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My golf-loving friend Bob Hope asked me what my handicap was, so I told him - the Congress.

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Michael Atiyah

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

Aim, Mathematics, Possible, Simple, Term
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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.

Dream, Heavens, Inspirational, Life, Mathematicians, Rigour

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.

Long, Math, Somebody, Took, Years

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.

Know, Knowing, Math, Sake, Space

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.

Algebra, Formally, Roots, Squares, True, Understanding

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.

Course, Creativity, Essential, Hindrance, Ideas, Imagination
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