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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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Mojżesz Presburger was one of the victims of the Holocaust.

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Renato Caccioppoli committed suicide at 55, mainly due to his disappointments towards politics. He is known for his work on functional analysis, his masterpiece is "Measure and integration of dimensionally oriented sets" (Misura e integrazione degli insiemi dimensionalmente orientati). He was nephew of the Russian revolutionary Mikhail Bakunin, he was also arrested due to its anti-fascism. His life (and death) are portraited in the Venice Film Festival awarded film Death of a Neapolitan Mathematician.

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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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Aleksandr Mikhailovich Lyapunov (Александр Михайлович Ляпунов) committed suicide:

In 1917 Lyapunov left St Petersburg to take up a post at the university in Odessa, on the Black Sea coast. He taught at the university but in the spring of 1918 his wife's health began to deteriorate rapidly. Natalia Rafailovna suffered from a form of tuberculosis and Lyapunov was greatly disturbed to watch her health fail. On 31 October 1918 Lyapunov's wife died and later that day Lyapunov shot himself. He died three days later in hospital.

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Matvei Petrovich Bronstein was a Soviet era theoretical physicist who was arrested in the night of August 6th during Stalins Great Terror. His crime was to believe in communism but not in Stalinism. He was aged just thirty and was executed in a Leningrad prison several months later, in February 1938. In fact, at the time of his arrest he already knew he was under observation by Stalins security apparatus. His wife, Lydia Chukovskaya, was finally allowed to see her husbands inquisition file in 1990 after the collapse of the Soviet regime. At the time of his arrest she was told he had been sentenced to a labour camp for ten years without the right of correspondence. In his file she found the arrest warrant issued by the Kiev state security department on the 5th August, it said:

M. P. Bronstein who is trying to escape arrest should be detained for an active involvement of a Leningrad counter-revolutionary organisation.

They were friends of Andrei Sakharov, a physicist who was involved in the Soviet nuclear weapons programme and was later known for advocating civil liberties and reforms in the Soviet Union. In fact, he won the Nobel peace prize for his efforts and the Sakharov prize is named in his honour and awarded annually by the European Parliament for people and organisations dedicated to human rights and freedoms.

Bronstein counts amongst one of the first pioneers of quantum gravity. Landau had claimed that the Heisenberg uncertainty principle called into question the reality of the electromagnetic field in that it could not be probed with arbitrary precision. Bronstein showed that Landaus analysis was incorrect by showing that it could so be probed by an arbitrarily massive measuring apparatus, but he showed that there was a quantum limit when it came to gravity and this limit became ma icrst when particles approached what is now called the Planck mass. This is the energy scale at which quantum gravity effects are expected to become manifest.

Bronstein of course was not the only physicist to suffer at Stalins hands. According to Gennady Gorelik, his biographer, two other talented physicists were arrested at the same time: Alexander Witt from Moscow and Semen Shubin from Sverdlosk. They were sentenced to five and eight years forced labour respectively. They also both died in the winter of 1938 in the Kolyma.

One imagines these examples can be multiplied many times.

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