IU?. I. Manin quotes
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“A proof only becomes a proof after the social act of "accepting it as a proof".”
-- 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 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 -
“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 -
“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 -
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“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 -
“Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.”
-- IU?. I. Manin
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Source : "Dictionary of Scientific Biography". Book edited by M. Steck, 1970-1990.
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“We know that nature is described by the best of all possible mathematics because God created it.”
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“Regulation of sexual behavior is the preferred route to wider social control.”
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“Grace is God's acceptance of us. Faith is our acceptance of God accepting us.”
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Source : Dorothy Norman, Alfred Stieglitz (1973). “Alfred Stieglitz: an American seer”
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“Happiness is lost by criticizing it; sorrow by accepting it.”
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