy was given for education, demanding that they pay attention to Leibniz’s “inappropriate and premature” activities; according to him, these classes were only a hindrance to Gottfried’s teaching. In his opinion, Livy was suitable for Leibniz, like a buskin for a pygmy; he believed that books suitable for older people should be taken away from the boy and given to him " Orbis pictus"Comenius and " Short Catechism» Luther. He would have convinced Leibniz’s educators of this if a scientist who lived in the neighborhood and a well-traveled nobleman, a friend of the owners of the house, had not accidentally witnessed this conversation; struck by the ill will and stupidity of the teacher, who measured everyone by the same standard, he began, on the contrary, to prove how absurd and inappropriate it would be if the first glimpses of a developing genius were suppressed by the severity and rudeness of the teacher. On the contrary, he believed that it was necessary to favor this boy, who promised something extraordinary, by all means; He immediately asked to send for Leibniz, and when, in response to his questions, Gottfried answered intelligently, he did not leave Leibniz’s relatives until he forced them to promise that Gottfried would be allowed into his father’s library, which had long been under lock and key. Leibniz wrote:

I triumphed as if I had found a treasure, because I was burning with impatience to see the ancients whom I knew only by name - Cicero and Quintilian, Seneca and Pliny, Herodotus, Xenophon and Plato, the writers of the Augustan century and many of the Latin and Greek fathers of the church. I began to read all this, depending on my inclination, and enjoyed the extraordinary variety of subjects. Thus, before I was twelve years old, I understood Latin fluently and began to understand Greek.

This story of Leibniz is confirmed by third-party evidence, proving that his outstanding abilities were noticed by both his comrades and the best teachers; Leibniz was especially friendly at school with the two Ittig brothers, who were much older than him and were considered among the best students, and their father was a physics teacher, and Leibniz loved him more than other teachers. Leibniz studied at the famous Leipzig School of St. Thomas.

His father's library allowed Leibniz to study a wide range of advanced philosophical and theological works that he would have only had access to as a student. By the age of ten, Leibniz had studied the books of Cicero, Pliny, Herodotus, Xenophanes and Plato. At the age of 12, Leibniz was already an expert in Latin; at the age of 13 he showed a poetic talent that no one suspected in him. On the Day of the Holy Trinity, one student was supposed to read a festive speech in Latin, but he fell ill, and none of the students volunteered to replace him; Leibniz's friends knew that he was a master of writing poetry and turned to him. Leibniz got down to business and in one day composed three hundred hexameters of Latin verse for this event, and, just in case, he specially tried to avoid at least a single combination of vowels; his poem aroused the approval of his teachers, who recognized Leibniz as an outstanding poetic talent.

Leibniz was also interested in Virgil; to a very old age he remembered almost the entire Aeneid by heart; in high school he was especially distinguished by Jacob Thomasius (German) Russian, who once told the boy that sooner or later he would acquire a famous name in the scientific world. At the age of fourteen, Leibniz also began to think about the true task of logic as classification of elements of human thinking; he said the following about it:

I not only knew how to apply rules to examples with extraordinary ease, which greatly amazed my teachers, since none of my peers could do the same; but even then I doubted many things and rushed around with new thoughts, which I wrote down so as not to forget. What I wrote down at the age of fourteen, I re-read much later, and this reading always gave me a lively feeling of pleasure.

Leibniz saw that logic divides simple concepts into well-known categories, the so-called premedications(in the language of scholasticism predrug meant the same thing as category), and he was surprised why complex concepts or even judgments are not subdivided in the same way so that one member follows or is derived from another. Gottfried came up with his own categories, which he also called predicates of judgments that form the content or inference material, just as ordinary predicates form judgment material; when he expressed this thought to his teachers, they did not answer him anything positive, but only said that “it is not suitable for a boy to introduce innovations in subjects that he has not yet studied enough.”

During his school years, Leibniz managed to read everything more or less outstanding that was at that time in the field of scholastic logic; interested in theological treatises, he read Luther's work on the criticism of free will, as well as many polemical treatises of the Lutherans, Reformed, Jesuits, Arminians, Thomists and Jansenists. These new activities of Gottfried alarmed his teachers, who were afraid that he would become a “cunning scholastic.” “They did not know,” Leibniz wrote in his autobiography, “that my spirit could not be filled with one-sided content.”

Gottfried Wilhelm Leibniz (German Gottfried Wilhelm Leibniz or German Gottfried Wilhelm von Leibniz). Born June 21 (July 1), 1646 - died November 14, 1716. German philosopher, logician, mathematician, mechanic, physicist, lawyer, historian, diplomat, inventor and linguist. Founder and first president of the Berlin Academy of Sciences, foreign member of the French Academy of Sciences.

Gottfried Wilhelm was born on July 1, 1646 in the family of Friedrich Leibnütz (German Friedrich Leibnütz or German Friedrich Leibniz) (1597-1652), professor of moral philosophy (ethics) at the University of Leipzig, and Katherina Schmuck, who was the daughter of an eminent professor jurisprudence. Leibniz's father was of Serbian-Lusatian origin. On his mother's side, Gottfried Wilhelm Leibniz apparently had purely German ancestors.

Leibniz's father very early noticed the genius of his son and tried to develop curiosity in him, often telling him small episodes from sacred and secular history; According to Leibniz himself, these stories sank deeply into his soul and were the most powerful impressions of his early childhood. Leibniz was not even seven years old when he lost his father; his father died, leaving behind a large personal library.

Leibniz wrote: “When I grew up, reading all kinds of historical stories began to give me extreme pleasure. The German books that came to my hand, I did not let go of until I had read them to the end. At first I studied Latin only at school and, without a doubt, , I would have moved with the usual slowness, if not for an incident that showed me a completely peculiar path. In the house where I lived, I came across two books left by a student. One of them was the works of Livy, the other was the chronological treasury of Calvisius. How As soon as these books fell into my hands, I devoured them."

Leibniz understood Calvisius without difficulty, because he had a German book on general history, which said approximately the same thing, but when reading he constantly found himself in a dead end. Leibniz had no idea either about the life of the ancients or about their manner of writing; also not accustomed to the sublime rhetoric of historiographers, which stands above ordinary understanding, Leibniz did not understand a single line, but this publication was old, with engravings, so he carefully examined the engravings, read the captions and, caring little about the dark places for him, simply skipped everything something I couldn't understand. He repeated this several times and leafed through the entire book; thus looking ahead, Leibniz began to understand the former a little better; delighted with his success, he moved on in this manner, without a dictionary, until at last most of what he read became quite clear to him.

Leibniz’s teacher soon noticed what his student was doing, and, without hesitation, he went to the persons to whom the boy was given for education, demanding that they pay attention to Leibniz’s “inappropriate and premature” activities; according to him, these classes were only a hindrance to Gottfried’s teaching. In his opinion, Livy was suitable for Leibniz as a buskin for a pygmy; he believed that books suitable for older people should be taken away from the boy and given to him “Orbis pictus” by Comenius and “Short Catechism” by Luther. He would have convinced Leibniz’s educators of this if a scientist who lived in the neighborhood and a well-traveled nobleman, a friend of the owners of the house, had not accidentally witnessed this conversation; struck by the ill will and stupidity of the teacher, who measured everyone by the same standard, he began, on the contrary, to prove how absurd and inappropriate it would be if the first glimpses of a developing genius were suppressed by the severity and rudeness of the teacher. On the contrary, he believed that it was necessary to favor this boy, who promised something extraordinary, by all means; He immediately asked to send for Leibniz, and when, in response to his questions, Gottfried answered intelligently, he did not leave Leibniz’s relatives until he forced them to promise that Gottfried would be allowed into his father’s library, which had long been under lock and key.

His father's library allowed Leibniz to study a wide range of advanced philosophical and theological works that he would have only had access to as a student.

By the age of ten, Leibniz had studied the books of Pliny, Xenophanes and. At the age of 12, Leibniz was already an expert in Latin; at the age of 13 he showed a poetic talent that no one suspected in him. On the Day of the Holy Trinity, one student was supposed to read a festive speech in Latin, but he fell ill, and none of the students volunteered to replace him; Leibniz's friends knew that he was a master of writing poetry and turned to him. Leibniz got down to business and in one day composed three hundred hexameters of Latin verse for this event, and, just in case, he specially tried to avoid at least a single combination of vowels; his poem aroused the approval of his teachers, who recognized Leibniz as an outstanding poetic talent.

Leibniz was also interested in; to a very old age he remembered almost the entire Aeneid by heart; In high school, he was especially distinguished by Jacob Thomasius, who once told the boy that sooner or later he would acquire a famous name in the scientific world. At the age of fourteen, Leibniz also began to think about the true task of logic as a classification of the elements of human thinking.

During his school years, Leibniz managed to read everything more or less outstanding that was at that time in the field of scholastic logic; interested in theological treatises, he read Luther's work on the criticism of free will, as well as many polemical treatises of the Lutherans, Reformed, Jesuits, Arminians, Thomists and Jansenists. These new activities of Gottfried alarmed his teachers, who were afraid that he would become a “cunning scholastic.” “They did not know,” Leibniz wrote in his autobiography, “that my spirit could not be filled with one-sided content.”

In 1661, at the age of fourteen (according to other sources - at the age of 15), Gottfried himself entered the same Leipzig University where his father once worked. In terms of training, Leibniz was significantly superior to many older students. While a student, Gottfried Wilhelm became acquainted with the works of Kepler, Galileo and other scientists. Among the professors of philosophy in Leipzig was Jacob Thomasius, who was considered a well-read man and had outstanding teaching talent. Leibniz himself admitted that Thomasius contributed significantly to the systematization of his heterogeneous but scattered knowledge; Thomasius lectured on the history of philosophy while others read only lectures on the history of philosophers, and in the lectures of Thomasius Leibniz discovered not only new information, but also new generalizations and new thoughts; These lectures contributed greatly to Godfrey's rapid acquaintance with the great ideas of the late 16th and early 17th centuries.

After 2 years, Leibniz moved to the University of Jena, where he studied mathematics. Leibniz listened to lectures by the mathematician Weigel in Jena, as well as lectures by some lawyers and the historian Bosius, who invited him to meetings of an educational society consisting of professors and students and called the “college of the inquisitive.”

In 1663, Leibniz published his first treatise, “On the Principle of Individuation” (“De principio individui”), in which he defended the nominalist doctrine of the reality of the individual, and received a bachelor's degree, and in 1664, a master's degree in philosophy.

The best of the professors appreciated Leibniz, and Jacob Thomasius had a particularly high opinion of him, who appreciated Gottfried’s first dissertation so highly that he himself wrote a preface to it, in which he publicly stated that he considered Leibniz quite capable of “the most difficult and intricate debates.” Leibniz then studied law in Leipzig, but failed to obtain a doctorate there. Everyone at the faculty was perplexed, because at the age of 20 Leibniz knew much more in the field of jurisprudence than all his teachers. The University of Leipzig refused to award him a doctorate in law, most likely due to his relative youth.

Upset by the refusal, Leibniz went to the University of Altdorf in Altdorf-Nuremberg, where he successfully defended his dissertation for the degree of Doctor of Law. The dissertation was devoted to the analysis of the issue of complicated legal cases and was called “On complicated legal cases” (“De asibus perplexis injure”). The defense took place on November 5, 1666; Leibniz's erudition, clarity of presentation and oratorical talent aroused universal admiration; The examiners were so delighted with Gottfried's eloquence that they asked him to remain at the university, but Leibniz rejected this offer, saying that "his thoughts were turned in a completely different direction."

After receiving his doctorate in law, Leibniz lived for some time in Nuremberg, where he was attracted by information about the famous Rosicrucian Order, which was then headed by the preacher Wölffer.

Gottfried took out the works of the most famous alchemists and wrote out from them the most obscure, incomprehensible and even barbarously absurd expressions and formulas, from which he compiled a kind of scientific note, in which, by his own admission, he himself could not understand anything. He presented this note to the chairman of the alchemical society with a request to accept his essay as clear evidence of a thorough acquaintance with the alchemical secrets; The Rosicrucians immediately brought Leibniz into their laboratory and considered him at least an adept. So Gottfried became a hired alchemist, although he did not have the proper knowledge in this discipline.

For a certain annual salary, he was entrusted with keeping the minutes of the society, and Leibniz for some time was the secretary of the society, keeping the minutes, conducting alchemical experiments, recording their results, and making excerpts from famous alchemical books; many members of society even turned to Leibniz for information, and he, in turn, learned all the necessary information in a very short time.

In 1666, Gottfried Wilhelm Leibniz wrote one of his many essays, “On the Art of Combinatoria” (“De arte kombinatoria”). Two centuries ahead of his time, 21-year-old Leibniz conceived a project to mathematize logic. He calls the future theory (which he never completed) “general characteristic.” It included all the logical operations whose properties he clearly understood. Leibniz’s ideal was to create a language of science that would make it possible to replace meaningful reasoning with calculus based on arithmetic and algebra: “... with the help of such means one can achieve ... amazing art in discovery and find an analysis that in other areas will give something similar to that what algebra has given in the field of numbers.” Leibniz repeatedly returned to the task of “mathematizing” formal logic, trying to use arithmetic, geometry and combinatorics - a field of mathematics of which he himself was the main creator; The material for this was traditional syllogistic, which by that time had reached a high degree of perfection.

Leibniz invented his own design of an adding machine, much better than Pascal's - he could perform multiplication, division, extraction of square and cube roots, as well as exponentiation. The stepped roller and movable carriage proposed by Gottfried formed the basis for all subsequent adding machines until the 20th century. “With the help of Leibniz’s machine, any boy can perform the most difficult calculations,” one of the French scientists said about this invention of Gottfried.

In 1673, Leibniz demonstrated his adding machine at a meeting of the Royal Society in London, and he was elected a member of the Society. From the secretary of the Oldenburg Society he received a statement of Newton's discoveries: the analysis of infinitesimals and the theory of infinite series. Immediately appreciating the power of the method, he began to develop it himself. In particular, he derived the first series for the number Pi.

In 1675, Leibniz completed his version of mathematical analysis, carefully considering its symbolism and terminology, reflecting the essence of the matter. Almost all of his innovations took root in science, and only the term “integral” was introduced by Jacob Bernoulli (1690); Leibniz himself initially called it simply a sum.

As the analysis developed, it became clear that Leibniz’s symbolism, unlike Newton’s, is excellent for denoting multiple differentiation, partial derivatives, etc. Leibniz’s school was also benefited by his openness and mass popularization of new ideas, which Newton did extremely reluctantly.

In 1676, shortly after the death of the Elector of Mainz, Leibniz entered the service of Duke Ernest August of Brunswick-Lüneburg (Hannover). He simultaneously served as adviser, historian, librarian and diplomat; He did not leave this post until the end of his life. On behalf of the Duke, Leibniz began working on the history of the Guelph-Braunschweig family. He worked on it for more than thirty years and managed to bring it to the “dark ages.”

At this time, Leibniz continued his mathematical research, discovered the “fundamental theorem of analysis,” and exchanged several kind letters with Newton, in which he asked to clarify unclear points in the theory of series. Already in 1676, Leibniz outlined the foundations of mathematical analysis in letters. The volume of his correspondence is colossal: it reached a truly astronomical number - approximately 15,000 letters.

In 1682, Leibniz founded the scientific journal Acta Eruditorum, which played a significant role in the dissemination of scientific knowledge in Europe. Gottfried Wilhelm published in this journal many articles on all branches of knowledge, mainly in law, philosophy and mathematics. In addition, he published extracts from various rare books, as well as abstracts and reviews of new scientific works, and in every possible way contributed to attracting new employees and subscribers. The Acta Eruditorum was first published in Leipzig. Leibniz involved his students - the Bernoulli brothers, Jacob and Johann - in his research.

The Duke of Brunswick died in 1698. His heir was George Ludwig, the future king of Great Britain. He retained Leibniz in his service, but treated him with disdain.

In 1700, Leibniz, acting mainly through Queen Sophia Charlotte, founded the Berlin Academy of Sciences and became its first president. At the same time he was elected a foreign member of the French Academy of Sciences.

In 1697, during a trip to Europe, the Russian Tsar met Leibniz. It was a chance meeting at Hanover's Koppenbrück Castle. Later, after the defeat of the Russian army at Narva, Leibniz composed a poem in honor of the Swedish king, in which he expressed the hope that Charles XII would defeat Peter I and expand the Swedish border “from Moscow to the Amur.” During the celebrations in 1711 dedicated to the wedding of the heir to the throne Alexei Petrovich with the representative of the ruling house of Hanover, Princess Sophia Christina of Brunswick, their second meeting took place. This time the meeting had a noticeable impact on the emperor. The following year, Leibniz had longer meetings with Peter, and, at his request, accompanied him to Teplitz and Dresden. This meeting was very important and subsequently led to Peter’s approval of the creation of the Academy of Sciences in St. Petersburg, which served as the beginning of the development of scientific research in Russia according to the Western European model.

From Peter Leibniz received the title of Privy Councilor of Justice and a pension of 2,000 guilders. Leibniz put forward the idea of ​​​​distributing scientific knowledge in Russia, proposed a project for scientific research in Russia related to its unique geographical position, such as the study of the Earth's magnetic field. Leibniz also proposed a project for a movement for the unification of churches, which was to be created under the auspices of the Russian emperor. Leibniz was very pleased with his relationship with Peter I.

The last time Gottfried Wilhelm Leibniz met Peter was in 1716, shortly before his death.

In 1708, Leibniz's infamous dispute with Newton broke out over the scientific priority of the discovery of differential calculus. It is known that Leibniz and Newton worked on differential calculus in parallel and that in London Leibniz became acquainted with some of Newton's unpublished works and letters, but came to the same results on his own. It is also known that Newton created his version of mathematical analysis, the “method of fluxions” (“fluxion” is Newton’s term; originally denoted by a dot over a value; the term “fluxion” means “derivative”), no later than 1665, although and published his results only many years later; Leibniz was the first to formulate and publish the “infinitesimal calculus” and developed a symbolism that turned out to be so convenient that it is still used today.

In 1693, when Newton finally published the first summary of his version of the analysis, he exchanged friendly letters with Leibniz. Newton reported: “Our Wallis added to his “Algebra”, which had just appeared, some of the letters that I wrote to you at one time. At the same time, he demanded of me that I openly state the method that I at that time hid from you by rearranging letters; I did it as briefly as I could. I hope that I did not write anything that would be unpleasant for you, but if this happened, then please let me know, because friends are dearer to me than mathematical discoveries".

After the first detailed publication of Newton's analysis (a mathematical supplement to Optics, 1704), an anonymous review appeared in Leibniz's journal Acta eruditorum with insulting allusions to Newton; the review clearly indicated that the author of the new calculus was Leibniz, but Leibniz himself strongly denied that the review was compiled by him, but historians found a draft written in his handwriting. Newton ignored Leibniz's article, but his students responded indignantly, after which a pan-European priority war broke out.

On January 31, 1713, the Royal Society received a letter from Leibniz containing a conciliatory formulation: he agreed that Newton arrived at the analysis independently, “on general principles similar to ours”; Newton demanded the creation of an international commission to clarify scientific priority. The Royal Society of London, having examined the case, recognized that Leibniz's method was essentially identical to Newton's method, and the primacy was recognized by the English mathematician. On April 24, 1713, this sentence was pronounced, which annoyed Leibniz.

Leibniz was supported by the Bernoulli brothers and many other mathematicians on the continent; in England, and partly in France, they supported Newton.

Caroline of Brandenburg-Ansbach tried with all her might, but to no avail, to reconcile the opponents; she wrote to Leibniz the following: “It is with real regret that I see that people of such scientific importance as you and Newton cannot make peace. The world could benefit endlessly if it were possible to bring you closer together, but great people are like women who quarrel over lovers. This is my judgment about your dispute, gentlemen!".

In her next letter she wrote: “I’m surprised, is it really that if you or Newton discovered the same thing at the same time, or one earlier, the other later, then it follows that you would tear each other to pieces! Both of you are the greatest people of our time. Prove to us that the world has nowhere emptiness; let Newton and Clark prove emptiness. We, Countess Bückeburg, Poellnitz and I, will be present and depict in the original "Learned Women" by Moliere".

Various third-rate scientists intervened in the dispute between Leibniz and Newton, some of whom wrote libels against Leibniz, and others against Newton. From the summer of 1713, Europe was flooded with anonymous pamphlets that defended Leibniz's priority and argued that "Newton arrogates to himself the honor that belongs to another"; the pamphlets also accused Newton of stealing the results of Hooke and Flamsteed. Newton's friends, for their part, accused Leibniz himself of plagiarism; According to their version, during his stay in London (1676), Leibniz at the Royal Society became acquainted with Newton’s unpublished works and letters, after which Leibniz published the ideas expressed there and passed them off as his own.

The dispute between Leibniz and Newton over scientific priority became known as "the most shameful squabble in the entire history of mathematics." This quarrel between two geniuses cost science dearly: the English mathematical school soon withered for a whole century, and the European one ignored many of Newton’s outstanding ideas, rediscovering them much later.

The last years of Leibniz's life were sad and restless. Ernst August's son, Georg Ludwig, who succeeded his father in 1698, did not like Leibniz. He looked upon him only as his court historiographer, who cost him a lot of extra money. Their relationship cooled even more when Georg Ludwig, under the name of George I, ascended to the English throne. Leibniz wanted to be invited to the London court, but he met with stubborn resistance from English scientists, since the notorious dispute that he had with Newton greatly damaged him in the eyes of the English; Leibniz tried unsuccessfully to reconcile with the king and win him over to his side. George I constantly reprimanded Leibniz for his sloppy history of his dynasty; this king immortalized himself with a rescript addressed to the Hanoverian government, where Leibniz was officially condemned, and the famous scientist was publicly named as a person who should not be trusted.

Gottfried Wilhelm Leibniz was surrounded by court intrigues; he was irritated by the attacks of the Hanoverian clergy. The last two years of his life in Hanover were especially difficult for Leibniz; he was in constant physical suffering; “Hannover is my prison,” he once said. The assistant assigned to Leibniz, Georg Eckhardt, on occasion followed Leibniz as a spy, reporting to the king and his minister Bernstorff that Leibniz was not working enough due to his decrepitude. When Leibniz fell ill with a long illness, Eckhardt wrote: “Nothing else will put him on his feet, but if the king and a dozen other monarchs give him hope for new pensions, then he will immediately begin to walk.”

At the beginning of August 1716, Leibniz felt better, and he finally decided to finish the Brunswick story. However, he caught a cold, had an attack of gout and rheumatic pains in the shoulders; Of all the medicines, Leibniz trusted only one, which was once given to him by a friend, a Jesuit. But this time Leibniz took too large a dose and felt unwell; the arriving doctor found the situation so dangerous that he himself went to the pharmacy for medicine, but during his absence Gottfried Wilhelm died.

None of the retinue of the Duke of Hanover accompanied Leibniz on his last journey; only his personal secretary followed the coffin. The Berlin Academy of Sciences, of which he was the founder and first president, did not pay attention to his death, but a year later B. Fontenelle made a famous speech in his memory to members of the Paris Academy of Sciences.

Leibniz's most important scientific achievements:

Leibniz, independently of Newton, created mathematical analysis - differential and integral calculus based on infinitesimals.

Leibniz created combinatorics as a science; Only in the entire history of mathematics he worked equally freely with both continuous and discrete.

He laid the foundations of mathematical logic.

He described the binary number system with the numbers 0 and 1, on which modern computer technology is based.

In mechanics, he introduced the concept of “living force” (the prototype of the modern concept of kinetic energy) and formulated the law of conservation of energy.

In psychology, he put forward the concept of unconsciously “small perceptions” and developed the doctrine of unconscious mental life.

Leibniz is also the finalizer of the philosophy of the 17th century and the predecessor of German classical philosophy, the creator of a philosophical system called monadology.

He developed the doctrine of analysis and synthesis, for the first time formulated the law of sufficient reason (to which, however, he gave not only a logical (relating to thinking) but also an ontological (relating to being) meaning: “... not a single phenomenon can turn out to be true or real, not a single statement is fair - without sufficient reason why exactly the situation is this way and not otherwise..."); Leibniz is also the author of the modern formulation of the law of identity; he coined the term “model” and wrote about the possibility of machine modeling of the functions of the human brain. Leibniz expressed the idea of ​​converting some types of energy into others, formulated one of the most important variational principles of physics - the “principle of least action” - and made a number of discoveries in special branches of physics.

He was the first to address the issue of the emergence of the Russian ruling dynasty, the first in German historiography to draw attention to the relationship of linguistic problems with genealogy, created a theory of the historical origin of languages ​​and gave their genealogical classification, and was one of the creators of the German philosophical and scientific lexicon.

Leibniz also introduced the idea of ​​the integrity of organic systems, the principle of the irreducibility of the organic to the mechanical, and expressed the idea of ​​the evolution of the Earth.