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

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.

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.