# Widely accepted mathematical results that were later shown wrong?

I wonder if there are any examples in the history of mathematics of a mathematical proof that was initially reviewed and widely accepted as valid, only to be disproved a significant amount of time later, possibly even after being used in proofs of other results?

(I realise it's a bit vague, but if there is significant doubt in the mathematical community then the alleged proof probably doesn't qualify. What I'm interested in is whether the human race as a whole is known to have ever made serious mathematical blunders.)

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I have a déjà vu :) Also, maybe community wiki (~big list)? –  efq Aug 13 '10 at 10:41
@ex Given that I have no other way to earn reputation than by asking questions (my math is a mere long-forgotten-university-level), I'd like at least one extra upvote before marking this CW so I can at least upvote some answers :) –  romkyns Aug 13 '10 at 10:44
mathoverflow.net/questions/27749/… is a similar question - only the subject of the proof was later confirmed to be true. –  romkyns Aug 13 '10 at 12:16
The story around the Grunwald-Wang theorem takes the cake on this one, especially Tate's commentary on his reaction to it as a graduate student (but one also has to keep in mind that in those days and earlier, the number of active research mathematicians was a tiny fraction of the number today). See section 5.3 of rzuser.uni-heidelberg.de/~ci3/brhano.pdf –  BCnrd Aug 13 '10 at 14:35
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Lebesgue famously "proved" that the projection of a Borel set in $\mathbb R^2$ is a Borel set in $\mathbb R$. Famously disproved by Souslin a decade later. See this answer by Gerald Edgar.

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This thread on the Italian tradition in algebraic geometry contains some important examples.

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Yes, that thread was mentioned in KConrad's comment of 15 August. –  Gerry Myerson Feb 25 '11 at 11:51