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- Algebra is the offer made by the devil to the mathematician. The devil says: `I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.'
- My own supervisor, William Hodge, the creator of the fertile theory of harmonic forms, was not a genius like Ramanujan but resembled Lefschetz.
- Michael Atiyah (3 April 2014). Michael Atiyah Collected Works: Volume 7: 2002-2013. Oxford University Press. p. 286. ISBN 978-0-19-968926-2.
- This 'Hodge conjecture' has by now achieved a considerable status, almost on a par with the Riemann hypothesis or the Poincaré conjecture.
- Michael Atiyah (28 April 1988). Collected Works: Michael Atiyah Collected Works: Volume 1: Early Papers; General Papers. Clarendon Press. pp. 250. ISBN 978-0-19-853275-0.
- I always want to try to understand why things work. I’m not interested in getting a formula without knowing what it means. I always try to dig behind the scenes, so if I have a formula, I understand why it’s there. And understanding is a very difficult notion. People think mathematics begins when you write down a theorem followed by a proof. That’s not the beginning, that’s the end. For me the creative place in mathematics comes before you start to put things down on paper, before you try to write a formula. You picture various things, you turn them over in your mind. You’re trying to create, just as a musician is trying to create music, or a poet. There are no rules laid down. You have to do it your own way. But at the end, just as a composer has to put it down on paper, you have to write things down. But the most important stage is understanding. A proof by itself doesn’t give you understanding. You can have a long proof and no idea at the end of why it works. But to understand why it works, you have to have a kind of gut reaction to the thing. You’ve got to feel it.
- On an article by Quanta magazine(when asked: Is there one big question that has always guided you?)