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
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
