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I am not sure that this is appropriate at MO, so if not, please, delete this.

This is inspired by David Hansen's question where he asks about mathematics done during the WWII. I would like to ask the opposite question:

what are some examples of mathematical research interrupted by a war?

Everyone is aware of the terrible damage inflicted by the war on the Polish mathematical school. The dramatic destinies of Stefan Banach (who lived in very difficult conditions during the WWII and died soon after it), Juliusz Schauder (killed by Gestapo), Józef Marcinkiewicz (killed by NKVD) and of many others have much influence on the conscience of mathematicians in Central Europe (including Russia, and I believe, not only here).

When I was a student an idea was popular in Soviet Union that war moves science. I must confess, I am a partisan of the opposite one: war kills science. I would be grateful to people here who would share their knowledge and give illustrations.

P.S. By war I mean any war, not necessarily WWII.

Sergei Akbarov
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    If people would explain why they voted to close this question, I would most likely delete it myself. – Sergei Akbarov Dec 17 '17 at 11:25
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    I voted to close because this is not a mathematical question. I appreciate that it raises issues that some people might like to discuss, but I do not think that this is the right place. The linked question by David Hansen was from 2010; I believe that it would be closed if it was asked today. – Neil Strickland Dec 17 '17 at 11:33
  • Ah, I see. I did not notice that David's question was old, excuse me. – Sergei Akbarov Dec 17 '17 at 11:36
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    You forgot Felix Hausdorff, who died a tragic death in an internment camp. This surely counts as interrupted research since during the first years of war he kept working tirelessly despite all hardship and would surely have continued to do so. –  Dec 17 '17 at 12:07
  • Yes, Hausdorff is another example, thank you, Emmanuele. – Sergei Akbarov Dec 17 '17 at 12:12
  • Why not consider the mathematicians whose careers were catapulted to success during the war? For instance, the war was monumental for the careers of mathematicians who worked on the Manhattan Project like Einstein and Oppenheimer. – nick012000 Dec 17 '17 at 12:20
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    I thought they were physisists. – Sergei Akbarov Dec 17 '17 at 12:30
  • @NeilStrickland I voted to close this. Or, maybe this can be moved somewhere... – Sergei Akbarov Dec 17 '17 at 12:37
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    @EmanueleTron, Hausdorff did not die in a camp. He and his wife committed suicide at home when they received a summons that would eventually lead to them being moved to a camp if they followed it. The effect on his research was the same, but the circumstances surrounding his death should still be recorded accurately. – KConrad Dec 17 '17 at 13:53
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    This question could be moved to the history of science and math stackexchange site. – KConrad Dec 17 '17 at 13:59
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    @KConrad yes, it seems to me, this would be a good solution. I don't know, which place is better, but I think this is not important. – Sergei Akbarov Dec 17 '17 at 14:05
  • @KConrad Thanks, I was under the erroneous impression that they committed suicide after deportation. –  Dec 17 '17 at 14:52
  • I don't think it is accurate to say that Banach "was an object of medical experiments during WWII". – Martin Argerami Dec 17 '17 at 15:04
  • @MartinArgerami I think you can correct this. Or tell me, I'll do this. – Sergei Akbarov Dec 17 '17 at 15:11
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    It's your question, and it's not a big deal. According to the same article you quoted, Banach was forced out of the university, and as means to survive he worked as a "lice-feeder" for a lab that prepared typhus vaccines. It was partially dangerous (although no one ever died from the practice), but it was not an experiment and he was a willing participant. – Martin Argerami Dec 17 '17 at 16:35
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    @MartinArgerami, I think this is a big exaggeration: "he was a willing participant". When a person has a choice between a starvation death, a concentration camp and "lice-feeding", and he chooses "lice-feeding", this is not called "a willing participant". – Sergei Akbarov Dec 17 '17 at 16:42
  • @SergeiAkbarov: unless he was offered "lice-feeding or concentration camp", he was a willing participant. The article is not clear on that point, and I have no other sources. Still, not an "experiment". – Martin Argerami Dec 17 '17 at 16:45
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    "Lice-feeding" was not an experiment? I thought it was... – Sergei Akbarov Dec 17 '17 at 16:46
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    Martin, he had no choice. It was not like: "You can work as a professor in our university, or if you wish, you can feed lices. What do you prefer?" – Sergei Akbarov Dec 17 '17 at 16:50
  • From the article: "Banach was employed as lice feeder at Professor Rudolf Weigl's Typhus Research Institute. Employment in Weigl's Institute provided many unemployed university professors and their associates protection from random arrest and deportation to Nazi concentration camps." The implication from the article seems to be that, without a university job and risking deportation, the institute worked as a safe haven. As for lice-feeding, the corresponding Wikipedia article doesn't describe it at all as an experiment, but as a method to produce a vaccine that was publicly released. – Martin Argerami Dec 17 '17 at 16:53
  • Gangsters come to your house and say: "you can either be killed immediately or we'll make a vaccine from you". I would not call this "safe haven". But I'll remove the mentioning of experiment. – Sergei Akbarov Dec 17 '17 at 17:15
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    May be the sister site dedicated to history of mathematics and sciences would be more appropriate for this? – Jyrki Lahtonen Dec 17 '17 at 17:37
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    @JyrkiLahtonen I have no objections. – Sergei Akbarov Dec 17 '17 at 17:38
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    I am undecided, leaving it for mods and the others to decide. I'm not sufficiently informed about whether this is on-topic at MathOverflow. On the other hand HSM.SE is still in beta, so the question might disappear if the site doesn't lift off. Unfortunately (but also understandably) political opinions of the affected mathematicians seem to have poisoned the discussion somewhat. HSM.SE might be more immune to that? – Jyrki Lahtonen Dec 17 '17 at 17:43
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    Jyrki, I don't know about HSM.SE, but the political views here do not differ much in my opinion. I expected more or less this picture. – Sergei Akbarov Dec 17 '17 at 17:50
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    @KConrad, Jyrki: Generally, segregating history of mathematics to another site is, in my opinion and experience, unfortunate. – Francois Ziegler Dec 17 '17 at 21:02
  • The title does not fit the question. A mathematical research can be interrupted because a mathematician decides to get involved in the war (for whatever reasons) and leaves math research (I can think of Turing or von Neumann, although I'm unable to claim that they completely left math research). A contrario, an inactive mathematician can have an unhappy destiny, and this does not affect mathematical research. – YCor Dec 18 '17 at 03:14
  • @YCor I corrected this. – Sergei Akbarov Dec 18 '17 at 03:52
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    I'm not the most competent person to turn this into a good answer, but Wolfgang Döblin comes to mind. – Michael Greinecker Dec 18 '17 at 11:10
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    I would rather say that war moves engineering. Without having any sources to go on other than my gut, I would think it reasonable that if you want a military edge in a war, you don't often go do science and discover new things. You take the things science says ought to be possible, and find ways to actually make it happen in the real world (the Manhattan project comes to mind). Or you take something that exists but is too expensive (or unreliable), and you find ways to make it much cheaper (or sturdier) so that you can supply your army (for instance, air planes during first world war) – Arthur Dec 18 '17 at 13:08
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    "[Leray's] main work in topology was carried out while he was in a prisoner of war camp in Edelbach, Austria from 1940 to 1945. He concealed his expertise on differential equations, fearing that its connections with applied mathematics could lead him to be asked to do war work." https://en.wikipedia.org/wiki/Jean_Leray – Steve Huntsman Dec 18 '17 at 13:56
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    @moderators: I tried to delete this after Neil Strickland's explanation, but the system warned me that this is not good since there were already some answers. I do not know, perhaps this should be moved to another site... Let this be your decision. – Sergei Akbarov Dec 19 '17 at 07:47
  • @EmanueleTron I think, you should add an answer about Hausdorff. – Sergei Akbarov Dec 19 '17 at 09:48
  • Wolfgang Döblin died in 1940 after discovering what we know as ito lemma... – Pierre Dec 20 '17 at 14:17
  • All of the answers so far, bar perhaps one attempt to answer this with anecdotes of people who were interrupted. That doesn't allow for the situation where these interruptions were merely noise compared to the total mathematical research of the time, or even that war boosted mathematical research. Perhaps a better approach would be to map a metric (such as papers published, or maybe you have a better one?) against the number of people dying in wars over time. – Oddthinking Dec 20 '17 at 15:42
  • @Oddthinking, you can ask another question about metric. I do not find answers here anecdotic. – Sergei Akbarov Dec 20 '17 at 15:57
  • @SergeiAkbarov: I wonder if this is a language barrier. These are mostly text book examples of anecdotal evidence. If you try to use them to form an opinion on the question of whether war has a tendency to interrupt mathematical research, you are falling for a logical fallacy. These answers are misleading. – Oddthinking Dec 20 '17 at 16:26
  • @Oddthinking, this is normal when people tell each other stories about what happened and what happens. An old tradition of mankind. And it happens very often that these stories are not just noise, they matter something. You can consider this as an excercise, whether the stories of Banach, or Hausdorff, or Doeblin, or Lindenbaum contain useful information, or not. At the same time nobody prevents you to gather statistics. – Sergei Akbarov Dec 20 '17 at 16:49
  • @SergeiAkbarov: You are offering a defence of logical fallacies? That's a new one on me. Shortcuts in thinking that lead to incorrect understandings do not become acceptable just because they are traditional. I repeat my call to answerers to do better. – Oddthinking Dec 20 '17 at 21:34
  • @Oddthinking, you should axiomatize your logic before accusing somebody in logical fallacies. And accusing all of humanity is an ungrateful task. – Sergei Akbarov Dec 20 '17 at 22:25
  • @SergeiAkbarov: No, it isn't necessary to formalise axioms in order to make informal fallacies. Here are a few you may recognise: Cherry Picking - e.g. only looking for examples that support war interrupting research. Hasty Generalisation - e.g. concluding that war interrupts research based on a few anecdotes. Appeal to tradition - e.g. arguing that because it is traditional to make fallacies, it must be the best way – Oddthinking Dec 20 '17 at 23:01
  • Red Herring fallacy - e.g. trying to divert the conversation continue in axiomatic logic, or accusing someone of being ungrateful when that has nothing to do with the discussion. Appeal to stone - e.g. denying that answers are anecdotes without any supporting reason. – Oddthinking Dec 20 '17 at 23:01
  • Let us continue this discussion in chat. – Sergei Akbarov Dec 21 '17 at 06:27
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    @Oddthinking I don't think answerers need to "do better": the anecdotes given are answers to the exact question displayed in the gray box. Now, the text of the OP might be problematic, where you see the assertion "war kills science" (an interesting topic, but undoubtedly beyond the scope of MO to address satisfactorily). But that's beyond the question asked, and no one is obliged to fix the text. (FWIW, I don't think this is a good question for MO, but MO sometimes indulges in creating big lists with sometimes interesting results, so as a site moderator I usually let the community decide.) – Todd Trimble Dec 21 '17 at 16:45
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    It doesn't obscure the meaning at all, but of course Schauder was executed by the Gestapo, not killed in Gestapo. – LSpice Dec 21 '17 at 17:44
  • @LSpice, in Russian "executed" is just a formal expression, as if an official, responsible for execution, declared that this was done (he would never say "killed"). But people on a street would most likely say "killed", since this is less formal. In English is this different? – Sergei Akbarov Dec 21 '17 at 19:32
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    It was not the verb ('executed' vs 'killed') but the preposition ('by' vs 'in') on which I was commenting. (I actually simply copied the language from your Wikipedia link.) – LSpice Dec 21 '17 at 19:46
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    @ToddTrimble: I agree that list questions are problematic to the Stack Exchange model. But this is also a pound a nail with a shoe/glass bottle question. The question calls for bad research, and the answers comply without challenge, giving a misleading answers to any reader in the future. – Oddthinking Dec 22 '17 at 00:49

18 Answers18

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When I was a student an idea was popular in Soviet Union that war moves science. I must confess, I am a partisan of the opposite one: war kills science. I would be grateful to people here who would share their knowledge and give illustrations on that score.

That is a hard task, since a killed scientist might never produce the work for which he would later have become famous, if he had not died earlier. But coming up with big names being killed (often intentionally) during war times is easy:

  • Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed.
  • Lavoisier was convicted and guillotined on 8 May 1794 in Paris, at the age of 50, along with his 27 co-defendants.

    Lavoisier's importance to science was expressed by Lagrange who lamented the beheading by saying: "Il ne leur a fallu qu’un moment pour faire tomber cette tête, et cent années peut-être ne suffiront pas pour en reproduire une semblable." ("It took them only an instant to cut off this head, and one hundred years might not suffice to reproduce its like.")

  • When the war broke out in 1914, Hasenöhrl volunteered at once into the Austria-Hungarian army. He fought as Oberleutnant against the Italians in Tyrol. He was wounded, recovered and returned to the front. He was then killed by a grenade in an attack on Mount Plaut (Folgaria) on 7 October 1915 at the age of 40.

    In 1907 he became Boltzmann's successor at the University of Vienna as the head of the Department of Theoretical Physics. He had a number of illustrious pupils there and had an especially significant impact on Erwin Schrödinger, who later won the Nobel Prize for Physics for his contributions to quantum mechanics.

  • Gentzen died in 1945 after the Second World War, because he was deprived of food after being arrested in Prague.
Thomas Klimpel
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    Lavoisier was a chemist. A famous mathematician executed during the revolution was Marquis de Condorcet. – Alexandre Eremenko Dec 17 '17 at 14:30
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    Isn't the original question asking specifically about WW2? – Yemon Choi Dec 17 '17 at 21:00
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    Indeed it's ambiguous whether the question is about WW2. But especially, the question is about mathematical research interrupted by the war, not just a list of mathematicians who were killed, or affected in any way. You can imagine math research interrupted by the war without somebody specifically killed, and imagine mathematicians killed but who were inactive at the time of war. Mentioning mathematicians killed (or interrupted in any way...) without mentioning what they were active about, does not, in my opinion, answer the question. – YCor Dec 18 '17 at 01:05
  • @YCor At that time, Gentzen worked on the V2. Archimedes was also constructing weapons at the time of his death. We cannot know what they would have worked on, if war were absent. But they are remembered today for the mathematics they created, not for their weapons. I use gentzen as name for my comments on blogs, so I thought I should mention Gentzen's death. But I wanted to put it in a proper context, but neither his work on V2 nor the fact that he was "deprived of food" are that context. I find that my answer strikes a nice balance... – Thomas Klimpel Dec 18 '17 at 10:26
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When I was a student an idea was popular in Soviet Union that war moves science.

I think this idea is correct in certain sense. If you include preparation to a war. Yes, some individual scientists were killed in action or in some other way as a result of the war. But on the other hand, if you mean by "war" the military competition in general, is not it clear that governments finance science, physics and mathematics first of all, to preserve their ability to develop top military technologies?

I witnessed a real boom in mathematics and science education, and in financing research both in Soviet Union and in the USA during the Cold war, and have no doubts about the real reasons of this boom. Especially nuclear bombs and space technology convinced the governments and the public that one has to invest in fundamental science and mathematics. (I don't have to explain that the whole enterprise of space exploration is a byproduct of military technology development during the Cold war, and also Internet, by the way, and computers too).

And examples from the earlier epochs in history are also ample and well-known. Governments financed research in Astronomy and Celestial mechanics in 18th century for the needs of navigation, to maintain their colonial empires, Napoleon created the principal French scientific centers, etc. There is no doubt that design of war machines gave jobs to physicists and mathematicians in Hellenistic times (Archimedes, for example).

War by itself is bad, of course. For science and for everything else. But preparation to war always was a powerful engine of development of science.

EDIT. Why this point of view is widespread among the former Soviet mathematicians. Soviet Union was a much more militarized society than Western countries. This partially explains the strength of Soviet mathematics (and physics). In other sciences Soviet Union was much weaker. So one can say that Soviet math/science education was so good, and here so many jobs for mathematicians because Soviet Union was a militarized society. After the launch of the first satellite (a byproduct of development of ballistic missiles), Americans made huge investment to the exact sciences and science education.

Alexandre Eremenko
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    Alexander, there is one thing in this position that I can't accept: if preparation to war is the only argument that can convince anybody (especially government), then everything that can't be applied in war (or does not promise immediate application in war), does not deserve research. I would say, the history of Soviet Union showed what happens when people are blinded by the idea of war. In my opinion this slogan - war moves science - is a speculation. Not everything in science follows from this. I do not know the statistics, but the role of war is doubtful for me. – Sergei Akbarov Dec 17 '17 at 14:46
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    Quoting V. I. Arnold: "All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA)." – Rodrigo de Azevedo Dec 17 '17 at 15:32
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    @RodrigodeAzevedo what about Non-commutative geometry? :) – Sergei Akbarov Dec 17 '17 at 15:35
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    I think V.I. Arnold exaggerated. Canadian friends told me once that the math department at the University of Alberta offers courses in fluid dynamics if and only if the key people are not desperately needed by an oil company. – Jyrki Lahtonen Dec 17 '17 at 17:33
  • @Sergei Akbarov: I did not say "everything". I said this is an important factor. What is the weight of this factor among others is subject to discussion. Possibly it is the most important, judging from previous history. – Alexandre Eremenko Dec 18 '17 at 00:48
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    @SergeiAkbarov then everything that can't be applied in war (or does not promise immediate application in war), does not deserve research Ah, Sergei, but there isn't anything that cannot be used for war and really smart generals knew it since the prehistoric times. And they also knew that, as Terry Pratchett put it, "while 99% of philosophy is about truth being beauty and beauty being truth, the remaining 1% says that if you use mirrors curved in a certain way to focus the sunlight on an enemy ship, etc" (Small Gods, quoting from memory). – fedja Dec 18 '17 at 05:40
  • @fedja the vast majority of useful things around are useful in our life without any connection to the war. It is much more convenient to recognize them useful because of their usefulness in everyday life, than to ask permission from "smart generals" for this (and praise after that their wisdom). The chain from a producer to the customer becomes much shorter. – Sergei Akbarov Dec 18 '17 at 06:01
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    @SergeiAkbarov It is much more convenient to recognize them useful because of their usefulness in everyday life If only that recognition had ever come as easily as you seem to imply! :-) But this is a sideline to the original question anyway, so I'll stop here. We can dispute it somewhere else, if you are in the mood. – fedja Dec 18 '17 at 06:08
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    @AlexandreEremenko the question is what plays a bigger role in the desire to develop your business: profit or fear (of neighbors, competitors, etc.) I don't believe that it is possible to separate one from another. But it is evident for me that playing on fear is a dishonest trick. – Sergei Akbarov Dec 18 '17 at 06:25
  • @fedja, this is normal that developement requires investitions. Of course it is much easier to persuade investors by treatening them. But some people consider this to be a prohibited method. – Sergei Akbarov Dec 18 '17 at 06:31
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    @SergeiAkbarov it is evident for me that playing on fear is a dishonest trick Agree 100% Have another globe? – fedja Dec 18 '17 at 06:35
  • @fedja, in each society, independently of globe, the members of this society can understand each other only if they take care of common rules of game. There are no other ways to solve problems but finding common agreement in communications. There is a problem in what I state in my post. It needs discussion, finding common points of view, for its solution. If you are agree then there is no need for us to seek another globe. – Sergei Akbarov Dec 18 '17 at 06:47
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    @SergeiAkbarov If you are agree then there is no need for us to seek another globe I agree. But let's try to convince some other people about that. Putin is on you, Trump on me. Deal? – fedja Dec 18 '17 at 13:21
  • @SergeiAkbarov: The fact is that computers, Internet, nuclear energy, space exploration, and GPS are byproducts of military research. Yes, they happen to be useful in ordinary life. But they were DEVELOPED and financed with military applications in mind. Can you give another comparable motivation of similar developments? – Alexandre Eremenko Dec 18 '17 at 15:01
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    @AlexandreEremenko this is a post factum judgement. You can't prove that these inventions -- computers, internet, etc. -- would have been impossible without the arms race. The other things, which were not less important for mankind, -- books, radio, cinema, television, motor, airplain -- were invented without military. Yes, in 20th century - the era of victorious state control - many things (maybe too many) became in one or another way connected to state and to military. But this doesn't prove the necessity of these mediators. – Sergei Akbarov Dec 18 '17 at 15:38
  • @Sergei Akbarov: yes of course this is a post factum judgment, as all history is. "Alternative history" (=what could happen if) is an empty speculation on my opinion. – Alexandre Eremenko Dec 18 '17 at 15:44
  • Alexandre, this lies in the nature of people: to analyse what happened, why this happened, what would happen if some mistakes would have not been made. I would call this "experience". People use this in their life to solve problems. Usually without reflection of "alternative history". – Sergei Akbarov Dec 18 '17 at 15:49
  • @fedja the necessity to persuade "smart generals" (with exaggeration of their smartness) follows from this cynical axiom, "war moves science". Things become much easier without it. And you underestimate the power of ideas. – Sergei Akbarov Dec 18 '17 at 15:52
  • @Sergei Akbarov: this is not an "axiom" but an experimental fact. And the "power of ideas" is not sufficient: someone has to pay salaries to mathematicians, and to finance math education. I suspect that Archimedes was payed mainly because of his usefulness to the state (construction of war machines). – Alexandre Eremenko Dec 18 '17 at 15:58
  • Alexandre, there must be statistics to persuade people that everything is so simple and cheap. – Sergei Akbarov Dec 18 '17 at 16:09
  • I see more positive idea about mathematics hidden in the V. I. Arnold quote. To whatever extent mathematics has been guided and limited by artificial human purposes like war, there is an opportunity to escape that and possibly return to nature through problems that don't have that kind of motivation by virtue of not having any at all. You know, recreational problems, palindromic primes, the Collatz conjecture, that sort of thing. Cryptography is a lesson that supports fedja's point about the generals finding a way to use it. But I don't see why it always has to turn out that way. – Dan Brumleve Dec 19 '17 at 01:24
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    @fedja: The exact quote: "That's why it's always worth having a few philosophers around the place. One minute it's all Is Truth Beauty and Is Beauty Truth, and Does A Falling Tree in the Forest Make A Sound if There's No one There to Hear It, and then just when you think they're going to start dribbling one of 'em says, Incidentally, putting a thirty-foot parabolic reflector on a high place to shoot the rays of the sun at an enemy's ships would be a very interesting demonstration of optical principles." – tomasz Dec 19 '17 at 15:57
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Mathematicians dying during the war, whether in military action, detention, taking their own life or due to other factors has certainly interrupted mathematical research. However, this is only one of the most dramatic and visible manifestations of war's effect on the mathematical community --- there are many others. There is a well-researched book that deals with all aspects of mathematical life in Nazi Germany, both before and during WWII:

Sanford L. Segal, Mathematicians under the Nazis, Princenton University Press, 2003 (ISBN 0-691-00451-X)

Specifically on the question of Teichmüller's repugnant actions before the war, I would like to recommend

M.R. Chowdhury, Landau and Teichmüller, Mathematical Intelligencer, vol. 17, no. 2, 1995

The author concludes that

Teichmüller was instrumental in perpetrating a heinous crime, the Landau boycott, which destroyed not only a truly great man and mathematician but also a great mathematical center.

Although this article focuses on Edmund Landau, of course he was not the only Göttingen professor affected by the Nazi doctrine of Aryan science, which through the infamous Berufsbeamtengesetz of 1933 eliminated other illustrious scientists from Göttingen, including Max Born, James Franck, Edward Teller, Eugene Wigner, Emmy Noether and Richard Courant. David Hilbert has famously remarked that as a consequence, mathematics in Göttingen does not exist any more (see this discussion of sources for the quote on the HSM stackexchange site).

If you are willing to explore the thesis that war is harmful to mathematical community, both World War I and World War II provide a lot of evidence. For example, French intellectual elite was decimated by the Great War and the country lost a whole generation of mathematicians. Several of Michèle Audin's books deal with these subjects.

Michèle Audin, Fatou, Julia, Montel: The Great Prize of Mathematical Sciences of 1918, and beyond. Springer, 2011 (ISBN 978-3-642-17854-2)

<p>Michèle Audin, Jacques Feldbau, Topologe: Das Schicksal eines jüdischen Mathematikers (1914 - 1945). Springer, 2012 (ISBN 978-3-642-25803-9)</p>
Victor Protsak
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Another example that comes to mind is Karl Schwarzschild, who discovered the first exact solution to Einstein's field equations (which is now named in his honor). He died just a few months after producing that solution in the trenches of WWI.

Yly
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    The original question seemed to be asking about WW2, not other conflicts – Yemon Choi Dec 17 '17 at 20:58
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    @YemonChoi: This thread appears to be deliberately conflict-agnostic, as far as I can tell. – Ryan Budney Dec 17 '17 at 21:15
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    @RyanBudney Perhaps Sergei will clarify his intent. I took the use of the definite article quite literally, but I see this is one of those threads where people are happy to answer the question in their own head rather than what is written (and to be fair perhaps Sergei welcomes the wider scope) – Yemon Choi Dec 17 '17 at 21:41
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    Actually, I was asking about any war, not necessarily WWII. – Sergei Akbarov Dec 17 '17 at 22:58
  • I'm happy with this answer, giving, unlike most other answers, mathematical context. – YCor Dec 18 '17 at 01:08
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    You beat me to Schwartzschild. He both produced the solution, and died, in the trenches (or at least within sound of gunfire, after criss-crossing Germany during the course of the war). Remarkably, the solution was only a month after Einstein published the equations in his 1915 paper, in Berlin; and his death was possibly the result of accidental exposure to his own side's experimental chemical weapons. Source: footnotes in doi:10.1007/978-0-8176-8283-5 Lots of pathos/regret here. – Norman Gray Dec 19 '17 at 12:11
  • Is he the one giving name to the famous Schwarzschild radius of black holes? – mathreadler Dec 21 '17 at 14:51
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I assume that most people may put focus on Polish or Soviet Union mathematical society when talking about this topic, but I personally would like to bring to attention another country which also severely suffered from WWII, namely China, through the experience of a talented, well-known, but low-profile mathematician, Wei-Liang Chow. The citations below are all taken from:

Wilson, W. Stephen; Chern, S. S.; Abhyankar, Shreeram S.; Lang, Serge; Igusa, Jun-ichi (October 1996). "Wei-Liang Chow". Notices of the American Mathematical Society. 43 (10): p.1117–1124.

Chow had ceased his research for about ten years due to WWII, according to S. S. Chern:

...The decline of Göttingen had the result of elevating Hamburg to a leading mathematical center in Germany. Her leading attraction was Emil Artin, the young professor who gave excellent lectures and whose interest extended over all areas of mathematics. Although WeiLiang was a Leipzig student, the German university system allowed him to live in Hamburg. Besides the contacts with Artin, he had a more important objective, which was to win the love of a young lady, Margot Victor. They were married in 1936, and I was fortunate to be present at the wedding.

After their marriage Wei-Liang returned to China and became a professor of mathematics at the Central University in Nanking, then the Chinese capital. The next years China was at war, with the coastal provinces occupied by the Japanese. We next saw each other in 1946 in Shanghai after the war ended. In a decade of war years WeiLiang had practically stopped his mathematical activities, and the question was whether it was advisable or even possible for him to come back to mathematics.

According to Jun-ichi Igusa, Chow was able to communicate with European mathematicians during the first few years of his stay in China as a Professor at the Central University in Nanking, but then the situation became worse:

In the later years of our meetings, Professorand Mrs. Chow often mentioned the time when they were in China. After their marriage in Hamburg in July of 1936, they left Nazi Germany for China, and Chow started teaching at the Central University in Nanjing in September of that year. However, only one year later they found that China was no better than Germany. Imperial Japan enlarged a small fight on July 7, 1937, at the Marco Polo Bridge near Beijing to a systematic invasion of China. On August 13 a skirmish occurred in Shanghai, and on December 13 the “Rape of Nanjing” started. Fortunately they escaped Nanjing in September of that year to Chow’s birthplace, Shanghai. Shanghai being an international city, they felt safer there. They told us, however, that Shanghai at that time was quite similar to the Shanghai described in S. Spielberg’s movie, Empire of the Sun. In the first two to three years in China, Chow was still able to communicate with mathematicians in Europe, especially with van der Waerden. However, during the remaining eight years before he came to the United States the situation became so bad that he was unable to continue his mathematics. He told us more than once that it was Professor Chern who encouraged and helped him to come back to mathematics. Chow came to the Institute for Advanced Study in Princeton in March of 1947 and to Hopkins in the fall of 1948. He went on to say that without Chern’s friendship that might not have taken place.

But miraculously, Chow managed to return to his work after the war and:

His return to mathematics was most successful; I would consider it a miracle. He began by spending the years 1947–49 at the Institute for Advanced Study, after which he accepted a position at Johns Hopkins University, from which he retired in 1977. At Johns Hopkins he served as chairman for more than ten years. He was also responsible for the American Journal of Mathematics, a Hopkins publication and the oldest American mathematical journal.

And many of his most prominent results, like Chow's moving lemma(1956) and Chow-Kodaira Theorem, were discovered after his return.

Dongyu Wu
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The question is really multifaceted so I add another answer. Sergei Akbarov explained in a comment:

Actually, I was asking about any war, not necessarily WWII.

WWI was really devastating, especially for French mathematicians. A good reference is the book of Michele Audin "Fatou, Julia, Montel", mentioned in Victor's answer. The reason was apparently that the French drafted most of their young mathematicians to the army, unlike the Germans and the British. A whole generation of young mathematicians was lost. She also discusses the consequences of this for the French mathematics. (Not all consequences were negative for mathematics itself: for example the rise of Bourbaki can be traced to this.)

In WWII relatively few known Western European mathematicians were killed in action, but many died in the Holocaust which was certainly related to the war. There is a very good but little known source:

Adolf Goodman, Univalent Functions, vol. II. The last chapter (Ch. 18) of this book contains a large list, with short biographies of mathematicians who died in the Holocaust.

KConrad
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Alexandre Eremenko
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Adolf Lindenbaum was executed by the Gestapo in 1941. His work was mainly in the fields of logic and set theory. For example, he proved that if any two non-empty sets admit a surjection between one and the other, then the axiom of choice holds.

Alfred Tarski mentions this in the preface of his book "Cardinal Algebras" to Lindenbaum,

It would be impossible for me to conclude this introduction without mentioning one more name - that of Adolf Lindenbaum, a former student and colleague of mine at the University of Warsaw. My close friend and collaborator for many years, he took a very active part in the earlier stages of the research which resulted in the present work, and the few references to his contributions that will be found in the book can hardly convey an adequate idea of the extent of my indebtedness. The wave of organized totalitarian barbarism engulfed this man of unusual intelligence and great talent - as it did millions of others.4

4 Adolf Lindenbaum was killed by the Gestapo in 1941.

The book also has the following dedication, which clearly includes Lindenbaum:

To the memory of my friends and students murdered in Poland during the Second World War

See also Adolf Lindenbaum's biography on MacTutor History of Mathematics.

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Asaf Karagila
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Felix Hausdorff managed to withstand World War I in Greifswald, but WWII took its toll on him. During Nazi rule he was forced to retire in 1935, then failed to emigrate to the USA, and finally in 1942 suicided together with his wife after receiving notice of their upcoming internment in Endenich.

He was still actively working in those years, despite having to live in harsh conditions under the dictatorship and not being allowed to publish in Germany. Besides papers in Fundamenta Mathematicae (e.g. this), his Nachlass shows that he kept working in topology and set theory almost until the very end. See also this question.

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In some sense Ramanujan's mathematical research was also interrupted by a WW1. For example in http://rsnr.royalsocietypublishing.org/content/48/1/107 (Ramanujan’s illness, by D.A.B. Young) we read:

These intentions were frustrated by the outbreak of war within four months of his arrival in England. Contact with much of continental mathematics abruptly ceased, and soon many Cambridge mathematicians, most significantly Littlewood, left on war service.

Another consequence, slower in impact but more serious for Ramanujan’s well being, was food shortages, especially of Indian comestibles. He was a Brahmin Hindu and a strict vegetarian, and although in coming to England he had com­promised certain Brahminical strictures including crossing the seas, he remained punctilious about dietary observance. In the absence of another Brahmin to cook for him, he had to buy and cook all his food. If he had established a routine in his life, he could have coped. But he was obsessional about his research, working for 30 hours at a stretch and then sleeping for 20. ‘Cooking only once a day or two’, as Alice Neville remembers his habit , must have resulted in malnutrition.

Also from the book http://www.springer.com/us/book/9783319255668 (My Search for Ramanujan, by K. Ono, A.D. Aczel):

Another reason why Hardy failed in his attempt to have Ramanujan elected a Fellow of Trinity College had to do with World War I... Hardy was opposed to war, even while he understood the necessity to defend Britain and the Continent from German aggression ... Then at some point during the war, he supported antiwar statements made by the eminent Cambridge logician Bertrand Russell, and that was enough to tar him with the pacifist brush. He was thus politically weakened and could not effectively fight for Ramanujan.

Ramanujan, humiliated and upset by the defeat of his nomination to become a fellow, also suffered physically. It was at this point that the wartime scarcity of fresh fruits and vegetables—the main staples of his vegetarian diet—began to affect his health adversely. He became desperately ill. Naturally heavy, he now lost weight. He talked less, even meeting his only main contact with the world, Hardy, less frequently.

P.S. There is an interesting article about the impact of the First World War on mathematics: http://hal.upmc.fr/hal-00830121 (Placing World War I in the History of Mathematics, by David Aubin and Catherine Goldstein).

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Zurab Silagadze
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According to the Wikipedia article, WWII brutally interfered in the work of Teichmüller several times, in several ruthless ways. The whole citation there from

Segal, Sanford L. (2003). Mathematicians Under the Nazis. Princeton University Press. p. 450.

is so significant that I decided to reproduce it here completely. I can hardly think of a more dramatic, controversial soul-heart-mind tearing destiny for a creative mathematician - or maybe anyone else too.

On 18 July 1939, Teichmüller was drafted into the Wehrmacht. He was originally only intended to do eight weeks training but World War II broke out before the eight weeks were up so he remained in the army, and took part in Operation Weserübung in April 1940. Afterwards, he was recalled to Berlin where he became involved in cryptographic work along with other mathematicians such as Ernst Witt, Georg Aumann, Alexander Aigner and Wolfgang Franz in the Cipher Department of the High Command of the Wehrmacht. In 1941, Bieberbach requested that Teichmüller be released from his military duties in order to continue teaching at the University of Berlin. This request was granted and he was able to teach at the university from 1942 to early 1943. However, after a state of totalen Krieg was declared in response to the German defeat at Stalingrad in February 1943, Teichmüller left his safe Berlin position and volunteered for combat on the Eastern Front, entering a unit which became involved in the Battle of Kursk. At the beginning of August, he received furlough when his unit reached Kharkov. By late August his unit had been surrounded by Soviet troops and largely wiped out, but in early September he attempted to rejoin them. He is reported to have reached somewhere east of the Dnieper, but west of Kharkov, (most likely Poltava) when he was killed in action on 11 September 1943.

მამუკა ჯიბლაძე
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    It is relevant context here that Teichmüller was apparently virulently antisemitic and an enthusiastic supporter of the Nazis. He should be distinguished from people who were more passively caught up in the war. – Neil Strickland Dec 17 '17 at 09:39
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    @NeilStrickland I believe this is a highly nontrivial matter to discuss. When I said about WWII brutally interfering in Teichmüller's work in several ways, I also had in mind the interaction between his "real life part" and his "mathematical part", which should obviously be highly nontrivial, although fortunately none of it can be traced from studying his mathematical contributions. For example I believe one might guess from the excerpt above that among most crucial things which made his further mathematical work impossible were consequences for his decisions of his understanding of patriotism – მამუკა ჯიბლაძე Dec 17 '17 at 10:27
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    From this point of view maybe one can even say that his destiny is more tragic than of those passively caught in the war - since one of the factors that systematically destroyed possibility of his further work was acting from inside himself. – მამუკა ჯიბლაძე Dec 17 '17 at 10:30
  • I realize this stance may be disputable but what I think is clear is that my post answers the question as well as any other answers might: it is about the unhappy destinies of mathematicians during the war, and illustrates very well that war kills science. – მამუკა ჯიბლაძე Dec 17 '17 at 10:45
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    @NeilStrickland this is actually a part of what I had in mind: the idea of separation inevitably leads to the horrors like this, it makes people, even talented ones, enemies. So I think, Teichmüller is a good illustration, among many others. – Sergei Akbarov Dec 17 '17 at 11:02
  • @SergeiAkbarov Exactly. And what is even more dramatic is that if, say, while he was able to think about mathematics, Teichmüller would encounter the work of, say, Schauder or Leray, he would probably study it with interest, appreciate and benefit from it researchwise, maybe not worried at all about their suffering. Of course one can never prove whether this would be so or not, but what I want to point out is that while this is very bad from one point of view, from another it is maybe very good since it shows complete independence of development of mathematical knowledge from moral dilemmas. – მამუკა ჯიბლაძე Dec 17 '17 at 11:11
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    Mamuka, this is strange for me: "from another it is maybe very good since it shows complete independence of development of mathematical knowledge from moral dilemmas" I would say, the dependence is obvious. – Sergei Akbarov Dec 17 '17 at 11:20
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    @SergeiAkbarov Yes it is sort of opposite side of your question - what I had in mind is that a moral monster might contribute to mathematical knowledge and it would not be rejected. More precisely, it could not be rejected. And vice versa - mathematicians might readily benefit from the mathematical work of those whom they (rightly or erroneously) consider evil in some other respect – მამუკა ჯიბლაძე Dec 17 '17 at 11:22
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    On my opinion, Teichmuller, an active Nazi, cannot be represented as a "victim" of the war. He's got what he deserved. His actions before the war harmed other mathematicians, and he was clearly one of those responsible for this war. – Alexandre Eremenko Dec 17 '17 at 14:01
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    @AlexandreEremenko I do not know much about Teichmuller, but the aim of my question was to blame the idea of fragmentation of science into "national sciences", not to blame concrete persons. I agree that this doesn't remove the responsibility of concrete people, but in my opinion, the first step - the idea of fragmentation - inevitably leads to the situations where people, being blinded by this idea, become moral monsters. The choice of axioms is more important than deduction of corollaries. – Sergei Akbarov Dec 17 '17 at 14:21
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    @AlexandreEremenko Sorry but your first two statements, regardless of being arguable or not, I think are not related in any way to the question or to my answer. As for the rest, I must admit I am completely ignorant about his actions against other mathematicians and became very interested to learn about it. Do you know any text to read about it? – მამუკა ჯიბლაძე Dec 17 '17 at 15:32
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    I have included a specific reference dealing with Teichmüller's actions in my answer. But really, I cannot fathom how one can in good faith misunderstand Teichmüller's role after reading or even simply browsing through Segal's book which allegedly served as a basis for this answer. – Victor Protsak Dec 17 '17 at 23:14
  • @VictorProtsak Thank you very much, I will study it with interest. The only information I had was that Wikipedia page that I linked to, now I will study these sources with great interest. But independently of that, - why do you conclude from my answer that I misunderstood Teichmüller's role in any way? – მამუკა ჯიბლაძე Dec 18 '17 at 05:42
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    @მამუკა ჯიბლაძე: There are many sources. Type "Teichmuller and Landau" on the Google. Landau was dismissed as a result of Teichmuller's actions. – Alexandre Eremenko Dec 18 '17 at 14:49
  • @AlexandreEremenko Thank you very much! The whole story is indeed way more dramatic and controversial than I would have ever imagined, and I admit I should know it beforehand. I am not sure whether I will be able to alter my answer appropriately. Let me add though that I still believe the essence and the message of it remains the same: yes, Teichmüller's actions most likely destroyed lots of possible fascinating contributions to mathematics, both his and, as I now see, others too. – მამუკა ჯიბლაძე Dec 18 '17 at 15:56
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    @მამუკა ჯიბლაძე: I agree with what you wrote, and don't think anything should be changed. I just wanted to emphasize that Teichmuller was not only a victim of the war but also one of those who made it possible. – Alexandre Eremenko Dec 18 '17 at 22:06
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Takagi's proof of the main results of Class Field Theory during WWI is a fascinating example, where a key role is played by Strasbourg leaving Germany and German mathematicians banned from traveling there. Here's a summary taken from my undergrad thesis, the sources are listed on the top of page 46 if you want to read more.

Takagi worked on the main results of class field theory in Japan during the war in seclusion from his German colleagues and was so shocked by the generality of his results that he doubted there validity for quite some time...

Although Takagi had already published his important class field theory paper in 1920, his results were not yet well known partly because of disruptions caused by the war. In particular Takagi presented his main papers in 1920 in Strasborg which changed hands after the war, and so the German mathematicians were not allowed to attend. It was only when Siegel persuaded Artin to read these papers in 1922 that Takagi’s results became generally known. The results of Artin’s investigations prompted by his reading of Takagi’s paper is the subject of the second chapter and so the rest of the story of class field theory will have to wait until then.

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Noah Snyder
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    You really wrote "there" at the end of the first paragraph? – KConrad Dec 18 '17 at 23:43
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    Why does Takagi presenting work in Strasbourg indicate he did not know which cities were still German, and why does it matter if he knew the postwar German cities? The effect of Germans not being allowed to attend seems more relevant than Takagi's geographic knowledge. – KConrad Dec 18 '17 at 23:46
  • Fair. Will edit. – Noah Snyder Dec 19 '17 at 00:53
  • I did not understand. Did Takagi leave mathematics after Strasbourg? – Sergei Akbarov Dec 19 '17 at 07:55
  • No, but he went back to Japan. As far as I know he didn’t have an opportunity to return to Europe until after Siegel and Artin read his work. – Noah Snyder Dec 19 '17 at 14:04
  • If he continued his work in mathematics, perhaps, this can't be called a "research interrupted by the war"? – Sergei Akbarov Dec 19 '17 at 14:09
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    A key part of research is communication between scholars, this communication was interrupted slowing down the progress of research, even though Takagi himself was still able to work. I think that’s part of what makes it an interesting example. – Noah Snyder Dec 19 '17 at 16:12
  • Yes, this is important, but sometimes people do research alone. Did he have papers after Strasbourg? – Sergei Akbarov Dec 19 '17 at 16:36
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Wolfgang Doeblin’s research on Stochastic Calculus was interrupted by his suicide during WW2 as he was close to be captured. His pli cacheté, held by the Académie des Sciences, was opened after 2000. It contains an alternative version or the Ito’s formula and Kolmogorov’s equation.

Sergei Akbarov
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AntoineL
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Huckle keeps an extensive list of mathematicians killed or imprisoned in World War II.

Ben McKay
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Eugenio Elia Levi's death during WWI had a profound impact on Italian mathematics. Though still quite young, Levi had signalled himself as a mathematician willing to recognize the relevance of the then emerging Lie theory, following the work of his mentor Bianchi. When he was just 22 he published the paper in which what will thereafter be called Levi factors were introduced. Moved by very strong patriot feelings, despite the fact that he could have been exempted from military duties, he voluntereed and was killed by a stray bullet after Caporetto's defeat.

Lie theory in Italy remained largely unexplored, with Luigi Bianchi being one of the few trying to convince his students of its relevance.

A "missed opportunity" for the Italian mathematics.

Nicola Ciccoli
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The following example is much less serious than many of those already reported. However, it seems that the fairly well known survey article

Plesner, A.I.; Rokhlin, V.A., Spectral theory of linear operators. II, Am. Math. Soc., Transl., II. Ser. 62, 29-175 (1967); translation from Usp. Mat. Nauk 1, No.1 (11), 71-191 (1946). ZBL0185.21002. Mi umn7016.

was delayed in its publication because the mathematical activities of one of the authors (Rokhlin) were interrupted by WWII. Part I (by Plesner alone) came out much earlier, in 1941, which is also when most of the preparation of part II were finished. In a previous answer, I quoted part of the introduction of the article, which relates that story.

Igor Khavkine
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    In the same vein, the entire publication of the (adapted) French version of Klein’s Encyklopädie was canceled in 1916 due to WWI. Thus for instance, Cartan’s remarkable survey “La théorie des groupes continus et la géométrie” (expanding Fano’s) was delayed until his Collected Works (1955): 40 years! – Francois Ziegler Dec 21 '17 at 23:55
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Henry Moseley

Henry Gwyn Jeffrey's Moseley (23 November 1887 – 10 August 1915) was an English physicist, whose contribution to the science of physics was the justification from physical laws of the previous empirical and chemical concept of the atomic number. This stemmed from his development of Moseley's law in X-ray spectra. Moseley's Law justified many concepts in chemistry by sorting the chemical elements of the periodic table of the elements in a logical order based on their physics. He published first the Long Form periodic table or Modern periodic table[citation needed] which is used till date.

When World War I broke out in Western Europe, Moseley left his research work at the University of Oxford behind to volunteer for the Royal Engineers of the British Army. Moseley was assigned to the force of British Empire soldiers that invaded the region of Gallipoli, Turkey, in April 1915, as a telecommunications officer. Moseley was shot and killed during the Battle of Gallipoli on 10 August 1915, at the age of 27. Experts have speculated that Moseley could have been awarded the Nobel Prize in Physics in 1916, had he not been killed. As a consequence, the British government instituted new policies for eligibility for combat duty.

Only twenty-seven years old at the time of his death, Moseley could, in the opinion of some scientists, have contributed much to the knowledge of atomic structure had he survived. Niels Bohr said in 1962 that the Rutherford's work "was not taken seriously at all" and that the "great change came from Moseley."

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Agile_Eagle
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I am not sure if this one fits as an answer. But as far as I know, Ludwig Wittgenstein was also a mathematician aside from being a world-class philosopher. This part of his biography caught my eye:

Born in Vienna into one of Europe's richest families, he inherited a fortune from his father in 1913. He initially made some donations to artists and writers and then, in a period of severe personal depression after the First World War, he gave away his entire fortune to his brothers and sisters. Three of his brothers committed suicide, with Wittgenstein contemplating it too.

He left academia several times—serving as an officer on the front line during World War I, where he was decorated a number of times for his courage; teaching in schools in remote Austrian villages where he encountered controversy for hitting children when they made mistakes in mathematics; and working as a hospital porter during World War II in London where he told patients not to take the drugs they were prescribed while largely managing to keep secret the fact that he was one of the world's most famous philosophers.

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polfosol
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    Hm... Interesting. But are there any evidences that he left mathematics because of war? – Sergei Akbarov Dec 20 '17 at 10:58
  • @SergeiAkbarov To be honest, I don't know much about Wittgenstein and his works. I just read the wikipedia article I mentioned in my answer. The reason I brought this up was because of a scene I remember from the movie Oxford Murders, where the professor talks about Wittgenstein and his great discoveries during war (How ironic!). You can watch it here. – polfosol Dec 20 '17 at 11:21
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    I really wouldn't call Wittgenstein a mathematician. Some of his work is in philosophy of mathematics, but that's about it (and I wouldn't say that qualifies). – Todd Trimble Dec 20 '17 at 11:54
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WWI was horrible for almost all of Europe in most regards. Before the war Germany had one of the largest schools of mathematicians in the world at the time - maybe peaking shortly after David Hilbert's collection of challenges for the coming century (in year 1900). For example Goettingen and Koenigsberg (nowadays Kaliningrad) were really inspiring cultural cities at the time which produced a long string of gifted mathematicians: Cantor, Minkowski, Klein to name just a few.

Martin Sleziak
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    mathreadler, this is true, but you should give a concrete example of a person who had to stop his research because of the circumstances you describe. – Sergei Akbarov Dec 21 '17 at 16:24