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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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Roger Cotes died both young (at the age of 33) and in a tragic way (from a "violent fever").

According to Boyer's History of Mathematics, Cotes obtained Euler's formula some decades before Euler in the equivalent form $\ln(\cos \theta + i \sin \theta) = i\theta$, being published in Philosophical Transactions, 1714. He also, along with De Moive, obtained the identities $\sin x = \frac{e^{ix} - e^{-ix}}{2i}$ and $\cos x = \frac{e^{ix} + e^{-ix}}{2}$.

Boyer quotes Newton as remarking : "If he had lived we would have known something."

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