Michael Atiyah Quotes

• In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.

  Michael Atiyah

  Inspirational, Life, Dream

  Michael Atiyah (2014). “Michael Atiyah Collected Works: 2002-2013”, p.267, Oxford University Press, USA

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• The aim of mathematics is to explain as much as possible in simple terms.

  Michael Atiyah

  Simple, Mathematics, Term

  Michael Atiyah (1988). “Collected Works: Michael Atiyah Collected Works: Volume 1: Early Papers; General Papers”, p.286, Oxford University Press

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• It is hard to communicate understanding because that is something you get by living with a problem for a long time. You study it, perhaps for years, you get the feel of it and it is in your bones. You can't convey that to anyone else. Having studied the problem for five years you may be able to present it in such a way that it would take somebody else less time to get to that point than it took you. But if they haven't struggled with the problem and seen all the pitfalls, then they haven't really understood it.

  Michael Atiyah

  Math, Years, Long

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• If you attack a mathematical problem directly, very often you come to a dead end, nothing you do seems to work and you feel that if only you could peer round the corner there might be an easy solution. There is nothing like having somebody else beside you, because he can usually peer round the corner.

  Michael Atiyah

  Peers, Might, Problem

  Michael Atiyah (1988). “Collected Works: Michael Atiyah Collected Works: Volume 1: Early Papers; General Papers”, p.214, Oxford University Press

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• Everything useful in mathematics has been devised for a purpose. Even if you don't know it, the guy who did it first, he knew what he was doing. Banach didn't just develop Banach spaces for the sake of it. He wanted to put many spaces under one heading. Without knowing the examples, the whole thing is pointless.

  Michael Atiyah

  Math, Knowing, Space

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• I dislike frontiers, political or intellectual, and I find that ignoring them is an essential catalyst for creative thought. Ideas should flow without hindrance in their natural course.

  Michael Atiyah

  Creativity, Ideas, Imagination

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• I'm not the sort of person who does my mathematics writing on paper. I do that at the last stage of the game. I do my mathematics in my head. I sit down for a hard day's work and I write nothing all day. I just think. And I walk up and down because that helps keep me awake, it keeps the blood circulating, and I think and think.

  Michael Atiyah

  Writing, Thinking, Blood

  "'I'm a bit of a jack of all trades'". Interview with James Meek, www.theguardian.com. April 21, 2004.

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• I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other.

  Michael Atiyah

  Thinking, Should Have, Law

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• If theory is the role of the architect, then such beautiful proofs are the role of the craftsman. Of course, as with the great renaissance artists, such roles are not mutually exclusive. A great cathedral has both structural impressiveness and delicate detail. A great mathematical theory should similarly be beautiful on both large and small scales.

  Michael Atiyah

  Beauty, Beautiful, Art

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• There is no clear-cut distinction between example and theory

  Michael Atiyah

  Cutting, Example, Theory

  Michael Atiyah (2014). “Michael Atiyah Collected Works: Volume 7: 2002-2013”, p.370, OUP Oxford

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• Any good theorem should have several proofs, the more the better.

  Michael Atiyah

  Should Have, Proof, Should

  "Interview with Michael Atiyah and Isadore Singer". Interview with Martin Raussen, Christian Skau, www.researchgate.net. February 2005.

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• No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the 'square root' of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors.

  Michael Atiyah

  Squares, Roots, Understanding

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• Would you rather be deaf or blind?

  Michael Atiyah

  Blind, Deaf

  14 Copy quote

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