> This Platonic feeling that even most abstruse mathematical ideas are somehow predestined to be in harmony with the physical world, always constituted for me one of the most irresistible attractions of our trade. Stéphane Mallarmé wanted to make us aware that poetry is made of words rather than ideas. To a certain degree, this is true about mathematics as well, but in a more profound sense, this is fundamentally wrong. (I suspect that this is wrong for poetry as well)

Yuri Manin – Reception speech at the Paris Academy of Sciences

> I see the process of mathematical creation as a kind of recognizing a preexisting pattern. When you study something—topology, probability, number theory, whatever—first you acquire a general vision of the vast territory, then you focus on a part of it. Later you try to recognize “what is there?” and “what has already been seen by other people?”. So you can read other papers and finally start discerning something nobody has seen before you.

Yuri Manin – Good proofs are proofs that make us wiser

> The central figure of a philosophic dialogue is a wise man, whereas modernity generally and systematically replaces wisdom by training. Wisdom seems to be an inborn faculty slowly ripened by life experience; as such it is rarely met and even more rarely put to any use. Training is a democratic surrogate for wisdom which, in spite of all of its (mainly aesthetic) drawbacks, is superior in one respect: it produces professionals.

Yuri Manin – Mathematics as Metaphor