A proof only becomes a proof after the social act of "accepting it as a proof".

- Iu?. I. Manin

The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between v…

- Iu?. I. Manin

To put it simply, we first explain what we are talking about, and then explain why what we are saying is true (pace Bertrand Russell).

- Iu?. I. Manin

Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.

- Iu?. I. Manin

A good proof is one that makes us wiser.

- Iu?. I. Manin

Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get a…

- Iu?. I. Manin

What binds us to space-time is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning. In a worl…

- Iu?. I. Manin