Vladimir Arnold quotes

Vladimir Arnold was a renowned Russian mathematician celebrated for his groundbreaking contributions to dynamical systems, topology, and singularity theory. His work helped shape modern mathematics and inspired generations of researchers. He made significant advances in the study of Hamiltonian dynamics and catastrophe theory. Here are 9 of his quotes:

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

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.

Vladimir Arnold

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

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

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

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.

Vladimir Arnold

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

Vladimir Arnold

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