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Vladimir Arnold
11 quotes
“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).”
Vladimir Arnold (1937–2010) first seen 1998 wikiquote, CC BY-SA 4.0 source
Recorded in: On teaching mathematics", as translated by A. V. Goryunov, in Russian Mathematical Surveys Vol. 53, no. 1 (1998), p. 229–236.
“It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” write simply: “There is a t_1 such that the image of t_1 under the natural mapping t_1 \mapsto {\rm Petya}(t_1) belongs to the set of dirty hands, and a t_2, t_1, such that the image of t_2 under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.”
Vladimir Arnold (1937–2010) first seen 1987 wikiquote, CC BY-SA 4.0 source
Recorded in: Conversation with Vladimir Igorevich Arnol’d" (Arnold interviewed by Smilka Zdravkovska), The Mathematical Intelligencer, December 1987, Volume 9, Issue 4, pp 28–32.
“A person, who had not mastered the art of the proofs in high school, is as a rule unable to distinguish correct reasoning from that which is misleading. Such people can be easily manipulated by the irresponsible politicians.”
Vladimir Arnold (1937–2010) first seen 1998 wikiquote, CC BY-SA 4.0 source
Recorded in: The antiscientifical revolution and mathematics" (1998, Vatican).
“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.”
Vladimir Arnold (1937–2010) said by 2010 at the latest wikiquote, CC BY-SA 4.0 source
Recorded in: 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 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.).”
Vladimir Arnold (1937–2010) first seen 2000 wikiquote, CC BY-SA 4.0 source
Recorded in: 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.
“In almost all textbooks, even the best, this principle is presented so that it is impossible to understand." (K. Jacobi, Lectures on Dynamics, 1842-1843). I have not chosen to break with tradition.”
Vladimir Arnold (1937–2010) said by 2010 at the latest wikiquote, CC BY-SA 4.0 source
“When you are collecting mushrooms, you only see the mushroom itself. But if you are a mycologist, you know that the real mushroom is in the earth. There’s an enormous thing down there, and you just see the fruit, the body that you eat. In mathematics, the upper part of the mushroom corresponds to theorems that you see. But you don’t see the things which are below, namely problems, conjectures, mistakes, ideas, and so on. You might have several apparently unrelated mushrooms and are unable to see what their connection is unless you know what is behind.”
Vladimir Arnold (1937–2010) said by 2010 at the latest wikiquote, CC BY-SA 4.0 source
“Such axioms, together with other unmotivated definitions, serve mathematicians mainly by making it difficult for the uninitiated to master their subject, thereby elevating its authority.”
Vladimir Arnold (1937–2010) said by 2010 at the latest wikiquote, CC BY-SA 4.0 source
“Mathematics is the part of physics where experiments are cheap.”
Vladimir Arnold (1937–2010) said by 2010 at the latest wikiquote, CC BY-SA 4.0 source
“The axiomization and algebraization of mathematics, after more than 50 years, has led to the illegibility so such a large number of mathematical texts that the threat of complete loss of contact with physics and the natural sciences has been realized.”
Vladimir Arnold (1937–2010) said by 2010 at the latest wikiquote, CC BY-SA 4.0 source
Recorded in: V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, 2012, p. ix.
“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.”
Vladimir Arnold (1937–2010) first seen 1995 wikiquote, CC BY-SA 4.0 source
Recorded in: Will Mathematics Survive? Report on the Zurich Congress" in The Mathematical Intelligencer, Vol. 17, no. 3 (1995), pp. 6–10.