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.
Maryam Mirzakhani, the first Iranian and first woman to win the Fields medal, died of breast cancer in July 2017. She was only 40 years of age.
Évariste Galois (1811 - 1832), aged 20, was killed in a duel. He is known for Galois theory and he wrote his most notable results down in the night before the duel. You can also find more information about him and why he was killed in this question.
Niels Henrik Abel (1802 - 1829), aged 26, died of tuberculosis. He is mainly known for proving the Abel-Ruffini theorem, that had been open for hunderds of years, but also for several other results. However, he was barely recognized during his lifetime and because of that he was very poor. He died two days before he got a letter that he was appointed as a professor at the Berlin university.
Srinivasa Ramanujan (1887 - 1920) died at the age of $32$, according to Wikipedia the cause was:
A 1994 analysis of Ramanujan's medical records and symptoms by Dr. D.A.B. Young concluded that it was much more likely he had hepatic amoebiasis, a parasitic infection of the liver widespread in Madras, where Ramanujan had spent time. He had two episodes of dysentery before he left India. When not properly treated, dysentery can lie dormant for years and lead to hepatic amoebiasis, a difficult disease to diagnose, but once diagnosed readily cured.
Bernhard Riemann (1826–1866) died at the age of 39. Paraphrasing the following from Wikipedia:
The son of a poor pastor, he enrolled at age 19 at the University of Göttingen to obtain a degree in Theology. There Gauss urged him to become a mathematician. When he was 31, there was an attempt to promote him to extraordinary professor status. When he was 33, Dirichlet died, and he became head of the department of mathematics.
He is known for Riemannian geometry (Riemann surfaces etc.), the Riemann integral (the first rigorous formulation of the integral), one of the most influential papers in analytic number theory, in which he stated the Riemann hypothesis, and a few other things.
In 1866, the Austro-Prussian War broke out. The armies of Prussia and Hanover clashed in Göttingen. Riemann fled the city. In Italy, he died of tuberculosis. (The war lasted just over two months, from June to August 1866.) He was 39. Much of his unpublished work was lost.
Eugenio Elia Levi (1883-1917), the one of Levi decomposition in Lie algebras, was killed in action during WWI to which he participated as a volunteer. It is often said that his early death played a role in the Italian school of geometry leavng largely unexplored the subject of Lie algebras and Lie groups.
Andreas Floer (1956-1991) who introduced what is nowadays called Floer homology, ICM plenary speaker in 1990, commited suicide at age of 34. He opened up a completely new subject (symplectic topology) and, in fact, the list of posthomous paper speaks in itself.
Frank Ramsey died before his 27th birthday. He started Ramsey theory, which is a very active field in mathematics.
Yutaka Taniyama (12 November 1927 – 17 November 1958) was a notable Japanese mathematician known for the Taniyama–Shimura or Taniyama–Shimura–Weil conjecture now referred to as the Modularity theorem which "states that elliptic curves over the field of rational numbers are related to modular forms."
Proof of a significant special case of the modularity theorem (for semistable elliptic curves) was an essential component of the proof of Fermat's last theorem.
From here:.
On 17 November 1958, Taniyama committed suicide. He left a note explaining how far he had gotten with his teaching duties, and apologizing to his colleagues for the trouble he was causing them. His mystifying suicide note read:
"Until yesterday I had no definite intention of killing myself. But more than a few must have noticed that lately I have been tired both physically and mentally. As to the cause of my suicide, I don't quite understand it myself, but it is not the result of a particular incident, nor of a specific matter. Merely may I say, I am in the frame of mind that I lost confidence in my future. There may be someone to whom my suicide will be troubling or a blow to a certain degree. I sincerely hope that this incident will cast no dark shadow over the future of that person. At any rate, I cannot deny that this is a kind of betrayal, but please excuse it as my last act in my own way, as I have been doing my own way all my life."
Mikhail Yakovlevich Suslin (1894-1919). Known for "Suslin sets" and the "Suslin hypothesis". He died of typhus following the Russian Revolution. He was 25. LINK
I recently read a very interesting book Naming Infinity about the Moscow school of mathematics.
Gotthold Eisenstein is a classic example. This prodigious young mathematician was held in the highest esteem by none other than Gauss himself, and he was also given encouragement and support by Jacobi and Kummer. He worked in number theory and analysis, publishing, for example, proofs on the laws of quadratic, cubic and quartic reciprocity. He always suffered from ill health, however, and died at the age of 29 of tuberculosis.
Pavel Urysohn, known for his eponymous Metrization Theorem and also eponymous Lemma. He died at the age of 26 in a drowning accident off the coast of Brittany, France. He did fundamental work in the then nascent field of point-set topology.
Joseph Liberman was killed in WW2 at the age of 23. He defended his thesis during a short vacation in Leningrad. The idea in his thesis is one of the most fruitful in comparison geometry, which was developed further by Alexandrov's school.
Jacques Herbrand (1908-1931) died et 23 in an accident during a mountain excursion. He made fundamental works in logic.
"This page features a collection of mathematicians who died under unfortunate or unfitting circumstances."
Some of those not already mentioned in previous answers are
Vladimir Markov, 1871-1897 (25, tuberculosis)
René Gâteaux, 1889-1914 (25, died in battle during WWI)
Stanisław Saks, 1897-1942 (44, murdered by the Gestapo)
Dénes Kőnig, 1884-1944 (60, suicide after Hungarian Nazi coup)
Dmitri Egorov, 1869-1931 (61, starvation while on hunger strike)
Archimedes, 287-212 (75, killed)
Let's add Hypatia and Hippasus (although we're straying into legend here).
In a footnote on page 4 of Mathematicians Fleeing from Nazi Germany, author Reinhard Siegmund-Schultze names over two dozen mathematicians murdered by the Nazis.
EDIT: I should also mention Walter Koppelman, murdered by a graduate student at Penn in 1970.
Raymond E. Paley (7 January 1907 – 7 April 1933) fulfills both conditions asked for in the question. He died young, with 26 years, just after having started his collaboration with Wiener (see Paley-Wiener integral), and in a tragic way. Namely, he was killed by an avalanche, while his death was witnessed by companions lower down the mountainside.
Source: Wikipedia
Oswald Teichmüller (1913–1943), was a gifted German mathematician who worked on Riemann surfaces, among other subjects. He was also a dedicated Nazi, who volunteered for combat on the Eastern Front and was killed in action in September 1943.
Heinrich Kornblum proved an analogue to Dirichlet's theorem on arithmetic progressions in the setting of polynomial rings over finite fields for his PhD thesis. Sadly he was called to fight in WWI and died in battle. His advisor, Edmund Landau, was tasked with typing and publishing the work of his student. You can find a source in Number Theory in Function Fields by Rosen.
Gustav Roch, well-known for his Riemann-Roch theorem, died at the age of 26 of tuberculosis, in 1866, just a few months after Riemann's death.
Wolfgang Döblin, interested in probability theory, and had Maurice Fréchet as doctoral advisor, committed suicide at the age of 25.
Lu Jiaxi (1935 - 1983) was a self-taught Chinese mathematician who solved a major problem in combinatorial design theory. He was born in a poor family and his father died when he was in junior middle school. Working in the factory for several years, he self-studied and got into university majoring in physics.
Fascinated by the Kirkman's schoolgirl problem while in university, he self-studied math and solved a generalized version of the problem in early 1960s, and he wrote a paper on it. However, being a physics teacher at a middle school in a remote city, his paper was rejected by Chinese math journals, and then the Cultural Revolution started. After the Cultural Revolution, he found out that the same problem was later solved and published in 1971 by Ray-Chaudhuri and R. M. Wilson.
He turned his attention to the problem of existence of large sets of disjoint Steiner triple systems, which was very much open at the time. As a school teacher, he could only worked in the evenings on the problem. His health was poor due to heavy work and poverty. He solved the problem and submitted it to Journal of Combinatorial Theory, Series A. The journal published first three of his papers in March 1983, it was then the Chinese mathematicians discovered him. Tragically, after attending the general conference of the Chinese Mathematical Society in October that year, he hurried back home, and in that very evening of his arrival he had a heart attack and died, leaving the seventh paper which was the last part of his proof unfinished. The President of the University of Toronto wrote to the principal of his school asking the principal to allow Lu Jiaxi to be transferred to a university, but it was too late.
Vladimir Voevodsky died on September 30, 2017 at the age of 51. He won the Fields medal in 2002 (due to the proof of the Milnor conjecture)
Ludwig Scheeffer (1859-1885) was a gifted mathematician. At 25 he became a Privatdozent in Munich. He died at only 26. In 1884, only 10 years after the invention of set theory and way before its breaktrough in 1891 he wrote in an Acta Mathematica paper about sets of first cardinality. Georg Cantor wrote an obituary which is reprinted in his collected papers pp. 368f.
Mukremin Nesheli.
He was a young Turkish mathematician. He had such strong mathematical abilities that the Canadian mathematician Langlands immediately recognized him and Langlands wanted to invite him to Yale University. But Mukremin was a leftist and was killed by a right-wing group in Turkey. This story always reminds me of Evariste Galois.
James Gregory also died very young. He discovered the basic ideas of Calc the same time Newton did...he died at 36 only 1 year after accepting a position at the University of Edinburgh
Oded Schramm died in a climbing accident at the age of 46. He is best known for his work on Schramm–Loewner evolution. He also contributed to Wikipedia.
Felix Hausdorff LINK
This is not "very young" but it is still tragic.
Hausdorff was a German Jewish mathematician. He is also known for his work in astronomy, philosohy, and even literature (under the pseudonym "Paul Mongré"). When the Nazis came to power in Germany, Hausdorff was retired, and he was allowed to remain in his house in Bonn. For a long time, the Nazi government ignored him, instead concentrating on purging active Jewish academics.
But finally in 1942 Hausdorff heard that they were coming to deport him to a camp. Felix, his wife, and his wife's sister committed suicide by taking barbiturates. He was 73.
https://www.realclearscience.com/blog/2015/02/mathematicians_die_in_horrible_ways.html refers to Kellen Myers's list, and exemplifies with:
Or what about Austrian American mathematician Kurt Gödel? Considered by some to be just as influential a logician and philosopher as Aristotle, he sadly succumbed to crippling paranoia later in life. In his sixties, he became convinced that his food was being poisoned, and would only trust the cooking of his wife Adele. When she was hospitalized for six months in 1977, Gödel refused to eat, and subsequently died of starvation.
https://www.usatoday.com/story/tech/2015/03/08/mathematician-deaths/24605901/ exemplifies with:
There's Alan Turing and Dénes Konig, both of whom killed themselves.
Wikipedia details Kőnig's rational suicide:
After the occupation of Hungary by the Nazis, he worked to help persecuted mathematicians. On October 15, 1944 the National Socialist Arrow Cross Party took over the country. Days later on October 19, 1944 he committed suicide to evade persecution from the Nazis being a Hungarian Jew.[1]
There are a few notable ones from Computer Science and Logic:
Alan Turing (famously) died at the age of 41, most likely due to suicide from mental issues cause by estrogen he was being forced to take
Gerhard Gentzen died at the age of 45, during WWII. His death isn't always viewed as a tragedy, since he was fighting for the Nazis. But he invented both Natural Deduction and Sequent Calculus, and was hugely fundamental in the study of logic.
Kurt Gödel wasn't young (71), but he suffered from extreme mental illness, so his death was tragic. He died when his wife was hospitalized and he refused to eat any food, for fear that others would poison him.
Roger Cotes, a contemporary of Newton and best known for the Newton-Cotes quadrature rules in numerical integration, died of a fever aged only 33.
Newton supposedly said of his death 'If he had lived we would have known something': this is extremely high praise given that Newton was generally not inclined to praise the work or intellect of others.
Archimedes of Syracuse (287 - 212 BC) died in a tragic episode of the Second Punic War between Rome and Carthage. At that time he was already 75 years old.
Syracuse was an important Greek colony on the island of Sicily with good relations to Rome. However, during the Second Punic War Syracuse ended up being under a long Roman siege. One reason for the length of the siege was the ingenuity of Archimedes.
Finally, the city fell and Archimedes was killed by an angry Roman soldier as he didn't want to interrupt his geometrical studies. His alleged last words were:
"Noli turbare circulos meos" ("Do not disturb my circles!")
C P Ramanujam, an Indian Mathematician, not to be confused with Srinivasa Ramanujan, one who worked with GH Hardy.
Ramanujam's achievements at High School had been outstanding and he had shown that he was extraordinarily gifted, so he entered Loyola College with great expectations. He continued his interest in chemistry but it was mathematics that he specialised in, taking Mathematics Honours after obtaining his Intermediate qualification. He was awarded a B.A. with Honours in Mathematics in 1957 but, strangely for such an outstanding student, he only obtained a second class degree. This may have been a result of starting his university education at so young an age before he was really ready, for the second class degree no way reflected his remarkable mathematical abilities. On the other hand it may have resulted from a lack of belief in himself which haunted Ramanujam throughout his life.
Ramanujam felt that he did not have what it takes to solve the big problems of mathematics, and he had no wish to solve small routine problems. Again, as in his undergraduate course, it would appear to be a psychological problem rather than a mathematical one but for Ramanujam, it was a very real problem and he became more and more frustrated.
Mumford writes
It was a stimulating experience to know and collaborate with C P Ramanujam. He loved mathematics and he was always ready to take up a new thread or pursue an old one with infectious enthusiasm. He was equally ready to discuss a problem with a first year student or a colleague, to work through an elementary point or puzzle over a deep problem. On the other hand he had high standards. He felt the spirit of mathematics demanded of him not merely routine developments but the right theorem an any given topic. He was sometimes tormented by these high standards, but, in retrospect, it is clear to us how often he succeeded in adding to our knowledge, results both new, beautiful and with a genuine original stamp.
Back in India after his year at the University of Warwick, Ramanujam asked for a Professorship at the Tata Institute ,but be based in Bangalore where a new branch dealing with applications of mathematics was being set up. This was agreed and he taught analysis in Bangalore but, again in the depths of depression caused by his illness, he tried again to leave the Institute and obtain a university teaching post. While waiting for an offer of such a post from the Indian Institute at Simla, he took his life with an overdose of barbiturates.
No one mentioned John and Alicia Nash (if Alicia was a theoretical physicist, then I think she counts), even though they died earlier in 2015, the year the question was posted.
They died in a car accident.
Sonya Kovalevskaya died at the age of 41, of the 'coronavirus' of her time. From Wikipedia:
In 1889, Kovalevskaya fell in love with Maxim Kovalevsky, a distant relation of her deceased husband, but insisted on not marrying him because she would not be able to settle down and live with him.
Kovalevskaya died of epidemic influenza complicated by pneumonia in 1891 at age forty-one, after returning from a vacation in Nice with Maxim...
Kovalevskaya's mathematical results, such as the Cauchy–Kowalevski theorem, and her pioneering role as a female mathematician in an almost exclusively male-dominated field...
Also her husband, paleontologist Vladimir Kovalevsky, had committed suicide 8 years earlier.
André-Louis Cholesky (1875-1918) was killed in action near the end of World War I:
Cholesky died from wounds received on the battle field on 31 August 1918 at 5 o'clock in the morning in the North of France. After his death one of his fellow officers, Commandant Benoit, published Cholesky's method of computing solutions to the normal equations for some least squares data fitting problems in Note sur une méthode de resolution des équations normales provenant de l'application de la méthode des moindres carrés à un système d'équations lineaires en nombre inferieure à celui des inconnues. Application de la méthode à la resolution d'un système defini d'équations lineaires, published in the Bulletin Géodesique in 1924.
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.
Blaise Pascal a French mathematician, physicist, and philosopher died at the age of 39.
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.
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.
These mathematicians (or very mathematical non-mathematicians) died young (<50) and/or from non-natural causes; I did not see these names:
Yom Tov Lipman Lipkin (c.1846-c.1876), smallpox. Codiscoverer of the Peaucellier-Lipkin linkage. A son of the famed Salanter rabbi, founder of the Mussar movement.
Hermann Minkowski (1864-1909), appendicitis. Number theorist, but best known for his work in relativity.
Janina Hosiasson (1899-1942), murdered by Gestapo. Foundations of probability and inference. Wife of:
Adolf Lindenbaum (1904-1941), murdered by Gestapo. Mathematical logic, published little, but collaborated widely, especially with Tarski.
Duro Kurepa (1907-1993), robbed and murdered during the post-Yugoslavia wars.
Carol Karp (1926-1972), cancer. Major founder of infinitary logic.
John Nash (1928-2015), car crash, wife also killed. Career cut short by schizophrenia.
Karel de Leeuw (1930-1978), murdered in his Stanford office by his perpetual grad student. Analyst.
Richard Montague (1930-1971), robbed and murdered at home, apparently by strangers he picked up cruising. Logic, philosophy, linguistics.
Robert Hamilton Boyer (1932-1966), murdered, a Texas tower massacre victim. General relativity, Boyer-Lindquist coordinates.
Frank Adams (1930-1989), car crash. Major topologist.
Alan Mekler (1947-1992), cancer. Applications of set theory and model theory to algebra.
Boris Weisfeiler (1941-?1985), disappeared while hiking in Chile during the Pinochet regime. Assumed kidnapped, tortured and murdered.
Zoltan Balogh (1953-2002), sudden illness (with history, also father Tibor died young). Set-theoretic topologist.
Elizabeth Gardner (1957-1988), cancer. Theoretical physicist specializing in disordered systems, her most mathematical work was the statistical physics of neural networks.
Moez Alimohamed (1967-1994), robbed and murdered outside his apartment. A UPenn math grad student, he had just finished his first paper/thesis. Published and degreed posthumously.
Michael B. Cohen (1992-2017), sudden illness. Up and coming superstar in CS, especially algorithms.
William Kingdom Clifford suffered from a nervous breakdown and exhaustion on at least two occasions, almost certainly due to overwork, before passing away at the age of 33 from tuberculosis on the island of Medeira, Portugal, while recovering from a collapse.
Clifford produced the correct algebraic description of three dimensional Cartesian vectors by combining the rotational algebra of complex numbers and Hamilton's quaternions with Gibbs and Heaviside's reworking of quaternions, and by building on the ideas of Grassman.
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.
Ada Lovelace, the 1st computer programmer, died at 36yo. From Wiki:
Lovelace died at the age of 36 on 27 November 1852,[48] from uterine cancer probably exacerbated by bloodletting by her physicians.[49] The illness lasted several months, in which time Annabella took command over whom Ada saw, and excluded all of her friends and confidants. Under her mother's influence, Ada had a religious transformation and was coaxed into repenting of her previous conduct and making Annabella her executor.[50] She lost contact with her husband after confessing something to him on 30 August which caused him to abandon her bedside. It is not known what she told him.[51] She was buried, at her request, next to her father at the Church of St. Mary Magdalene in Hucknall, Nottinghamshire. A memorial plaque, written in Latin, to her and her father is in the chapel attached to Horsley Towers.[citation needed]
Misha Alekhnovich (1978-2006), a very talented mathematician in the area of Complexity Theory: http://people.cs.uchicago.edu/~razborov/files/misha_sigact.pdf See also: http://people.cs.uchicago.edu/~razborov/files/foreword.pdf
Takeo Nakasawa was a Japanese mathematician who died at age 33. He published 4 papers introducing the subject of matroid theory. At the same time this subject was independently discovered elsewhere by Hassler Whitney, leading to Nakasawa's contributions being lost until much later. After this, he became a bureaucrat in Japanese-controlled Manchuria in 1938. Quoting wikipedia:
With the defeat of Japan in 1945, the Soviets took control of Manchuria and Nakasawa was carted off to Siberia. He died of dystrophia at the age of 33 in Khabarovsk in the Soviet Union in 1946.
In Europe, the First World War 1914-18, also called the Great War, was an extremely traumatic event, that stopped an era of well-being and progress (often referred to as La belle époque).
The European war 1914-18 involved all social components of the major European nations, with intellectuals and students in the forefront. The consequences were disastrous in terms of loss of human lives and careers of excellent scholars cut short. A drama that changed the destiny of a generation of scientists in many countries, the scientific community itself, and the course of scientific research.
Among the scientists, many mathematicians of many European countries died in the battlefield and in the trenches during the Great War.
I mention here, in particular, the tragedy of what has been called the incomprensible écatombe in France. In particular, 800 students of the École Normale Supérieure of Paris took part in the war, and 239 of them lost their lives. Among them, also many mathematicians (see $[1]$).
The war left a deep wound and a traumatic memory in the country, which influenced also the Bourbaki group: they described the post-war period in France as a “mathematic desert”, and they attributed the causes to the loss of a generation, decimated by the war.
According to some historian of mathematics, the trauma of the war influenced the abstract nature of the mathematics of the Bourbaki group. The historian of mathematics David Aubin writes:
Dans les années 1930, le groupe de mathématiciens Bourbaki a promu une vision abstraite et universelle de sa discipline en rupture avec celle de ses prédécesseurs. Le sacrifice de nombreux jeunes mathématiciens durant la Première Guerre mondiale a sans doute fortement contribué à ce revirement.
[During the years 1930, the Bourbaki group of mathematicians has prompted an abstract and universal vision of their subject, in rupture with the one of their predecessors. The sacrifice of many young mathematicians during the First World War has undoubtedly contributed to this reversal] ( $[2]$, p.1, my transl.)
And in his book L’Élite sous la mitraille $[1]$ David Aubin writes:
Au course des semaines le plus sanglantes de l’histoire de France, entre le 22 août et le 20 octobre 1914, douze mathématiciens élèves de l’École Normale supérieure de la rue d’Ulm, à Paris, tous agrégés de mathématiques et, pour la plupart, auteurs de travaux remarqués, publiés et recencés dans le repertoire de reference, le “Jahrbuch über die Fortschritte der Mathematik” (JFM), sont tués sur le champs de bataille du Nord et de l’Est. Dans les années qui suivent, dix autres jeunes mathematicians connaîtront le même sort.
During the bloodiest weeks of the history of France, between the 22th of August and the 20th of October 1914, twelve mathematicians, all former students of the École Normale Supérieure de la rue d’Ulm, in Paris, all of them agrégés of mathematics and, for the most part, authors of works reported, published and reviewed in the bibliographic repertory, the “Jahrbuch über die Fortschritte der Mathematik” (JFM), are killed on the battlefield of the North and the East. In the following years, ten other young mathematicians will suffer the same fate. (p. 7, my transl. )
In 1923, built thanks to a subscription, the Monument aux morts de l’École Normale Superiéure [Monument to the Victims of the École Normale Superiéure] in Rue de l’Ulm, by the sculptor Paul Landowski, was inaugurated.
Out of $239$ normaliens whose name appears on the monument to the victims, $22$ are agrégés of mathematics.
Below the Tableau that gives the list of those mathematicians who died in the First World War: as the table shows, fourteen of them died in 1914, four in 1915, three in 1916 and another, Paul Viple, some days after the Armistice, because of the injuries sustained on the 25th of October 1918. (source $[1]$, p. 10)
$$\;$$
We can notice the name of René Gateaux, whose name is known for the Gateux derivative, and whose works on functional analysis impressed the famous Italian mathematician Vito Volterra. $$\;$$
Below an image of the Monument to the Victims of the École Normal Supérieure:
References
$[1]$ Aubin, David, L’élite sous la mitraille. Les normaliens, les mathématiques et la Grande Guerre, 1900-1925, Editions Rue d’Ulm/Presse de l’École normale supériueure, 2018.
$[2]$ Aubin, David, ‘Des mathématiciens sous la Grande Guerre’, https://www.pourlascience.fr/sd/histoire-sciences/des-mathematiciens-sous-la-grande-guerre-20451.php
Sophie Germaine and hypatia.Sophie Germaine died at the age of 55 due to breast cancer. Hypatia was brutally murdered by a mob of Christian fanatics. They pulled her from her carriage on a street in Alexandria, dragged her to a church, stripped her naked, beat her to death and/or flayed her, tore off her limbs, and burned her remains.Damascius adds that they also cut out her eyeballs.
