For example, the Weber's proof of Kronecker–Weber theorem. I would like to know such proofs. It seems to be important for me to remember that a widely accepted proof might be wrong.
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1$\begingroup$ Can we ask that answers in mathoverflow.net/questions/879 not be repeated here? (Unfortunately, that probably won't work.) $\endgroup$– GEdgarAug 11, 2013 at 1:24
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$\begingroup$ I. R. Shafarevich, Construction of fields of algebraic numbers with given solvable Galois group (1954) math.stackexchange.com/questions/25242/… $\endgroup$– Makoto KatoAug 11, 2013 at 3:47
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1$\begingroup$ Pontryagin proved that $\pi_{n+2}(\mathbb{S}^n) = 0$ in 1938. However, he and G.W. Whiteheand corrected it in 1950 independently. $\endgroup$– Makoto KatoAug 11, 2013 at 3:48
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1 Answer
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There are many variations on this theme in MathOverflow.
Widely accepted mathematical results that were later shown wrong
Failures that lead eventually to new mathematics
Most interesting mathematics mistake
How to refer to a theorem that you have shown to be wrong
What are some correct results discovered with incorrect or no proofs
Examples where physical heuristics led to incorrect answers
Oldest bug in computer algebra
What mistakes did the italian algebraic geometers actually make
Italian school of algebraic geometry and rigorous proofs
Can a mathematical definition be wrong
Mathematicians whose works were criticized by contemporaries but became widely accepted later
Have we ever lost any mathematics
Examples of conjectures that were widely believed to be true but later proved false
Statements which were given as axioms which later turned out to be false
and for good measure
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$\begingroup$ a good list here with fresh material: math.stackexchange.com/questions/139503/… $\endgroup$– zyxSep 4, 2013 at 0:55
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$\begingroup$ (accumulating material in comments for the next edit) $\endgroup$– zyxSep 5, 2013 at 0:53