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When I first thought of this question, I wanted to ask: If you could give one mathematician his remaining life until an average age for the time he lived in, who would you choose? However, this question is a bit too subjective for SE. So I decided to modify it to: Which mathematicians died very young or in a tragic way?

Two obvious candidates are Galois and Abel. I included more detail about them in an answer. But I'd like to know whether there are more examples.

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    $\begingroup$ Just go to www-history.mcs.st-andrews.ac.uk/Indexes/_500_AD.html and choose within your age range. I voted to close this question: what does it have to do with history of science or math? $\endgroup$ – Alexandre Eremenko Nov 27 '15 at 21:42
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    $\begingroup$ The nature of Alan Turing's death is still debated so I won't post it as an answer. $\endgroup$ – uhoh Jul 18 '17 at 6:37
  • $\begingroup$ we also have Thales $\endgroup$ – Guy Fsone Jul 21 '17 at 14:29
  • $\begingroup$ @GuyFsone You mean Thales of Miletus, who, according to the oracle of delphi died in his 70's, or a different Thales? $\endgroup$ – kimchi lover Sep 11 '17 at 1:12
  • $\begingroup$ Thales was not young of course he died in a tragic way $\endgroup$ – Guy Fsone Sep 11 '17 at 7:51

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The list is already too long, and can be made much longer, so let me refer to two lists instead of mentioning individuals.

The book by A. Goodman, Univalent functions, vol. II (Mariner Publishing Co., Inc., Tampa, FL, 1983, MR0704184) has an Appendix which contains a long list of mathematicians victims of the Nazi regime in Europe. Certainly not all of them died young, but they died in a tragic way, no doubt.

There is also a (incomplete) list on Wikipedia of mathematicians who committed suicide https://en.wikipedia.org/wiki/Category:Mathematicians_who_committed_suicide.

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