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I was reading about the Four color theorem and discovered that it took so many years to prove the theorem with many proof attempts that led to failures.

In fact, it is stated here that:

One attempted proof, given in 1879 by Alfred Kempe, was believed to be correct until Percy Heawood showed in 1890 that it was flawed; another proof, proposed in 1880, was shown to be incorrect in 1891. The first correct proof was given in 1976 by Kenneth Appel and Wolfgang Haken.

...

Since then the proof has been regenerated in several different ways, and simplified to some extent, but no one has yet been able to produce a proof that is simple enough and clear enough for any person to comprehend. For this reason there is still some doubt among some mathematicians about the correctness of Appel and Haken's proof, though most mathematicians accept the proof as valid.

So, do you know any similar situation like this? Or, alternatively, do you know any problem that is known to take so many years to solve (even though the correct proof is very long and complicated as for the four-color theorem) but with many proof attempts that led to failures?

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    Fermat's last theorem is the classic example that comes to mind. – 2017-01-26
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    Does anybody know of any major (famous) problem that remained unsolved for many years that did **not** have multiple failed attempts at a proof? – 2017-01-26
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    @MarkFischler: I think (smooth) Poincare conjecture in dimensions $>4$ is one such example. Before Smale, I think, nobody had an idea (correct or not). The case n=3 is different, of course. – 2017-01-26
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    @MarkFischler Another example would be the Triangle Removal Lemma. People's usual response to learning that it's a theorem is to be surprised. – 2017-02-14

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If I remember correctly, the Earnshaw's theorem was stated and pseudo-proven in the 19th century (there are obvious counterexamples to Maxwell's version), but a rigorous mathematical proof came only in the 21st.

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Maybe here you'll find some examples:

https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Problems_solved_since_1995