When a mathematician created a set by naming it, he was giving a birth to a new mathematical being
- The naming of sets was a mathematical act, just as the naming of G-d was a religious one
- I've never suspected that neo-Nominalism played such a prominent role in the emergence of the Moscow School of Mathematics
The thesis of this article is that French mathematicians (Lebesgue, Borel, Baire, Du Bois-Reymond, Brouwer) being
Carthesians, believed that
- if one cannot think of an object, it cannot exist
- (if one cannot imagine transfinite numbers, these do not exist).
But Imyaslav mathematicians in Russia believed that
- by naming a mathematical object it automatically comes into existence, and
- so they were fully open to German advances in the set theory.
- They had no conceptual problem with, say, proving the existence of an object that cannot be properly defined.
- Their open mind allowed Egorov and Luzin to found a new school of mathematics.
By Loren Graham and Jean-Michel Kantor