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I wonder what the quotes from mathematicians are about their views on academic research vs. math competitions. I can't find much, but I have found one:

Math competitions are to research what spelling bees are to writing. - Bill Thurston

What are other quotes related to this topic in the history of mathematics?

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Here's a page containing quotes from mathematicians such as Tao, Shimura and Wiles (and which includes a much-expanded version of the Thurston quote):

https://www.lesswrong.com/posts/EdFDwjsLNpgtTMJAp/great-mathematicians-on-math-competitions-and-genius

Part of the quote by Wiles:

While there have been periods, notably in the thirteenth, fourteenth and fifteenth centuries when mathematicians would engage in timed duels with each other, nowadays this is not the custom. In fact time is very much on your side. However the transition from a sprint to a marathon requires a new kind of stamina and a profoundly different test of character. We admire someone who can win a gold medal in five successive Olympics games not so much for the raw talent as for the strength of will and determination to pursue a goal over such a sustained period of time. Real mathematical theorems will require the same stamina whether you measure the effort in months or in years

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