IU?. I. Manin quotes

A proof only becomes a proof after the social act of "accepting it as a proof".
-- IU?. I. Manin

#Mathematics #Social #Accepting

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 scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit.
-- IU?. I. Manin

#Law #Games #Example

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 by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.
-- IU?. I. Manin

#Goal #Small Steps #Definitions

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

#Talking #Pace #Firsts

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 world of light there are neither points nor moments of time; beings woven from light would live "nowhere" and "nowhen"; only poetry and mathematics are capable of speaking meaningfully about such things.
-- IU?. I. Manin

#Space #Light #Flying

Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.
-- IU?. I. Manin

#Math #Logic #Biology

A good proof is one that makes us wiser.
-- IU?. I. Manin

#Ontology #Logic #Proof

The new art must be based upon science - in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.

We know that nature is described by the best of all possible mathematics because God created it.

I changed the course of my life, from the rigidity of mathematics and the corporate rhythm to a more bohemian world.

I'd like to take some calculus, too. I have absolutely no ability in that direction and not much interest, either, but there's something going on in mathematics that I don't understand, and I'd like to find out what it is.

Regulation of sexual behavior is the preferred route to wider social control.

Grace is God's acceptance of us. Faith is our acceptance of God accepting us.

You know Hachi, your life depends only on ourselves. I’m still convinced about this… But I’ve also learned to accept that people… don’t all become as strong, and it made me kinder than before.

I get people to truly accept themselves unconditionally, whether or not their therapist or anyone loves them.

There is nothing so wrong as accepting a thing merely because men who have done things say it should be so.

Happiness is lost by criticizing it; sorrow by accepting it.