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The twentieth century return to Middle Age scholastics taught us a lot about formalisms. Probably it is time to look outside again. Meaning is what really matters.
Yuri Manin
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Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.
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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.
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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).
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A proof only becomes a proof after the social act of "accepting it as a proof".
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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.
Yuri Manin
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In every walk with nature one receives far more than he seeks.
John Muir
Yuri Manin
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Born:
February 16, 1937
Died:
January 7, 2023
(aged 85)
Bio:
Yuri Ivanovitch Manin is a SovietGerman mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Known for:
A course in mathematical logic (1977)
Gauge Field Theory and Complex Geometry (1988)
Linear Algebra and Geometry (1989)
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