Vladimir I. Arnold Quotes

Vladimir Igorevich Arnold was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics—KAM theory, and topological Galois theory .

Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks and popular mathematics books, he influenced many mathematicians and physicists. Many of his books were translated into English. His views on education were particularly anti-Bourbaki.



Wikipedia  

✵ 12. June 1937 – 3. June 2010
Vladimir I. Arnold: 8   quotes 0   likes

Famous Vladimir I. Arnold Quotes

“At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering.”

"Will Mathematics Survive? Report on the Zurich Congress" in The Mathematical Intelligencer, Vol. 17, no. 3 (1995), pp. 6–10.
Context: At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste... Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics.

“In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic.”

"On teaching mathematics", as translated by A. V. Goryunov, in Russian Mathematical Surveys Vol. 53, no. 1 (1998), p. 229–236.
Context: In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy's warning that ugly mathematics has no permanent place under the Sun).

“They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy's warning that ugly mathematics has no permanent place under the Sun).”

"On teaching mathematics", as translated by A. V. Goryunov, in Russian Mathematical Surveys Vol. 53, no. 1 (1998), p. 229–236.
Context: In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy's warning that ugly mathematics has no permanent place under the Sun).

“In the last 30 years, the prestige of mathematics has declined in all countries. I think that mathematicians are partially to be blamed as well—foremost, Hilbert and Bourbaki—the ones who proclaimed that the goal of their science was investigation of all corollaries of arbitrary systems of axioms.”

Interview translated from the Russian into English and republished in the book Boris A. Khesin; Serge L. Tabachnikov (editors), Arnold: Swimming Against the Tide (2014) Google Books preview http://books.google.com/books?id=aBWHBAAAQBAJ&pg=PA4 pages 4–5.

“All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and by other institutions dealing with missiles, such as NASA.).”

"Polymathematics: is mathematics a single science or a set of arts?", in Mathematics: Frontiers and Perspectives (2000), edited by V. I. Arnold, M. Atiyah, P. Lax, and B. Mazur, pp. 403–416.

Similar authors

Vitaly Ginzburg photo
Vitaly Ginzburg 2
Russian Physicist
Borís Pasternak photo
Borís Pasternak 40
Russian writer
Aleksandr Solzhenitsyn photo
Aleksandr Solzhenitsyn 120
Russian writer
Wassily Leontief photo
Wassily Leontief 10
Russian economist
Maxim Gorky photo
Maxim Gorky 10
Russian and Soviet writer
Vladimir Nabokov photo
Vladimir Nabokov 193
Russian-American novelist, lepidopterist, professor
Vladimir Lenin photo
Vladimir Lenin 336
Russian politician, led the October Revolution
Anna Akhmatova photo
Anna Akhmatova 99
Russian modernist poet
Mikhail Bulgakov photo
Mikhail Bulgakov 63
Russian author primarily known for his novel "Master and Ma…
John Nash photo
John Nash 23
American mathematician and Nobel Prize laureate