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Before Abel embarked to proving the insolubility of the quintic with radicals, he thought he had found a solution and sent his work in a letter to the Danish mathematician Carl Ferdinand Degen in 1821. Is this letter in existence today? Do we have any evidence of this purported "solution" and what it looked like? It's great fun to be looking at the blunders of the greatest mathematicians.

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    $\begingroup$ The paper Abel's Surviving Manuscripts includes an inventory of surviving letters. This list does not include his letter to Degen of 1821, but does include his letter to Degen of 1824 which is currently held by the Royal Danish Library. Much of his original writing was lost in a fire. $\endgroup$ – Nick Jun 5 at 22:41
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    $\begingroup$ Very good question. Note that even though the letter does not exist now, there still could be evidence that it existed. $\endgroup$ – Mark Sapir Jun 8 at 15:12

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