Question: How old was Aristotle when he died?

Pythagoras

“His philosophy spread, all of Hellas began to admire him, and the best and wisest men came to Samos to listen to his teachings. His fellow citizens, however, forced him to participate in all embassies and public affairs. Pythagoras felt how difficult it was, obeying the laws of the fatherland, to engage in philosophy at the same time, and saw that all former philosophers had lived their lives in a foreign land. After considering all this, moving away from public affairs and, as some say, considering the low assessment of his teachings by the Samosi insufficient, he left for Italy, considering his homeland a country where he is more capable of educate people.”


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras settled in the Greek colony of Crotone in southern Italy, where he found many followers.


Question: How old was Aristotle when he died?

Pythagoras

They were attracted not only by the mystical philosophy, which he convincingly stated, but also by the lifestyle he prescribed with elements of healthy asceticism and strict morality.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras preached the moral refinement of an ignorant people, which can be achieved where the power belongs to the caste of wise and knowledgeable people, and to whom the people obey something unconditionally, like children to parents, and otherwise consciously, obeying moral authority.


Question: How old was Aristotle when he died?

Pythagoras

Tradition ascribes to Pythagoras the introduction of the words philosophy and philosopher.


Question: How old was Aristotle when he died?

Pythagoras

The disciples of Pythagoras formed a kind of religious order, or brotherhood of initiates, consisting of a caste of selected like-minded people who literally deify their teacher, the founder of the order.


Question: How old was Aristotle when he died?

Pythagoras

This order actually came to power in Crotone, but due to antiPythagorean sentiments at the end of the 6th century BC.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras had to retire to another Greek colony of Metapont, where he died.


Question: How old was Aristotle when he died?

Pythagoras

Almost 450 years later, during the time of Cicero (1st century BC), Metapont showed the crypt of Pythagoras as one of the attractions.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras had a wife named Feano, son Telavg and daughter Miya (according to another version, son Arimnest and daughter Arignot) [4].


Question: How old was Aristotle when he died?

Pythagoras

According to Yamblich, Pythagoras led his secret society for thirty-nine years, then the approximate date of death of Pythagoras can be attributed to 491 BC.


Question: How old was Aristotle when he died?

Pythagoras

, by the beginning of the Greco - Persian wars.


Question: How old was Aristotle when he died?

Pythagoras

Diogenes, referring to Heraclides (4th century BC), says that Pythagoras died peacefully at the age of 80, or at the age of 90 (according to unnamed other sources).


Question: How old was Aristotle when he died?

Pythagoras

This shows the date of death of 490 BC. e.


Question: How old was Aristotle when he died?

Pythagoras

(or 480 BC, which is unlikely).


Question: How old was Aristotle when he died?

Pythagoras

Eusebius of Caesarea in his chronography marked 497 BC. e.


Question: How old was Aristotle when he died?

Pythagoras

like the year Pythagoras died.


Question: How old was Aristotle when he died?

Pythagoras

The defeat of the Pythagorean alliance


Question: How old was Aristotle when he died?

Pythagoras

Among the followers and disciples of Pythagoras there were many members of the nobility who tried to change the laws in their cities in accordance with the Pythagorean teachings.


Question: How old was Aristotle when he died?

Pythagoras

This was superimposed by the usual struggle of that era between the oligarchic and democratic parties in ancient Greek society.


Question: How old was Aristotle when he died?

Pythagoras

The discontent of the majority of the population, who do not share the ideals of the philosopher, resulted in bloody riots in Crotone and Tarent.


Question: How old was Aristotle when he died?

Pythagoras

Yamblich, citing Apollonius, who used the archives from Croton, describes the defeat of the Pythagoreans in Crotone as follows:


Question: How old was Aristotle when he died?

Pythagoras

“The Pythagoreans formed a large community (there were more than three hundred of them), but it was only a small part of the city, which was no longer ruled according to the same customs and customs. However, while the Crotonians owned their land, and Pythagoras was with them, the state structure that existed since the foundation of the city was preserved, although there were dissatisfied, waiting for an opportunity for coup. But when Sybaris was conquered, Pythagoras left, and the Pythagoreans, who ruled the conquered land, did not distribute it by lot, as most wanted, then hidden hatred broke out, and many citizens opposed them... The relatives of the Pythagoreans were even more irritated that they gave their right hand only to their own, and those close to them only to their parents, and that they provided their property for public use, and it is separated from the property of relatives. When relatives began this enmity, the rest willingly joined the conflict... Many years later... the Crotonians were seized by regret and remorse, and they decided to return to the city those Pythagoreans who were still alive.”


Question: How old was Aristotle when he died?

Pythagoras

Many Pythagoreans died, and survivors scattered throughout Italy and Greece.


Question: How old was Aristotle when he died?

Pythagoras

German historian F. Schlosser notes about the defeat of the Pythagoreans: “The attempt to transfer caste and clerical life to Greece and, contrary to the spirit of the people, to change its political structure and mores according to the requirements of abstract theory.” [5]


Question: How old was Aristotle when he died?

Pythagoras

According to Porphyrius, Pythagoras himself died as a result of the anti-Pythagorean rebellion in Metapont, but other authors do not confirm this version, although they willingly convey the story of a depressed philosopher starved himself to death in the sacred temple.


Question: How old was Aristotle when he died?

Pythagoras

Philosophical doctrine


Question: How old was Aristotle when he died?

Pythagoras

The teachings of Pythagoras should be divided into two components: a scientific approach to understanding the world and the religious-mystical way of life preached by Pythagoras.


Question: How old was Aristotle when he died?

Pythagoras

The merits of Pythagoras in the first part are unknown for certain, as he was later credited with everything created by followers within the framework of the school of Pythagoreism.


Question: How old was Aristotle when he died?

Pythagoras

The second part prevails in the teachings of Pythagoras, and it remained in the minds of most ancient authors.


Question: How old was Aristotle when he died?

Pythagoras

Empedocles' poem “Purification” gives quite complete information about the ideas developed by Pythagoras about the migration of souls and food prohibitions based on them [6].


Question: How old was Aristotle when he died?

Pythagoras

In the surviving works, Aristotle never directly refers directly to Pythagoras, but only to the “so-called Pythagoreans”.


Question: How old was Aristotle when he died?

Pythagoras

In lost works (known from extracts), Aristotle views Pythagoras as the founder of a semi-religious cult that forbade eating beans and had a golden thigh, but did not belong to sequences of thinkers, predecessors of Aristotle.


Question: How old was Aristotle when he died?

Pythagoras

Plato treated Pythagoras with the deepest respect and respect.


Question: How old was Aristotle when he died?

Pythagoras

When Pythagorean Philolaus first published 3 books outlining the main provisions of Pythagoreism, Plato, on the advice of friends, immediately bought them for a lot of money.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras's work as a religious innovator of the 6th century BC


Question: How old was Aristotle when he died?

Pythagoras

was to create a secret society that not only set itself political goals (which is why the Pythagoreans were defeated in Crotone), but mainly the liberation of the soul through moral and physical purification with the help of secret teaching (the mystical doctrine of the cycle of migrations of the soul).


Question: How old was Aristotle when he died?

Pythagoras

According to Pythagoras, the eternal soul moves from heaven to the mortal body of man or animal and undergoes a series of migrations until it earns the right to return to heaven.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras acusmats (sayings) contain ritual instructions: about the cycle of human lives, behavior, sacrifices, burials, nutrition.


Question: How old was Aristotle when he died?

Pythagoras

Acousmats are formulated concisely and easily understood by any person, they also contain postulates of universal morality.


Question: How old was Aristotle when he died?

Pythagoras

The more complex philosophy, within which mathematics and other sciences developed, was intended for the “initiated”, that is, selected people worthy of owning secret knowledge.


Question: How old was Aristotle when he died?

Pythagoras

The scientific component of Pythagoras's teachings developed in the 5th century BC.


Question: How old was Aristotle when he died?

Pythagoras

through the efforts of his followers (Archit of Tarent, Philolaus of Croton, Hippas of Metapont), but faded away in the 4th century BC.


Question: How old was Aristotle when he died?

Pythagoras

, while the mystical and religious component developed and reborn in the form of neopiphagoreism during the Roman Empire.


Question: How old was Aristotle when he died?

Pythagoras

The merit of the Pythagoreans was to put forward the idea of quantitative laws of the development of the world, which contributed to the development of mathematical, physical, astronomical and geographical knowledge.


Question: How old was Aristotle when he died?

Pythagoras

Things are based on numbers, Pythagoras taught, to know the world means to know the numbers that control it.


Question: How old was Aristotle when he died?

Pythagoras

By studying numbers, the Pythagoreans developed numerical relationships and found them in all areas of human activity.


Question: How old was Aristotle when he died?

Pythagoras

Numbers and proportions were studied in order to know and describe the human soul, and after knowing, to control the process of migration of souls with the ultimate goal of sending the soul to a certain higher divine state.


Question: How old was Aristotle when he died?

Pythagoras

As I. D. Rozhansky: “Despite the remnants of magical thinking, the main idea of Pythagoras that all things are based on numbers or ratios of numbers turned out to be very fruitful” [7].


Question: How old was Aristotle when he died?

Pythagoras

As Stobey noted: “Apparently, Pythagoras read the science of numbers the most (sciences), he moved it forward, taking it beyond trade use and expressing, modeling all things with numbers” (1,” Proemy”, 6, p. 20) [7].


Question: How old was Aristotle when he died?

Pythagoras

Despite the popular opinion that Pythagoras allegedly was a vegetarian, Diogenes Laertes writes that Pythagoras occasionally ate fish, refrained only from arable bulls and sheep, and the rest allowed animals to eat.


Question: How old was Aristotle when he died?

Pythagoras

His contemporary Heraclitus acted as a critic of Pythagoras: “Pythagoras, Mnesarch's son, was engaged in collecting information more than all people in the world and, pulling these works for himself, passed them off as his own wisdom, polyknowledge and fraud” [8].


Question: How old was Aristotle when he died?

Pythagoras

According to Diogenes Laerte, in the continuation of the famous saying of Heraclitus “Polyknowledge does not teach the mind”, Pythagoras is mentioned among others: “otherwise it would have taught Hesiod and Pythagoras, as well as Xenophanes and Hecateus ” [8].


Question: How old was Aristotle when he died?

Pythagoras

Scientific achievements


Question: How old was Aristotle when he died?

Pythagoras

In the modern world, Pythagoras is considered a great mathematician and cosmologist of antiquity, but early evidence is up to the 3rd century BC.


Question: How old was Aristotle when he died?

Pythagoras

do not mention such merits.


Question: How old was Aristotle when he died?

Pythagoras

As Yamblich writes about the Pythagoreans: “They also had a wonderful custom to attribute everything to Pythagoras and not at all appropriate the glory of discoverers, except perhaps in a few cases.”


Question: How old was Aristotle when he died?

Pythagoras

Ancient authors of our era [9] give Pythagoras the authorship of the well-known theorem: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.


Question: How old was Aristotle when he died?

Pythagoras

This opinion is based on the information of the Apollodor Calculator (the person is not identified) and on poetic lines (the source of the poems is unknown):


Question: How old was Aristotle when he died?

Pythagoras

“On the day Pythagoras opened his famous drawing,


Question: How old was Aristotle when he died?

Pythagoras

He made a glorious sacrifice for him with bulls.”


Question: How old was Aristotle when he died?

Pythagoras

Modern historians suggest that Pythagoras did not prove the theorem, but could convey to the Greeks this knowledge, known in Babylon 1000 years before Pythagoras (according to Babylonian clay tablets with records mathematical equations).


Question: How old was Aristotle when he died?

Pythagoras

Although there is doubt about the authorship of Pythagoras, there are no weighty arguments to challenge this.


Question: How old was Aristotle when he died?

Pythagoras

Aristotle touches on the development of ideas about cosmology in his work “Metaphysics”, but Pythagoras's contribution is not voiced in it in any way.


Question: How old was Aristotle when he died?

Pythagoras

According to Aristotle, cosmological theories were studied by the Pythagoreans in the middle of the 5th century BC.


Question: How old was Aristotle when he died?

Pythagoras

, but apparently not Pythagoras himself.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras is credited with the discovery that the Earth is a ball, but the most authoritative author in this matter, Theophrastus, gives the same discovery to Parmenides.


Question: How old was Aristotle when he died?

Pythagoras

And Diogenes Laertes reports that the judgment about the spherical shape of the Earth was expressed by Anaximander of Miletus, with whom Pythagoras studied in his youth.


Question: How old was Aristotle when he died?

Pythagoras

At the same time, the scientific merits of the Pythagorean school in mathematics and cosmology are undeniable.


Question: How old was Aristotle when he died?

Pythagoras

Aristotle's point of view, reflected in his unpreserved treatise “On the Pythagoreans”, was conveyed by Yamblich [10].


Question: How old was Aristotle when he died?

Pythagoras

According to Aristotle, the true Pythagoreans were acousmatics, followers of the religious and mystical doctrine of the migration of souls.


Question: How old was Aristotle when he died?

Pythagoras

Acousmatics considered mathematics as a teaching coming not so much from Pythagoras as from the Pythagorean Hippas.


Question: How old was Aristotle when he died?

Pythagoras

In turn, Pythagorean mathematicians, in their own opinion, were inspired by the guiding teachings of Pythagoras for an in-depth study of their science.


Question: How old was Aristotle when he died?

Pythagoras

Works by Pythagoras


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras did not write treatises.


Question: How old was Aristotle when he died?

Pythagoras

It was impossible to compile a treatise from oral instructions for the common people, and secret occult teaching for the chosen ones could not be entrusted to the book.


Question: How old was Aristotle when he died?

Pythagoras

Yamblich comments on the absence of Pythagoras's works:


Question: How old was Aristotle when he died?

Pythagoras

“Their persistence in not disclosing the doctrine is also remarkable: so many years before Philolaus's generation, no one seems to have encountered a single Pythagorean work. Philolaus was the first Pythagoreans to publish three sensational books, which Dion of Syracuse is said to have bought in a hundred minutes at the direction of Plato, when Philolaus fell into extreme need.”


Question: How old was Aristotle when he died?

Pythagoras

Diogenes lists the titles of these books attributed to Pythagoras: “On Education”, “On the State” and “On Nature”.


Question: How old was Aristotle when he died?

Pythagoras

However, none of the authors in the first 200 years after the death of Pythagoras, including Plato, Aristotle and their successors at the Academy and Lyceum, quotes from the works of Pythagoras or at least points to the existence of such labors.


Question: How old was Aristotle when he died?

Pythagoras

Since the beginning of the new era, ancient writers do not know the works of Pythagoras, as reported by Plutarch, Josephus Flavius and Galen [11].


Question: How old was Aristotle when he died?

Pythagoras

In the 3rd century BC


Question: How old was Aristotle when he died?

Pythagoras

there was a compilation of Pythagorean statements, known as the “Sacred Word”, from which the so-called “Golden Verses” later arose (sometimes referred to as the 4th century BC without good reason).


Question: How old was Aristotle when he died?

Pythagoras

For the first time, quotes from these verses were quoted by Chrysippus in the 3rd century BC.


Question: How old was Aristotle when he died?

Pythagoras

, although perhaps the compilation was not yet complete at that time.


Question: How old was Aristotle when he died?

Pythagoras

The final excerpt from The Golden Verses translated by I. Peter says:


Question: How old was Aristotle when he died?

Pythagoras

Be firm: the divine race is present in mortals


Question: How old was Aristotle when he died?

Pythagoras

To them, proclaiming, the sacred nature reveals everything.


Question: How old was Aristotle when he died?

Pythagoras

If it's not alien to you, you'll fulfill your orders


Question: How old was Aristotle when he died?

Pythagoras

You will heal your soul and save you from many disasters.


Question: How old was Aristotle when he died?

Pythagoras

The dishes, I said, leave the ones I indicated in the cleansing


Question: How old was Aristotle when he died?

Pythagoras

And be guided by true knowledge — the best charioteer.


Question: How old was Aristotle when he died?

Pythagoras

If you leave your body and go free air


Question: How old was Aristotle when he died?

Pythagoras

You will become imperishable, and eternal, and a god who does not know death.


Question: How old was Aristotle when he died?

Pythagoras

See also


Question: How old was Aristotle when he died?

Pythagoras

A crater on the moon is named after Pythagoras.


Question: How old was Aristotle when he died?

Pythagoras

Pythagorean theorem


Question: How old was Aristotle when he died?

Pythagoras

Pythagorov system


Question: How old was Aristotle when he died?

Pythagoras

Numerology


Question: How old was Aristotle when he died?

Pythagoras

Pythagoreism


Question: How old was Aristotle when he died?

Pythagoras

Notes


Question: How old was Aristotle when he died?

Pythagoras

Literature


Question: How old was Aristotle when he died?

Pythagoras

Zhmud L. ME.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras and early Pythagoreans.


Question: How old was Aristotle when he died?

Pythagoras

— MOSCOW, 2012.


Question: How old was Aristotle when he died?

Pythagoras

— 445 p. ISBN 978-5-91244-068-7


Question: How old was Aristotle when he died?

Pythagoras

Zhmud L. ME.


Question: How old was Aristotle when he died?

Pythagoras

Pythagoras and his school.


Question: How old was Aristotle when he died?

Pythagoras

— M.: Nauka, 1990.


Question: How old was Aristotle when he died?

Pythagoras

— ISBN 5-02-027292-2


Question: How old was Aristotle when he died?

Pythagoras

Zhmud L. ME.


Question: How old was Aristotle when he died?

Pythagoras

Science, philosophy and religion in early Pythagoreism.


Question: How old was Aristotle when he died?

Pythagoras

— SPb., 1994.


Question: How old was Aristotle when he died?

Pythagoras

— 376 p. — ISBN 5-86050-066-1


Question: How old was Aristotle when he died?

Pythagoras

CS1 maint: Multiple names: authors list (link)


Question: How old was Aristotle when he died?

Pythagoras

, Ed.


Question: How old was Aristotle when he died?

Pythagoras

A. IN. Lebedev said.


Question: How old was Aristotle when he died?

Pythagoras

Moscow, Nauka Publ., 1989.


Question: How old was Aristotle when he died?

Pythagoras

— pp. 138—149.


Question: How old was Aristotle when he died?

Pythagoras

Leontyev A. IN. The tradition of Pythagoras in Aristoksen and Diecearch//Man.


Question: How old was Aristotle when he died?

Pythagoras

Nature.


Question: How old was Aristotle when he died?

Pythagoras

Society.


Question: How old was Aristotle when he died?

Pythagoras

Current issues.


Question: How old was Aristotle when he died?

Pythagoras

Proceedings of the 11th International Conference of Young Scientists December 27-30, 2000 — SPb.: St. Petersburg University Press.


Question: How old was Aristotle when he died?

Pythagoras


Question: How old was Aristotle when he died?

Pythagoras

— P. 298—301.


Question: How old was Aristotle when he died?

Pythagoras

Leontyev A. IN. To the Question of the Image of Pythagoras in the Ancient Tradition of the 6th—5th Centuries BC


Question: How old was Aristotle when he died?

Pythagoras

//Mnemon.


Question: How old was Aristotle when he died?

Pythagoras

Research and publications on the history of the ancient world.


Question: How old was Aristotle when he died?

Pythagoras

Under the editorship of Professor E.


Question: How old was Aristotle when he died?

Pythagoras

D. Frolova.


Question: How old was Aristotle when he died?

Pythagoras

— Issue 3.


Question: How old was Aristotle when he died?

Pythagoras

— Saint Petersburg, 2004.


Question: How old was Aristotle when he died?

Pythagoras

Panchenko D. IN. Pythagorean paradox//Indo-European linguistics and classical philology — XII: Materials of readings dedicated to the memory of prof. AND. M. Tronsky.


Question: How old was Aristotle when he died?

Pythagoras

June 23-25, 2008 — Page 355—363.


Question: How old was Aristotle when he died?

Pythagoras

CS1 maint: Date and year (link)


Question: How old was Aristotle when he died?

Pythagoras

Sources and links


Question: How old was Aristotle when he died?

Pythagoras

Yamblich,


Question: How old was Aristotle when he died?

Pythagoras

Diogenes Laerte,


Question: How old was Aristotle when he died?

Pythagoras

Porphyry,


Question: How old was Aristotle when he died?

Pythagoras

in the Alexander Kobrinsky Library


Question: How old was Aristotle when he died?

Pythagoras

Besonide,


Question: How old was Aristotle when he died?

Pythagoras

Category: Ancient Greek astronomers


Question: How old was Aristotle when he died?

Pythagoras

Category:Astronomers alphabetically


Question: How old was Aristotle when he died?

Pythagoras

Category: Ancient Greek mathematicians


Question: How old was Aristotle when he died?

Pythagoras

Category:Ancient Greek philosophers


Question: How old was Aristotle when he died?

Pythagoras

Category:6th-century BC philosophers


Question: How old was Aristotle when he died?

Pythagoras

Category:6th-century BC mathematicians


Question: How old was Aristotle when he died?

Pythagoras

Category:6th-century BC astronomers


Question: How old was Aristotle when he died?

Pythagoras

Category:Music theorists


Question: How old was Aristotle when he died?

Pythagoras


Question: How old was Aristotle when he died?

Pythagoras

Category:Presocratics


Question: How old was Aristotle when he died?

Pythagoras

Category:Natural philosophers


Question: How old was Aristotle when he died?

Pythagoras

Category:Teachers alphabetically


Question: How old was Aristotle when he died?

Pythagoras

Category:Ascetics


Question: How old was Aristotle when he died?

Pythagoras

Category:Esotericists


Question: Who was the creator of the topology?

Henri Poincare

Jules Henri Poincaré (French: Jules Henri Poincaré; April 29, 1854 — July 17, 1912) was a French,,,, and.


Question: Who was the creator of the topology?

Henri Poincare

Head of the Paris Academy of Sciences (1906), member of the French Academy (1908) [1] and more than 30 academies around the world, including a foreign corresponding member of the St. Petersburg Academy of Sciences (1895).


Question: Who was the creator of the topology?

Henri Poincare

Historians rank Henri Poincaré among the greatest mathematicians of all time [2].


Question: Who was the creator of the topology?

Henri Poincare

He is considered, along with Hilbert, the last universal mathematician, scientist able to cover all the mathematical results of his time [3].


Question: Who was the creator of the topology?

Henri Poincare

He wrote more than 500 articles and books [4].


Question: Who was the creator of the topology?

Henri Poincare

“It is no exaggeration to say that it is not


Question: Who was the creator of the topology?

Henri Poincare

there was an area of modern mathematics, “pure” or “applied”, which he would not enrich with remarkable methods and results” [5].


Question: Who was the creator of the topology?

Henri Poincare

His biggest achievements include:


Question: Who was the creator of the topology?

Henri Poincare

Creating a topology.


Question: Who was the creator of the topology?

Henri Poincare

Qualitative theory of differential equations.


Question: Who was the creator of the topology?

Henri Poincare

The theory of automorphic functions.


Question: Who was the creator of the topology?

Henri Poincare

Development of new, extremely effective methods of celestial mechanics.


Question: Who was the creator of the topology?

Henri Poincare

Creating the mathematical foundations of the theory of relativity, as well as generalizing the principle of relativity for all physical phenomena.


Question: Who was the creator of the topology?

Henri Poincare

A visual model of Lobachevsky's geometry.


Question: Who was the creator of the topology?

Henri Poincare

Biography


Question: Who was the creator of the topology?

Henri Poincare

Early years and training (1854—1879)


Question: Who was the creator of the topology?

Henri Poincare

Henri Poincare was born on April 29, 1854 in Nancy, Lorraine, France.


Question: Who was the creator of the topology?

Henri Poincare

His father, Leon Poincare (1828—1892), was Professor of Medicine at the School of Medicine (from 1878 at the University of Nancy).


Question: Who was the creator of the topology?

Henri Poincare

Henri's mother, Eugénie Launois, devoted all her free time to raising her children, Henri's son and youngest daughter Alina.


Question: Who was the creator of the topology?

Henri Poincare

There are other celebrities among Poincaré's relatives: cousin Raymond became President of France (from 1913 to 1920), another cousin, a famous physicist, was the Inspector General of Public Education France, and from 1917 to 1920 he was Rector of the University of Paris [6].


Question: Who was the creator of the topology?

Henri Poincare

Since childhood, Henri has gained a reputation as an absent-minded person, which he has preserved for life [2].


Question: Who was the creator of the topology?

Henri Poincare

As a child, he suffered diphtheria, which was complicated by temporary paralysis of his legs and soft palate.


Question: Who was the creator of the topology?

Henri Poincare

The disease lasted for several months, during which he could neither walk nor talk.


Question: Who was the creator of the topology?

Henri Poincare

During this time, he developed a lot of auditory perception and, in particular, developed an unusual ability — color perception of sounds, which he had left for the rest of his life [2].


Question: Who was the creator of the topology?

Henri Poincare

Good home preparation allowed Henri, at the age of eight and a half, to enter the second year of study at the lyceum.


Question: Who was the creator of the topology?

Henri Poincare

There he was noted as a diligent and inquisitive student with extensive erudition.


Question: Who was the creator of the topology?

Henri Poincare

At this stage, his interest in mathematics was moderate — after a while he moved to the Department of Literature, where he mastered Latin, German and English perfectly; later this helped Poincaré communicate actively with colleagues.


Question: Who was the creator of the topology?

Henri Poincare

On August 5, 1871, Poincaré received a bachelor's degree in literature with a grade of “good”.


Question: Who was the creator of the topology?

Henri Poincare

A few days later, Henri expressed a desire to participate in the exams for the degree of bachelor of science (natural), which he managed to pass, but only with a grade of “satisfactory”, since in written In the math exam, he answered the wrong question out of absent-mindedness [2].


Question: Who was the creator of the topology?

Henri Poincare

In subsequent years, Poincaré's mathematical talents were more and more pronounced.


Question: Who was the creator of the topology?

Henri Poincare

In October 1873, he became a student at the prestigious Polytechnic School in Paris, where he won first place in the entrance exams.


Question: Who was the creator of the topology?

Henri Poincare

Charles Hermite was his math mentor.


Question: Who was the creator of the topology?

Henri Poincare

The following year, Poincare published his first scientific paper on differential geometry in the Annals of Mathematics.


Question: Who was the creator of the topology?

Henri Poincare

After two years of study (1875), Poincaré was admitted to the Mining School, the most authoritative special higher education institution at that time.


Question: Who was the creator of the topology?

Henri Poincare

There, a few years later (1879), under the guidance of Hermite, he defended his doctoral dissertation, about which Gaston Darboux, who was a member of the commission, said: “At first glance, it became clear to me that the work goes beyond the ordinary and more than deserves to be accepted. It contained quite enough results to provide a lot of good dissertations with material.”


Question: Who was the creator of the topology?

Henri Poincare

The first scientific achievements (1879—1882)


Question: Who was the creator of the topology?

Henri Poincare

After receiving his degree, Poincaré began teaching at the University of Caen in Normandy (December 1879).


Question: Who was the creator of the topology?

Henri Poincare

At the same time, he published his first serious articles — they are devoted to the class of automorphic functions he introduced.


Question: Who was the creator of the topology?

Henri Poincare

There, in Caen, he met his future wife Louise Poulain d'Andecy.


Question: Who was the creator of the topology?

Henri Poincare

On April 20, 1881, their wedding took place.


Question: Who was the creator of the topology?

Henri Poincare

They had a son and three daughters [7].


Question: Who was the creator of the topology?

Henri Poincare

The originality, breadth and high scientific level of Poincaré's works immediately put him among the greatest mathematicians in Europe and attracted the attention of other prominent mathematicians.


Question: Who was the creator of the topology?

Henri Poincare

In 1881, Poincaré was invited to take the position of lecturer at the Faculty of Sciences at the University of Paris and accepted the invitation.


Question: Who was the creator of the topology?

Henri Poincare

At the same time, from 1883 to 1897, he taught mathematical analysis at the Higher Polytechnic School.


Question: Who was the creator of the topology?

Henri Poincare

In 1881-1882, Poincaré created a new branch of mathematics — the qualitative theory of differential equations.


Question: Who was the creator of the topology?

Henri Poincare

He showed how it is possible to obtain practically important information about the behavior of a family of solutions without solving equations (as this is not always possible).


Question: Who was the creator of the topology?

Henri Poincare

He successfully applied this approach to solving problems of celestial mechanics and mathematical physics.


Question: Who was the creator of the topology?

Henri Poincare

Leader of French mathematicians (1882—1899)


Question: Who was the creator of the topology?

Henri Poincare

A decade after completing the study of automorphic functions (1885—1895), Poincaré devoted himself to solving several of the most complex problems of astronomy and mathematical physics.


Question: Who was the creator of the topology?

Henri Poincare

He studied the stability of planetary figures formed in the liquid (molten) phase, and discovered, in addition to ellipsoidal ones, several other possible equilibrium figures.


Question: Who was the creator of the topology?

Henri Poincare

In 1885, King Oscar II of Sweden organized a math competition and offered participants a choice of four topics.


Question: Who was the creator of the topology?

Henri Poincare

The first was the most difficult: to calculate the motion of the gravitating bodies of the solar system


Question: Who was the creator of the topology?

Henri Poincare

Poincare showed that this problem (the so-called three-body problem) does not have a complete mathematical solution.


Question: Who was the creator of the topology?

Henri Poincare

Nevertheless, Poincare soon proposed effective methods for its approximate solution.


Question: Who was the creator of the topology?

Henri Poincare

In 1889, Poincare won an award at the Swedish Competition (together with his friend and future biographer Paul Appel, who studied another topic).


Question: Who was the creator of the topology?

Henri Poincare

One of the two judges, Mittag-Leffler, wrote about Poincaré's work: “The awarded memoir will be among the most significant mathematical discoveries of the century.”


Question: Who was the creator of the topology?

Henri Poincare

The second judge, Weierstrass, said that Poincare's work “will begin a new era in the history of celestial mechanics” [2].


Question: Who was the creator of the topology?

Henri Poincare

For this success, the French government awarded Poincaré the Order of the Legion of Honor.


Question: Who was the creator of the topology?

Henri Poincare

In the autumn of 1886, Poincaré, 32, headed the Department of Mathematical Physics and Probability Theory at the University of Paris.


Question: Who was the creator of the topology?

Henri Poincare

Poincaré's recognition as a leading mathematician of France was his election as president of the French Mathematical Society (1886) and a member of the Paris Academy of Sciences (1887).


Question: Who was the creator of the topology?

Henri Poincare

In 1887, Poincaré summarized the Cauchy theorem for the case of several complex variables and laid the foundation for the theory of deductions in a multidimensional complex space.


Question: Who was the creator of the topology?

Henri Poincare

In 1889, Poincaré's fundamental Course in Mathematical Physics was published in 10 volumes, and in 1892-1893, two volumes of the monograph “New Methods of Celestial Mechanics” were published (the third volume was published in 1899).


Question: Who was the creator of the topology?

Henri Poincare

Since 1893, Poincaré was a member of the prestigious Longitude Bureau (elected its president in 1899).


Question: Who was the creator of the topology?

Henri Poincare

Since 1896, he moved to the University Department of Celestial Mechanics, which he held until the end of his life.


Question: Who was the creator of the topology?

Henri Poincare

During the same period, continuing his work on astronomy, he simultaneously implemented a long-thought-out idea of creating high-quality geometry, or topology: since 1894, he began publishing articles on building a new, exceptionally promising science.


Question: Who was the creator of the topology?

Henri Poincare

Recent years


Question: Who was the creator of the topology?

Henri Poincare

In August 1900, Poincaré led the logic section of the First World Congress of Philosophy, held in Paris.


Question: Who was the creator of the topology?

Henri Poincare

There he made a keynote speech “On the Principles of Mechanics”, where he outlined his conventionalist philosophy: the principles of science are temporary conditional agreements adapted to experience, but do not have direct analogues in reality.


Question: Who was the creator of the topology?

Henri Poincare

He later substantiated this platform in detail in the books “Science and Hypothesis” (1902), “The Value of Science” (1905) and “Science and Method” (1908).


Question: Who was the creator of the topology?

Henri Poincare

In them, he also described his vision of the essence of mathematical creativity, in which intuition plays a major role, and logic is assigned the role of a strict justification for intuitive insights.


Question: Who was the creator of the topology?

Henri Poincare

The clear style and depth of thought provided these books with significant popularity, they were immediately translated into many languages.


Question: Who was the creator of the topology?

Henri Poincare

At the same time, the Second International Congress of Mathematicians was held in Paris, where Poincaré was elected chairman (all congresses were timed to coincide with the World Exhibition of 1900).


Question: Who was the creator of the topology?

Henri Poincare

In 1903, Poincaré was included in a group of three experts who considered evidence in the Dreyfus case.


Question: Who was the creator of the topology?

Henri Poincare

On the basis of a unanimously adopted expert opinion, the Court of Cassation found Dreyfus not guilty.


Question: Who was the creator of the topology?

Henri Poincare

The main area of interest of Poincare in the 20th century is physics (especially electromagnetism) and the philosophy of science.


Question: Who was the creator of the topology?

Henri Poincare

Poincare shows a deep understanding of electromagnetic theory, his insightful remarks are highly appreciated and taken into account by Lorenz and other leading physicists.


Question: Who was the creator of the topology?

Henri Poincare

From 1890, Poincare published a series of articles on Maxwell's theory, and in 1902 began lecturing on electromagnetism and radio communications.


Question: Who was the creator of the topology?

Henri Poincare

In his articles of 1904-1905, Poincaré was far ahead of Lorenz in understanding the situation, actually creating the mathematical foundations of the theory of relativity (the physical foundation of this theory was developed by Einstein in 1905 year).


Question: Who was the creator of the topology?

Henri Poincare

In 1906, Poincaré was elected President of the Paris Academy of Sciences.


Question: Who was the creator of the topology?

Henri Poincare

In 1908, he fell seriously ill and was unable to read his report “The Future of Mathematics” himself at the Fourth Mathematical Congress.


Question: Who was the creator of the topology?

Henri Poincare

The first operation was successful, but after 4 years, Poincaré's condition deteriorated again.


Question: Who was the creator of the topology?

Henri Poincare

He died in Paris after embolism surgery on July 17, 1912 at the age of 58.


Question: Who was the creator of the topology?

Henri Poincare

He was buried in the family crypt at Montparnasse Cemetery.


Question: Who was the creator of the topology?

Henri Poincare

Poincare probably foresaw his unexpected death, as in his last article he described an unsolved problem (“the last Poincare theorem”), which he had never done before.


Question: Who was the creator of the topology?

Henri Poincare

A few months later, this theorem was proved by George Birkhoff.


Question: Who was the creator of the topology?

Henri Poincare

Later, with the assistance of Birkhoff, the Poincare Institute for Theoretical Physics was established in France [2].


Question: Who was the creator of the topology?

Henri Poincare

Contribution to science


Question: Who was the creator of the topology?

Henri Poincare

mini|left|bust of A. Poincare at the Polytechnic


Question: Who was the creator of the topology?

Henri Poincare

Poincaré's mathematical activity was interdisciplinary in nature, so that in a little over thirty years of his intense creative activity, he left fundamental works almost all areas of mathematics [5].


Question: Who was the creator of the topology?

Henri Poincare

Poincaré's works, published by the Paris Academy of Sciences in 1916—1956, consist of 11 volumes.


Question: Who was the creator of the topology?

Henri Poincare

These are works on the topology he created, automorphic functions, the theory of differential equations, multidimensional complex analysis, integral equations, non-Euclidean geometry, probability theory, theory numbers, celestial mechanics, physics, philosophy of mathematics and philosophy of science [8].


Question: Who was the creator of the topology?

Henri Poincare

In all the various fields of his work, Poincaré has received important and profound results.


Question: Who was the creator of the topology?

Henri Poincare

Although his scientific heritage includes many major works on “pure mathematics” (general algebra, algebraic geometry, number theory, etc.), still significantly predominate works, the results of which have direct application.


Question: Who was the creator of the topology?

Henri Poincare

This is especially evident in his works over the past 15—20 years.


Question: Who was the creator of the topology?

Henri Poincare

Nevertheless, Poincare's discoveries, as a rule, were of a general nature and were later successfully applied in other fields of science.


Question: Who was the creator of the topology?

Henri Poincare

Poincare's creative method was based on creating an intuitive model of the problem: he always solved the problems completely in his head first, and then wrote down the solution.


Question: Who was the creator of the topology?

Henri Poincare

Poincaré had a phenomenal memory and could quote books read and conversations word for word (Henri Poincaré's memory, intuition and imagination even became the subject of a real psychological studies).


Question: Who was the creator of the topology?

Henri Poincare

In addition, he has never worked on one task for a long time, believing that the subconscious has already received the task and continues to work even when he is thinking about other things [6].


Question: Who was the creator of the topology?

Henri Poincare

Poincaré described his creative method in detail in the report “Mathematical Creativity” (Psychological Society of Paris, 1908).


Question: Who was the creator of the topology?

Henri Poincare

Paul Painleve assessed the importance of Poincare for science as follows [6]:


Question: Who was the creator of the topology?

Henri Poincare

He has grasped it, deepened it all.


Question: Who was the creator of the topology?

Henri Poincare

With an extraordinarily inventive mind, he knew no limits to his inspiration, tirelessly paving new paths, and in the abstract world of mathematics he repeatedly discovered unexplored areas.


Question: Who was the creator of the topology?

Henri Poincare

Wherever the human mind penetrated, no matter how difficult and thorny its path was — be it problems of wireless telegraphy, X-rays, or the origin of the Earth — Henri Poincaré walked next to us... Together with the great French mathematician, the only person left us whose mind could embrace everything that was created by the mind of other people, penetrate the very essence of everything that has befallen today human thought, and to see something new in it.


Question: Who was the creator of the topology?

Henri Poincare

Automorphic functions


Question: Who was the creator of the topology?

Henri Poincare

Throughout the 19th century, almost all prominent mathematicians in Europe participated in the development of the theory of elliptic functions, which turned out to be extremely useful in solving differential equations.


Question: Who was the creator of the topology?

Henri Poincare

However, these functions did not fully live up to expectations, and many mathematicians began to wonder whether it was possible to expand the class of elliptical functions so that the new functions were applicable and for equations where elliptic functions are useless.


Question: Who was the creator of the topology?

Henri Poincare

Poincare first found this idea in an article by Lazarus Fuchs, the most prominent specialist in linear differential equations at that time (1880).


Question: Who was the creator of the topology?

Henri Poincare

For several years, Poincare developed Fuchs's idea far, creating a theory of a new class of functions, which he, with Poincare's usual indifference to priority issues, proposed to name Fuchs functions ( French: les fonctions fuchsiennes) — although he had every reason to give this class its name.


Question: Who was the creator of the topology?

Henri Poincare

It ended with Felix Klein proposing the name “automorphic functions”, which was entrenched in science [9].


Question: Who was the creator of the topology?

Henri Poincare

Poincare brought the decomposition of these functions into series, proved the addition theorem and the theorem on the possibility of uniforming algebraic curves (that is, representing them through automorphic functions; this is the 22nd problem Hilbert, solved by Poincare in 1907).


Question: Who was the creator of the topology?

Henri Poincare

These discoveries “can rightly be considered the pinnacle of the entire development of the theory of analytical functions of a complex variable in the XIX century” [10].


Question: Who was the creator of the topology?

Henri Poincare

When developing the theory of automorphic functions, Poincare discovered their connection with Lobachevsky's geometry, which allowed him to present many questions of the theory of these functions in geometric language [11].


Question: Who was the creator of the topology?

Henri Poincare

He published a visual model of Lobachevsky's geometry, with the help of which he illustrated the material on the theory of functions.


Question: Who was the creator of the topology?

Henri Poincare

After Poincare's work, elliptical functions turned from a priority direction of science into a limited special case of a more powerful general theory.


Question: Who was the creator of the topology?

Henri Poincare

Automorphic functions discovered by Poincare make it possible to solve any linear differential equation with algebraic coefficients and are widely used in many areas of exact sciences [12].


Question: Who was the creator of the topology?

Henri Poincare

Differential equations and mathematical physics


Question: Who was the creator of the topology?

Henri Poincare

After defending his doctoral dissertation on the study of special points of a system of differential equations, Poincaré wrote a number of memoirs under the general title “On curves determined by differential equations equations” (1881-1882 for equations of the 1st order, supplemented in 1885—1886 for equations of the 2nd order).


Question: Who was the creator of the topology?

Henri Poincare

In these articles, he built a new branch of mathematics, which was called the “qualitative theory of differential equations”.


Question: Who was the creator of the topology?

Henri Poincare

Poincare showed that even if the differential equation is not solved through known functions, nevertheless, extensive information about properties and features can be obtained from the very type of equation the behavior of its decision family.


Question: Who was the creator of the topology?

Henri Poincare

In particular, Poincare studied the nature of the course of integral curves on the plane, gave a classification of special points (saddle, focus, center, node), introduced the concepts of the limit cycle and the cycle index, and proved that the number of limit cycles is always of course, except for a few special cases [13].


Question: Who was the creator of the topology?

Henri Poincare

Poincare also developed a general theory of integral invariants and solutions of equations in variations.


Question: Who was the creator of the topology?

Henri Poincare

For equations in finite differences, he created a new direction — asymptotic analysis of solutions [14].


Question: Who was the creator of the topology?

Henri Poincare

He applied all these achievements to study practical problems of mathematical physics and celestial mechanics, and the methods used became the basis of his topological work.


Question: Who was the creator of the topology?

Henri Poincare

Special points of integral curves


Question: Who was the creator of the topology?

Henri Poincare

saddle


Question: Who was the creator of the topology?

Henri Poincare

Focus


Question: Who was the creator of the topology?

Henri Poincare

Center


Question: Who was the creator of the topology?

Henri Poincare

Node


Question: Who was the creator of the topology?

Henri Poincare

Poincare also worked extensively on partial differential equations, mainly in the study of problems of mathematical physics.


Question: Who was the creator of the topology?

Henri Poincare

He significantly supplemented the methods of mathematical physics, in particular, made a significant contribution to the theory of potential [15], the theory of thermal conductivity, studied oscillations of three-dimensional bodies, and a number of problems in the theory electromagnetism.


Question: Who was the creator of the topology?

Henri Poincare

He also wrote works on the substantiation of the Dirichlet principle, for which he developed the so-called sweeping method (French: méthode de balayage) in his article “On Partial Differential Equations” [6].


Question: Who was the creator of the topology?

Henri Poincare

Algebra and number theory


Question: Who was the creator of the topology?

Henri Poincare

Already in his first works, Poincaré successfully applied the group-theoretic approach, which became the most important tool for him in many further studies, from topology to the theory of relativity [2].


Question: Who was the creator of the topology?

Henri Poincare

Poincare was the first to introduce group theory into physics; in particular, he was the first to study the Lorentz transformation group.


Question: Who was the creator of the topology?

Henri Poincare

He also made a great contribution to the theory of discrete groups and their representations.


Question: Who was the creator of the topology?

Henri Poincare

In the early period of his work, Poincaré studied cubic ternary and quaternary forms [16].


Question: Who was the creator of the topology?

Henri Poincare

Topology


Question: Who was the creator of the topology?

Henri Poincare

The subject of topology was clearly defined by Felix Klein in his Erlangen Program (1872): it is the geometry of invariants of arbitrary continuous transformations, a kind of qualitative geometry.


Question: Who was the creator of the topology?

Henri Poincare

The term “topology” itself (instead of the previously used Analysis situs) was previously proposed by Johann Benedict Listing.


Question: Who was the creator of the topology?

Henri Poincare

Some important concepts were introduced by Enrico Betty and Bernhard Riemann.


Question: Who was the creator of the topology?

Henri Poincare

However, the foundation of this science, and developed in sufficient detail for a space of any number of dimensions, was created by Poincaré.


Question: Who was the creator of the topology?

Henri Poincare

His first article on this topic appeared in 1894 [7], it aroused general interest, and Poincaré published five additions to this pioneer work from 1899 to 1902.


Question: Who was the creator of the topology?

Henri Poincare

The last of these supplements contained the famous Poincare hypothesis.


Question: Who was the creator of the topology?

Henri Poincare

Research in geometry led Poincare to an abstract topological definition of homotopy and homology.


Question: Who was the creator of the topology?

Henri Poincare

He also introduced the basic concepts and invariants of combinatorial topology for the first time, such as Betty numbers, a fundamental group, and proved a formula connecting the number of edges, vertices and faces of an n-dimensional polyhedron (Euler-Poincare formula), gave the first accurate formulation of the intuitive concept of dimension [17].


Question: Who was the creator of the topology?

Henri Poincare

Multivariate complex analysis


Question: Who was the creator of the topology?

Henri Poincare

Poincare generalized the Cauchy theorem for the case of several complex variables, founded the theory of deductions for a multidimensional case, and laid the foundation for studies of bigolomorphic mappings of regions of a complex spaces.


Question: Who was the creator of the topology?

Henri Poincare

Astronomy and celestial mechanics


Question: Who was the creator of the topology?

Henri Poincare

Poincare published two classical monographs: “New Methods of Celestial Mechanics” (1892—1899) and “Lectures


Question: Who was the creator of the topology?

Henri Poincare

on celestial mechanics” (1905—1910).


Question: Who was the creator of the topology?

Henri Poincare

In them, he successfully applied the results of his research to the problem of the motion of three bodies, studying in detail the behavior of the solution (periodicity, stability, asymptoticism, etc.).


Question: Who was the creator of the topology?

Henri Poincare

He introduced methods of a small parameter (Poincare's theorem on the expansion of integrals by a small parameter), fixed points, integral invariants, equations in variations, studied the convergence of asymptotic decompositions [18].


Question: Who was the creator of the topology?

Henri Poincare

Summarizing Bruns's theorem (1887), Poincare proved that the three-body problem is fundamentally not integrable [19].


Question: Who was the creator of the topology?

Henri Poincare

In other words, the general solution of the three-body problem cannot be expressed in terms of algebraic or unambiguous transcendental functions of coordinates and velocities of bodies [20].


Question: Who was the creator of the topology?

Henri Poincare

His work in this area is considered the greatest achievements in celestial mechanics since Newton [7].


Question: Who was the creator of the topology?

Henri Poincare

These works by Poincare contain ideas that later became the basis for the mathematical “theory of chaos” (see, in particular, Poincare's return theorem) and the general theory of dynamical systems.


Question: Who was the creator of the topology?

Henri Poincare

Poincare wrote important works for astronomy on the equilibrium figures of a gravitating rotating liquid.


Question: Who was the creator of the topology?

Henri Poincare

He introduced an important concept of bifurcation points, proved the existence of equilibrium figures different from the ellipsoid, including ring-shaped and pear-shaped figures, and studied their stability [21].


Question: Who was the creator of the topology?

Henri Poincare

For this discovery, Poincare received a gold medal from the Royal Astronomical Society of London (1900).


Question: Who was the creator of the topology?

Henri Poincare

Physics and other works


Question: Who was the creator of the topology?

Henri Poincare

As a member of the Longitude Bureau, Poincare participated in the measurement work of this institution and published several substantive works on geodesy, gravimetry and tidal theory [2].


Question: Who was the creator of the topology?

Henri Poincare

From the late 1880s until the end of his life, Poincaré devoted a lot of effort to Maxwell's electromagnetic theory and its supplemented version by Lorenz.


Question: Who was the creator of the topology?

Henri Poincare

He actively corresponded with Heinrich Hertz and Lorenz, often giving them the right ideas [2].


Question: Who was the creator of the topology?

Henri Poincare

In particular, Poincare wrote Lorenz's transformations in their modern form, while Lorenz had previously proposed an approximate version of them.


Question: Who was the creator of the topology?

Henri Poincare

[22] However, it was Poincare who named these transformations after Lorenz.


Question: Who was the creator of the topology?

Henri Poincare

For Poincaré's contribution to the development of relativity, see below.


Question: Who was the creator of the topology?

Henri Poincare

It was at the initiative of Poincaré that young Antoine Henri Becquerel began to study the relationship between phosphorescence and X-rays (1896), and during these experiments, the radioactivity of uranium compounds was discovered [2].


Question: Who was the creator of the topology?

Henri Poincare

Poincare was the first to derive the law of attenuation of radio waves.


Question: Who was the creator of the topology?

Henri Poincare

In the last two years of his life, Poincare was keenly interested in quantum theory.


Question: Who was the creator of the topology?

Henri Poincare

In a detailed article “On the Theory of Quantum” (1911), he proved that it is impossible to obtain Planck's law of radiation without the quantum hypothesis, thereby burying all hopes to somehow preserve the classical theory [23].


Question: Who was the creator of the topology?

Henri Poincare

Scientific terms related to the name Poincare


Question: Who was the creator of the topology?

Henri Poincare

Poincare hypothesis


Question: Who was the creator of the topology?

Henri Poincare

Poincare Group


Question: Who was the creator of the topology?

Henri Poincare

Poincare duality


Question: Who was the creator of the topology?

Henri Poincare

Poincare Cartana integral


Question: Who was the creator of the topology?

Henri Poincare

Poincare lemma


Question: Who was the creator of the topology?

Henri Poincare

Poincare metric


Question: Who was the creator of the topology?

Henri Poincare

Poincare model of Lobachevsky space


Question: Who was the creator of the topology?

Henri Poincare

Poincare Dulac Normal Form


Question: Who was the creator of the topology?

Henri Poincare

Poincare display


Question: Who was the creator of the topology?

Henri Poincare

Poincare's last theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare sphere


Question: Who was the creator of the topology?

Henri Poincare

Cauchy—Poincare theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare—Bendixon theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare—Birkhoff—Witt theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare—Volterra theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare vector field theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare's return theorem


Question: Who was the creator of the topology?

Henri Poincare

Poincare theorem on classification of circle homeomorphisms


Question: Who was the creator of the topology?

Henri Poincare

Poincare theorem on the decomposition of integrals by a small parameter


Question: Who was the creator of the topology?

Henri Poincare

Poincare theorem on the growth rate of an entire function


Question: Who was the creator of the topology?

Henri Poincare

and many others.


Question: Who was the creator of the topology?

Henri Poincare

Poincare's role in the creation of relativity


Question: Who was the creator of the topology?

Henri Poincare

Poincare's works in the field of relativistic dynamics


Question: Who was the creator of the topology?

Henri Poincare

The name Poincare is directly related to the success of the theory of relativity.


Question: Who was the creator of the topology?

Henri Poincare

He was actively involved in the development of Lorentz's theory.


Question: Who was the creator of the topology?

Henri Poincare

This theory assumed that there is a fixed ether, and the speed of light relative to the ether does not depend on the speed of the source.


Question: Who was the creator of the topology?

Henri Poincare

When moving to a moving reference frame, Lorentz transformations are performed instead of Galilean transformations (Lorenz considered these transformations to be a real change in the size of bodies) [24].


Question: Who was the creator of the topology?

Henri Poincare

It was Poincare who gave the correct mathematical formulation of these transformations (Lorenz himself proposed only their first-order approximation) and showed that they form a group of transformations [22].


Question: Who was the creator of the topology?

Henri Poincare

Back in 1898, long before Einstein, Poincaré, in his work Measurement of Time, formulated a general (not only for mechanics) principle of relativity, and then even introduced four-dimensional space-time, the theory of which was later developed by German Minkowski [24].


Question: Who was the creator of the topology?

Henri Poincare

However, Poincare continued to use the concept of ether, although he was of the opinion that it would never be detected — see Poincare's report at the Physical Congress, 1900 [25].


Question: Who was the creator of the topology?

Henri Poincare

In the same report, Poincaré for the first time suggested that the simultaneous events were not absolute, but constituted a conditional agreement (“convention”).


Question: Who was the creator of the topology?

Henri Poincare

It has also been suggested that the speed of light is the limit.


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare

Under the influence of criticism of Poincare, Lorenz proposed a new version of his theory in 1904.


Question: Who was the creator of the topology?

Henri Poincare

In it, he suggested that at high speeds, Newton's mechanic needs to be corrected.


Question: Who was the creator of the topology?

Henri Poincare

In 1905, Poincare developed these ideas far in his article “On the Dynamics of the Electron”.


Question: Who was the creator of the topology?

Henri Poincare

A preliminary version of the article appeared on June 5, 1905 in Comptes Rendus, the expanded one was completed in July 1905, published in January 1906, for some reason in a little-known Italian mathematical magazine.


Question: Who was the creator of the topology?

Henri Poincare

This final article again and clearly formulates the universal principle of relativity for all physical phenomena (in particular, electromagnetic, mechanical and also gravitational), with transformations Lorentz, as the only possible coordinate transformations that maintain the same record of physical equations for all reference systems.


Question: Who was the creator of the topology?

Henri Poincare

Poincare found an expression for the four-dimensional interval as an invariant of Lorentz transformations:


Question: Who was the creator of the topology?

Henri Poincare

r


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare

i


Question: Who was the creator of the topology?

Henri Poincare

c


Question: Who was the creator of the topology?

Henri Poincare

t


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare

{\ displaystyle r^ {2} + {(ict)} ^ {2}}


Question: Who was the creator of the topology?

Henri Poincare

, a four-dimensional formulation of the principle of least action.


Question: Who was the creator of the topology?

Henri Poincare

In this article, he also proposed a first sketch of a relativistic theory of gravity; in his model, gravity spread on the air at the speed of light, and the theory itself was non-trivial enough to remove the restriction obtained by Laplace from below on the speed of propagation of the gravitational field.


Question: Who was the creator of the topology?

Henri Poincare

[24] The preliminary summary was published before Einstein's work was submitted to the journal, the last, large article also arrived before Einstein's, but by the time it was published Einstein's first article on relativity has already been published.


Question: Who was the creator of the topology?

Henri Poincare

Poincare and Einstein: similarities and differences


Question: Who was the creator of the topology?

Henri Poincare

Einstein, in his first works on the theory of relativity, used essentially the same mathematical model as Poincare: Lorentz transformations, relativistic formula for adding velocities, etc.


Question: Who was the creator of the topology?

Henri Poincare

However, unlike Poincare, Einstein made a strong conclusion: it is ridiculous to involve the concept of ether only to prove the impossibility of observing it.


Question: Who was the creator of the topology?

Henri Poincare

He completely abolished both the concept of ether, which Poincaré continued to use [26], and the concepts of absolute motion and absolute time based on the ether hypothesis.


Question: Who was the creator of the topology?

Henri Poincare

It was this theory, at the suggestion of Max Planck, that was called the theory of relativity (Poincaré preferred to talk about subjectivity or convention, see below).


Question: Who was the creator of the topology?

Henri Poincare

All new effects that Lorenz and Poincare considered dynamic properties of ether in Einstein's theory of relativity stem from the objective properties of space and time, that is, transferred by Einstein from dynamics to kinematics [27].


Question: Who was the creator of the topology?

Henri Poincare

This is the main difference between the approaches of Poincare and Einstein, disguised by the external similarity of their mathematical models: they understood the deep physical (and not just the mathematical) essence of these models.


Question: Who was the creator of the topology?

Henri Poincare

The transfer to kinematics allowed Einstein to create a holistic and universal theory of space and time, as well as solve previously unyielding problems within its framework — for example, the intricate question of different types mass, the dependence of mass on energy, the ratio of local and “absolute” time, etc.


Question: Who was the creator of the topology?

Henri Poincare

[27] Now this theory is called the “special theory of relativity” (SRT).


Question: Who was the creator of the topology?

Henri Poincare

Another significant difference between the positions of Poincare and Einstein was that the Lorentz reduction in length, the increase in inertia with speed, etc.


Question: Who was the creator of the topology?

Henri Poincare

Poincare understood relativistic conclusions as absolute effects [25], and Einstein understood relativistic conclusions as relative effects that did not have physical consequences in his own reference frame [28].


Question: Who was the creator of the topology?

Henri Poincare

What for Einstein was real physical time in a moving reference frame, Poincare called time “apparent”, “visible” (French: temps apparent) and clearly distinguished it from “true time” ( French: le temps vrai) [29].


Question: Who was the creator of the topology?

Henri Poincare

Probably, the lack of depth analysis of the physical essence of the SRT in Poincaré's works [30] was the reason that physicists did not pay the attention they deserved to these works; accordingly, the wide resonance of Einstein's first article was caused by a clear and in-depth analysis of the foundations of the physical picture under study.


Question: Who was the creator of the topology?

Henri Poincare

In the subsequent discussion of relativity, Poincaré was not mentioned (even in France); when Poincaré was nominated for the Nobel Prize in 1910, his list of merits did not say anything about relativity theory [31].


Question: Who was the creator of the topology?

Henri Poincare

The rationale for the new mechanic was also different.


Question: Who was the creator of the topology?

Henri Poincare

In Einstein's articles of 1905, the principle of relativity from the very beginning is not affirmed as a conclusion for dynamic considerations and experiments, but is based on physics as a kinematic axiom (also for all phenomena without exception).


Question: Who was the creator of the topology?

Henri Poincare

From this axiom and from the constancy of the speed of light, the Lorenz-Poincare mathematical apparatus is obtained automatically.


Question: Who was the creator of the topology?

Henri Poincare

The rejection of ether made it possible to emphasize that the “resting” and “moving” coordinate systems are completely equal, and when moving to a moving coordinate system, the same effects are found already in the resting one.


Question: Who was the creator of the topology?

Henri Poincare

Einstein, by his later admission, was not familiar with Poincare's latest publications at the time he began working on relativity (probably only with his 1900 work, at least not with the works of 1904), nor with the last article by Lorenz (1904).


Question: Who was the creator of the topology?

Henri Poincare

“Poincare's Silence”


Question: Who was the creator of the topology?

Henri Poincare

Shortly after Einstein's work on relativity appeared (1905), Poincaré stopped publishing on the topic.


Question: Who was the creator of the topology?

Henri Poincare

In none of the works of the last seven years of his life did he mention either the name of Einstein or the theory of relativity (except for one case when he referred to Einstein's theory of the photoelectric effect).


Question: Who was the creator of the topology?

Henri Poincare

Poincare continued to discuss the properties of the ether and mentioned absolute movement regarding the ether [32].


Question: Who was the creator of the topology?

Henri Poincare

The meeting and conversation between the two great scientists took place only once — in 1911 at the First Solvey Congress.


Question: Who was the creator of the topology?

Henri Poincare

In a letter to his Zurich friend Dr. Zangger dated November 16, 1911, Einstein wrote sadly [33]:


Question: Who was the creator of the topology?

Henri Poincare

Poincare [in relation to relativistic theory] rejected everything completely and showed, for all his subtlety of thought, a poor understanding of the situation.


Question: Who was the creator of the topology?

Henri Poincare

(Paise may have the insertion in parentheses).


Question: Who was the creator of the topology?

Henri Poincare

Despite his rejection of the theory of relativity, Poincaré personally treated Einstein with great respect.


Question: Who was the creator of the topology?

Henri Poincare

The characteristic of Einstein, which Poincaré gave at the end of 1911, has been preserved [2].


Question: Who was the creator of the topology?

Henri Poincare

The description was requested by the administration of the Zurich Higher Polytechnic School in connection with the invitation of Einstein to the post of professor at the school.


Question: Who was the creator of the topology?

Henri Poincare

Mr. Einstein is one of the most original minds I have known; despite his youth, he has already taken pride of place among the most prominent scientists of his time.


Question: Who was the creator of the topology?

Henri Poincare

Most of all, he admires the ease with which he adapts [] to new concepts and knows how to extract all the consequences from them.


Question: Who was the creator of the topology?

Henri Poincare

He does not hold on to classical principles and, when he faces a physical problem, is ready to consider any possibility.


Question: Who was the creator of the topology?

Henri Poincare

Thanks to this, his mind anticipates new phenomena that can be experimentally tested over time.


Question: Who was the creator of the topology?

Henri Poincare

I do not want to say that all these foresights will stand the test the day it becomes possible; on the contrary, since it searches in all directions, one should expect that most paths, but at the same time, it must be hoped that one of the directions he has indicated will be the right one, and that is enough.


Question: Who was the creator of the topology?

Henri Poincare

This is exactly what we should do.


Question: Who was the creator of the topology?

Henri Poincare

The role of mathematical physics is to ask questions correctly; only experience can solve them.


Question: Who was the creator of the topology?

Henri Poincare

The future will show more clearly what Mr. Einstein's significance is, and a university that can bind a young master to it will learn a lot of honors from this.


Question: Who was the creator of the topology?

Henri Poincare

In April 1909, Poincare, at Hilbert's invitation, came to Göttingen and gave a number of lectures there, including on the principle of relativity.


Question: Who was the creator of the topology?

Henri Poincare

Poincare never mentioned in these lectures not only Einstein, but also Göttingen Minkowski.


Question: Who was the creator of the topology?

Henri Poincare

Many hypotheses have been expressed about the reasons for the “silence of Poincare”.


Question: Who was the creator of the topology?

Henri Poincare

Some historians of science have suggested that Poincaré's resentment against the German school of physicists was to blame, which underestimated his merits in creating relativistic theory [25].


Question: Who was the creator of the topology?

Henri Poincare

Others consider this explanation implausible, since Poincaré has never been seen in resentment about priority disputes in his life, and Einstein's theory was preferred not only in Germany, but also in Great Britain and even in France itself (for example, Langevin) [28].


Question: Who was the creator of the topology?

Henri Poincare

Even Lorenz, whose theory Poincare sought to develop, preferred to talk about the “Einstein principle of relativity” after 1905 [2].


Question: Who was the creator of the topology?

Henri Poincare

The following hypothesis was also put forward: Kaufman's experiments conducted during these years questioned the principle of relativity and the formula for the dependence of inertia on speed, so it is possible that Poincare decided to simply wait with conclusions until these issues are clarified [2].


Question: Who was the creator of the topology?

Henri Poincare

In Göttingen, Poincaré made an important prediction: relativistic amendments to the theory of gravity should explain the centuries-old shift in the perihelion of Mercury.


Question: Who was the creator of the topology?

Henri Poincare

The prediction soon came true (1915), when Einstein completed the development of general relativity.


Question: Who was the creator of the topology?

Henri Poincare

Poincare's position is slightly clarified by his lecture “Space and Time”, which he gave in May 1912 at the University of London.


Question: Who was the creator of the topology?

Henri Poincare

Poincare considers the principle of relativity and new laws of mechanics to be primary in the restructuring of physics.


Question: Who was the creator of the topology?

Henri Poincare

The properties of space and time, according to Poincaré, should be derived from these principles or established conventionally.


Question: Who was the creator of the topology?

Henri Poincare

Einstein did the opposite — he deduced dynamics from the new properties of space and time.


Question: Who was the creator of the topology?

Henri Poincare

Poincare still considers the transition of physicists to a new mathematical formulation of the principle of relativity (Lorentz transformation instead of Galilean ones) a matter of agreement [25]:


Question: Who was the creator of the topology?

Henri Poincare

What will be our attitude to these new [relativistic] ideas?


Question: Who was the creator of the topology?

Henri Poincare

Will they force us to change our conclusions?


Question: Who was the creator of the topology?

Henri Poincare

Not at all; we accepted the well-known conditional agreement because it seemed convenient to us... Now some physicists want to accept a new conditional agreement.


Question: Who was the creator of the topology?

Henri Poincare

This does not mean that they were forced to do so; they find this new agreement more convenient, that's all.


Question: Who was the creator of the topology?

Henri Poincare

And those who do not hold their opinion and do not want to give up their old habits can rightfully maintain the old agreement.


Question: Who was the creator of the topology?

Henri Poincare

Between us, I think they're going to do this for a long time to come.


Question: Who was the creator of the topology?

Henri Poincare

From these words, one can understand why Poincaré not only did not complete his journey to the theory of relativity, but even refused to accept the theory already created.


Question: Who was the creator of the topology?

Henri Poincare

This is also evident from a comparison of Poincare's and Einstein's approaches.


Question: Who was the creator of the topology?

Henri Poincare

Poincare understands what Einstein understands as relative, but objective, as purely subjective, conditional (conventional).


Question: Who was the creator of the topology?

Henri Poincare

The difference in the positions of Poincare and Einstein and its possible philosophical roots have been studied in detail by historians of science [34].


Question: Who was the creator of the topology?

Henri Poincare

Louis de Broglie, the founder of quantum mechanics, and the first winner of the Poincare Medal (1929) [35], blames his positivist views [36]:


Question: Who was the creator of the topology?

Henri Poincare

A little more, and Henri Poincaré, not Albert Einstein, would be the first to build the theory of relativity in all its commonality, thereby honoring French science with the honor of this discovery... However, Poincaré never took a decisive step, and gave Einstein the honor to discern all the consequences from the principle of relativity and, in particular, by analyzing the measurements of length and time in depth to find out the true physical the nature of the relationship established by the principle of relativity between space and time.


Question: Who was the creator of the topology?

Henri Poincare

Why didn't Poincare reach the end of his conclusions?


Question: Who was the creator of the topology?

Henri Poincare

... Poincare, as a scientist, was primarily a pure mathematician... Poincare took a somewhat skeptical position in relation to physical theories, believing that in general there is infinitely much logically equivalent points of view and pictures of reality, from which the scientist, guided solely by considerations of convenience, chooses one.


Question: Who was the creator of the topology?

Henri Poincare

Probably, this nominalism sometimes prevented him from admitting the fact that among the logically possible theories there are those that are closer to physical reality, at least better consistent with intuition physics, and thus can help him more... The philosophical propensity of his mind for “nominalistic convenience” prevented Poincaré from understanding the meaning of the idea of relativity in all its grandeur.


Question: Who was the creator of the topology?

Henri Poincare

French historian of science Jean Ulmo came to the same conclusions: Poincaré was unable to find a physical interpretation of relativity, “because he adhered to a false philosophy — philosophy of recipe, convention, arbitrary representation, into which phenomena can always be squeezed, as a last resort, with a stretch” [37].


Question: Who was the creator of the topology?

Henri Poincare

Evaluation of Poincare's contribution to special relativity


Question: Who was the creator of the topology?

Henri Poincare

Poincare's contribution to the creation of a special theory of relativity (STO) by contemporary physicists and later historians of science is assessed in different ways.


Question: Who was the creator of the topology?

Henri Poincare

Their range of views ranges from neglecting this contribution to claiming that Poincaré's understanding was no less complete and profound than that of other founders, including Einstein.


Question: Who was the creator of the topology?

Henri Poincare

However, the vast majority of historians adhere to a fairly balanced point of view, assigning both (as well as Lorenz and who later joined the development of the theory of Planck and Minkowski) a significant role in the successful development of relativistic ideas.


Question: Who was the creator of the topology?

Henri Poincare

P. S. Kudryavtsev, aware of the history of physics [38], highly appreciates the role of Poincare.


Question: Who was the creator of the topology?

Henri Poincare

He quotes D. D. Ivanenko and V. K. Fredericks that “Poincaré's article, from a formal point of view, contains not only a parallel work by Einstein, but in some parts and much later — almost three years — Minkowski's article, and in part even surpasses the latter.”


Question: Who was the creator of the topology?

Henri Poincare

Einstein's contribution, according to P. S. Kudryavtsev, was that it was he who managed to create a holistic theory of maximum generality and clarify its physical essence.


Question: Who was the creator of the topology?

Henri Poincare

A. A. Tyapkin in the epilogue to the collection “The Principle of Relativity” writes [39]:


Question: Who was the creator of the topology?

Henri Poincare

So which of the scientists should we consider to be the creators of the SRT?


Question: Who was the creator of the topology?

Henri Poincare

... Of course, the Lorentz transformations discovered before Einstein include the entire content of the SRT.


Question: Who was the creator of the topology?

Henri Poincare

But Einstein's contribution to their explanation, to the construction of a holistic physical theory and to the interpretation of the main consequences of this theory is so significant and fundamental that Einstein rightfully considers the creator of the service station.


Question: Who was the creator of the topology?

Henri Poincare

However, the high appreciation of Einstein's work does not give any reason to consider him the sole creator of the SRT and to neglect the contribution of other scientists.


Question: Who was the creator of the topology?

Henri Poincare

Einstein himself wrote in a welcoming letter in 1953 to the organizing committee of the conference dedicated to the 50th anniversary of the theory of relativity (held in 1955): “I hope that the merits will be duly noted G. A. Lorenz and A. Poincare” [40].


Question: Who was the creator of the topology?

Henri Poincare

Personality and beliefs


Question: Who was the creator of the topology?

Henri Poincare

Reviews of Poincare as a person are most often enthusiastic.


Question: Who was the creator of the topology?

Henri Poincare

In any situation, he always chose a noble position.


Question: Who was the creator of the topology?

Henri Poincare

In scientific disputes, he was firm, but correct.


Question: Who was the creator of the topology?

Henri Poincare

He has never been involved in scandals, priority disputes, insults.


Question: Who was the creator of the topology?

Henri Poincare

Indifferent to fame: he repeatedly voluntarily gave up scientific priority, even if he had serious rights to it; for example, he introduced the terms “Fuchs functions,” “Klein group,” “Poisson stability,” “Betty numbers” — although he had every reason to call these objects by his own name.


Question: Who was the creator of the topology?

Henri Poincare

As noted above, he was the first to write out the Lorentz transformation in its modern form (along with Larmor), but named them after Lorentz, who had previously given their incomplete approximation [41].


Question: Who was the creator of the topology?

Henri Poincare

Poincare's friends note his modesty, wit, tolerance, sincerity and goodwill.


Question: Who was the creator of the topology?

Henri Poincare

Outwardly, he could give the impression of a closed and unsociable person, but in reality this behavior was the result of his shyness and constant concentration [2].


Question: Who was the creator of the topology?

Henri Poincare

Despite his absent-mindedness, Poincaré punctually observed the once established regime of the day: breakfast at 8 o'clock, lunch at 12 pm, dinner at 7 pm.


Question: Who was the creator of the topology?

Henri Poincare

I never smoked and did not like it when others smoked.


Question: Who was the creator of the topology?

Henri Poincare

He did not play sports, although he liked walking.


Question: Who was the creator of the topology?

Henri Poincare

He was indifferent to religion [42].


Question: Who was the creator of the topology?

Henri Poincare

At that time of general rampant nationalism, he condemned chauvinistic actions.


Question: Who was the creator of the topology?

Henri Poincare

Poincaré believed that the greatness of France should be achieved due to the moral dignity of its sons, the fame of its literature and art, and thanks to the discoveries of its scientists [2]:


Question: Who was the creator of the topology?

Henri Poincare

The homeland is not just a syndicate of interests, but a combination of noble ideas and even noble passions for which our fathers fought and suffered, and France, full of hatred, would no longer be France.


Question: Who was the creator of the topology?

Henri Poincare

philosophy


Question: Who was the creator of the topology?

Henri Poincare

Poincare wrote in Science and Hypothesis that “there is no reality that is completely independent of the mind that comprehends it” [25].


Question: Who was the creator of the topology?

Henri Poincare

He believed that the basic principles of any scientific theory are neither a priori speculative truths (as, for example, Kant believed), nor an idealized reflection of objective reality (point of view Einstein).


Question: Who was the creator of the topology?

Henri Poincare

They, in his opinion, are conditional agreements, the only absolute condition of which is consistency.


Question: Who was the creator of the topology?

Henri Poincare

The choice of certain scientific principles from a variety of possible, generally speaking, is arbitrary, but in reality the scientist is guided, on the one hand, by the desire for maximum simplicity of the theory, on the other hand, the need for its successful practical use.


Question: Who was the creator of the topology?

Henri Poincare

But even when these requirements are met, there is some freedom of choice due to the relative nature of the requirements themselves.


Question: Who was the creator of the topology?

Henri Poincare

This philosophical doctrine was later called conventionalism.


Question: Who was the creator of the topology?

Henri Poincare

It corresponds well to the practice of choosing mathematical models in natural science [43], but its applicability to physics, where it is important to choose not only models, but also concepts correlated with reality, caused controversy [25].


Question: Who was the creator of the topology?

Henri Poincare

During Poincaré's time, the third wave of positivism was gaining momentum, in which, in particular, mathematics was proclaimed part of logic (an idea preached by outstanding scientists such as Russell and Frege) or an empty set of axiomatic theories (Gilbert and his school) [44].


Question: Who was the creator of the topology?

Henri Poincare

Poincare was categorically against such formalistic views [25].


Question: Who was the creator of the topology?

Henri Poincare

He believed that the mathematician's activity is based on intuition, and science itself does not allow full analytical justification [45].


Question: Who was the creator of the topology?

Henri Poincare

Logic is necessary only insofar as without strict logical justification, intuitively obtained statements cannot be considered credible.


Question: Who was the creator of the topology?

Henri Poincare

In accordance with these principles, Poincare rejected not only Russell's logicism and Hilbert's formalism, but also Cantor's set theory [46] — although before the discovery of paradoxes he showed interest in it and tried to use.


Question: Who was the creator of the topology?

Henri Poincare

He strongly stated that he rejects the concept of actual infinity (that is, the infinite set as a mathematical object) and recognizes only potential infinity [25].


Question: Who was the creator of the topology?

Henri Poincare

In order to avoid paradoxes, Poincaré demanded that all mathematical definitions be strictly predicative, that is, they should not contain references not only to the concept to be defined, but also to the set containing it — otherwise the definition, including the new element, changes the composition of this set, and a vicious circle arises [25].


Question: Who was the creator of the topology?

Henri Poincare

Many of Poincare's thoughts were later adopted by Brower and other intuitionists.


Question: Who was the creator of the topology?

Henri Poincare

Honors and awards


Question: Who was the creator of the topology?

Henri Poincare

Awards and titles received by Poincare:


Question: Who was the creator of the topology?

Henri Poincare

1885: Poncelet Prize, Academy of Sciences of Paris


Question: Who was the creator of the topology?

Henri Poincare

1886: Elected President of the French Mathematical Society


Question: Who was the creator of the topology?

Henri Poincare

1887: Elected a member of the Paris Academy of Sciences


Question: Who was the creator of the topology?

Henri Poincare

1889: Math Competition Winning Award, King Oscar II of Sweden


Question: Who was the creator of the topology?

Henri Poincare

1889: Legion of Honor


Question: Who was the creator of the topology?

Henri Poincare

1893: Elected a member of the Bureau of Longitude (this is the historical name of the Paris Institute of Celestial Mechanics)


Question: Who was the creator of the topology?

Henri Poincare

1894: Elected a foreign member of the Royal Society of London


Question: Who was the creator of the topology?

Henri Poincare

1895: Elected a foreign corresponding member of the St. Petersburg Academy of Sciences


Question: Who was the creator of the topology?

Henri Poincare

1896 Jean Reynaud Prize, Paris Academy of Sciences


Question: Who was the creator of the topology?

Henri Poincare

1896: Elected President of the French Astronomical Society


Question: Who was the creator of the topology?

Henri Poincare

1899: Award, American Philosophical Society


Question: Who was the creator of the topology?

Henri Poincare

1900: Royal Astronomical Society Gold Medal, London


Question: Who was the creator of the topology?

Henri Poincare

1901: Sylvester Medal, Royal Society, London


Question: Who was the creator of the topology?

Henri Poincare

1903: Gold Medal of the A.


Question: Who was the creator of the topology?

Henri Poincare

N. AND. Lobachevsky (Physical and Mathematical Society of Kazan) as a reviewer of David Gilbert


Question: Who was the creator of the topology?

Henri Poincare

1905: Boyaya Prize, Hungarian Academy of Sciences


Question: Who was the creator of the topology?

Henri Poincare

1905: Matteucci Medal, Italian Scientific Society


Question: Who was the creator of the topology?

Henri Poincare

1905: Order of the North Star (Sweden) [47]


Question: Who was the creator of the topology?

Henri Poincare

1906: Elected President of the Paris Academy of Sciences


Question: Who was the creator of the topology?

Henri Poincare

1908: Elected a member of the French Academy (not to be confused with the Paris Academy of Sciences)


Question: Who was the creator of the topology?

Henri Poincare

1909: Gold Medal, French Association for the Advancement of Science


Question: Who was the creator of the topology?

Henri Poincare

1911: Catherine Bruce Medal, Pacific Astronomical Society


Question: Who was the creator of the topology?

Henri Poincare

1912: Elected Director of the French Academy


Question: Who was the creator of the topology?

Henri Poincare

Poincare is named after:


Question: Who was the creator of the topology?

Henri Poincare

A crater on the far side of the Moon.


Question: Who was the creator of the topology?

Henri Poincare

Asteroid 2021 Poincare.


Question: Who was the creator of the topology?

Henri Poincare

International Poincare Prize for works in mathematical physics.


Question: Who was the creator of the topology?

Henri Poincare

Institute for Mathematics and Theoretical Physics in Paris ().


Question: Who was the creator of the topology?

Henri Poincare

University and street in Nancy [48].


Question: Who was the creator of the topology?

Henri Poincare

A street in Paris (20th arrondissement).


Question: Who was the creator of the topology?

Henri Poincare

Works


Question: Who was the creator of the topology?

Henri Poincare

Main works (see also):


Question: Who was the creator of the topology?

Henri Poincare

Cours de physique mathématique, 1889—1892 (Mathematical Physics course in 12 volumes based on his lectures at the Sorbonne)


Question: Who was the creator of the topology?

Henri Poincare

Les methods nouvelles de la mécanique céleste, t.


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare

R., 1892—97 (New methods of celestial mechanics)


Question: Who was the creator of the topology?

Henri Poincare

Analysis situs, 1895 (as topology was originally called); 1899—1902 Poincare published 5 substantive additions to this pioneering work


Question: Who was the creator of the topology?

Henri Poincare

Calcull des probabilités, 1896 (Calculation of probabilities, reprinted 1912 and 1923)


Question: Who was the creator of the topology?

Henri Poincare

La Science et l'hypothèse, 1902 (Science and Hypothesis)


Question: Who was the creator of the topology?

Henri Poincare

Valeur de la science, 1905 (The Value of Science)


Question: Who was the creator of the topology?

Henri Poincare

Leçons de mécanique céleste, t.


Question: Who was the creator of the topology?

Henri Poincare


Question: Who was the creator of the topology?

Henri Poincare

P., 1905—1906 (Lectures on Celestial Mechanics)


Question: Who was the creator of the topology?

Henri Poincare

Théorie de Maxwell et les oscillations hertziennes, 1907 (Maxwell and Hertz Wave Theory)


Question: Who was the creator of the topology?

Henri Poincare

Science et méthode, 1908 (Science and Method)


Question: Who was the creator of the topology?

Henri Poincare

Dernières Pensées, 1913 (Last Thoughts, Posthumously)


Question: Who was the creator of the topology?

Henri Poincare

Uvres, t.


Question: Who was the creator of the topology?

Henri Poincare

1—11, 1916—1956 (Writings, posthumously)


Question: Who was the creator of the topology?

Henri Poincare

Translations into Russian


Question: Who was the creator of the topology?

Henri Poincare

Poincare A.


Question: Who was the creator of the topology?

Henri Poincare

Moscow: Nauka, 1971.


Question: Who was the creator of the topology?

Henri Poincare

NEW METHODS OF CELESTIAL MECHANICS, parts 1, 2 of 3.


Question: Who was the creator of the topology?

Henri Poincare

Poincare A.


Question: Who was the creator of the topology?

Henri Poincare

Moscow: Nauka, 1972.


Question: Who was the creator of the topology?

Henri Poincare

NEW METHODS OF CELESTIAL MECHANICS, part 3 of 3.


Question: Who was the creator of the topology?

Henri Poincare

TOPOLOGY: Analysis situs (457); Supplement to Analysis situs (549); Second Supplement to Analysis situs (594); On some algebraic surfaces (Third Supplement to Analysis situs) (623); O cycles of algebraic surfaces (Fourth Supplement to Analysis situs) (641); Fifth Supplement to Analysis situs (676); On geodetic lines on convex surfaces (735); On one geometric theorem (775); P. S. Aleksandrov said.


Question: Who was the creator of the topology?

Henri Poincare

Poincare and topology (808).


Question: Who was the creator of the topology?

Henri Poincare

NUMBER THEORY: On ternary and quaternary cubic forms (819).


Question: Who was the creator of the topology?

Henri Poincare

On the arithmetic properties of algebraic curves (901).


Question: Who was the creator of the topology?

Henri Poincare

Poincare A.


Question: Who was the creator of the topology?

Henri Poincare

Moscow: Nauka, 1974.


Question: Who was the creator of the topology?

Henri Poincare

MATH: Fuchs group theory (9).


Question: Who was the creator of the topology?

Henri Poincare

On fuchs functions (63).


Question: Who was the creator of the topology?

Henri Poincare

On groups of linear equations (145).


Question: Who was the creator of the topology?

Henri Poincare

Fuchs functions and the equation ∆u=eu (235).


Question: Who was the creator of the topology?

Henri Poincare

On curves on algebraic surfaces (310).


Question: Who was the creator of the topology?

Henri Poincare

On curves on an algebraic surface (351).


Question: Who was the creator of the topology?

Henri Poincare

THEORETICAL PHYSICS: Notes on the kinetic theory of gases (385).


Question: Who was the creator of the topology?

Henri Poincare

Electricity and optics (introduction) (413).