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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.

Yuri 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.

Yuri Manin
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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).

Yuri Manin
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A proof only becomes a proof after the social act of "accepting it as a proof".

Yuri Manin
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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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Yuri Manin

Yuri Manin
Creative Commons

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:
  1. A course in mathematical logic (1977)
  2. Gauge Field Theory and Complex Geometry (1988)
  3. Linear Algebra and Geometry (1989)

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