Mathematical research interrupted by a war

Question

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.

Answer 1

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.

Answer 2

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)

Michèle Audin, Jacques Feldbau, Topologe: Das Schicksal eines jüdischen Mathematikers (1914 - 1945). Springer, 2012 (ISBN 978-3-642-25803-9)

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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.

Answer 9

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).

Answer 10

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.

Answer 11

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.

Answer 12

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.

Answer 13

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

Answer 14

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.

Answer 15

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.

Answer 16

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."

Answer 17

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.

Answer 18

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.