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If you're interested in another example of how success breeds stagnation, see On Proof and Progress in Mathematics by William Turston, available at http://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-...

In particular look at section 6 where he describes how his research into foliations had the effect of killing the field for a number of years. He contrasts this to how his different approach to geometrization of 3-manifolds lead to the healthy growth of the field. By, among other things, his efforts at exposition, and his deliberate withholding of results he already knew the answer to so that other people could prove them instead.



This is an excellent article, from a researcher who knows what he's talking about (Thurston is a Fields medalist). Section 6 begins on the page numbered 173.


his deliberate withholding of results he already knew the answer to so that other people could prove them instead

That's extraordinary! I never heard of such a thing. Are other cases known?


Gauss seems to have proved lots of (surely publishable) things that he didn't publish. I don't know what his reasons were.


According to Erdos, Gauss was very discouraging to his students, because when they came and told him that they'd proven something, he would tell them he'd proven it years before.

from "The man who loved only numbers.' by Paul Hoffman.




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