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 various objects. The goal of a proof is to make such a statement convincing… — IU?. I. Manin Copy Share Image
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 an output text which seemingly carries new knowledge. The basic examples are furnished by… — IU?. I. Manin Copy Share Image
To put it simply, we first explain what we are talking about, and then explain why what we are saying is true (pace Bertrand… — IU?. I. Manin Copy Share Image
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… — IU?. I. Manin Copy Share Image
The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or… — IU?. I. Manin Copy Share Image
Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. — IU?. I. Manin Copy Share Image
Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one… — IU?. I. Manin Copy Share Image
A proof only becomes a proof after the social act of "accepting it as a proof". — IU?. I. Manin Copy Share Image
