Thinking time: New maths theories come from random moments

For mathematicians sustained effort and deep thought lay groundwork for discovery

American topologist Stephen Smale used to do his research on the beach in Rio de Janeiro.

American topologist Stephen Smale used to do his research on the beach in Rio de Janeiro.

Where does new mathematics come from? The great French mathematician Henri Poincaré, a brilliant expositor of the scientific method, described how he grappled for months with an arcane problem in function theory.

Exasperated by lack of progress, he went on holidays and forgot about the problem. But, as he was boarding a bus, the answer came to him in a flash. He was later able to return to his office and complete a proof of the result.

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