13 world class mathematicians on doing mathematical research

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11 pointsypk3 comments

My favorite part is from Ed Witten, a leading theoretical physicist, and also a Fields’ Medalist, who replied:

“There isn’t a clear task. If you are a researcher you are trying to figure out what the question is as well as what the answer is.

You want to find the question that is sufficiently easy that you might be able to answer it, and sufficiently hard that the answer is interesting. You spend a lot of time thinking and you spend a lot of time floundering around.”

I find the same thing true. Problem solving is me cycling through questions until I ask the right one. The question I start with is always either too specific or too general to narrow my search. But after enough iterations, the right one trickles through.

The last guy says you have to start with an intuition, and then prove it.

But I think you can start with the proof, and an intuition can come to you along the way. It's just that it probably won't be about that proof.

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