Mathematical Dreams – Michael Atiyah

Source: Quanta, Mar 2016

Is that generally how your ideas arrive?

This was a spectacular version. The crazy part of mathematics is when an idea appears in your head. Usually when you’re asleep, because that’s when you have the fewest inhibitions. The idea floats in from heaven knows where. It floats around in the sky; you look at it, and admire its colors. It’s just there. And then at some stage, when you try to freeze it, put it into a solid frame, or make it face reality, then it vanishes, it’s gone. But it’s been replaced by a structure, capturing certain aspects, but it’s a clumsy interpretation.

Have you always had mathematical dreams?

I think so. Dreams happen during the daytime, they happen at night. You can call them a vision or intuition. But basically they’re a state of mind — without words, pictures, formulas or statements. It’s “pre” all that. It’s pre-Plato. It’s a very primordial feeling. And again, if you try to grasp it, it always dies. So when you wake up in the morning, some vague residue lingers, the ghost of an idea. You try to remember what it was and you only get half of it right, and maybe that’s the best you can do.

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