Inspired by this post I would like to ask whether there were any well-known (deceased) mathematicians who were marxists? In the early 1930s, Ernst Kolman approved the publication of the Russian translation of Marx's mathematical works (and eventually retracted previously held views) but can hardly be called a distinguished mathematician. Chandler Davis and Laurent Schwartz are additional well-known cases. To repeat: I am only interested in those that are already dead.
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1$\begingroup$ A question for those who voted to close the question: Just curious, why didn't you vote to close this: hsm.stackexchange.com/questions/14835/… ? $\endgroup$– Mikhail KatzCommented Jun 17 at 8:00
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2$\begingroup$ Is this a list question, or are you merely asking to confirm whether there were any Marxist mathematicians ever? $\endgroup$– giddsCommented Jun 17 at 8:01
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$\begingroup$ @gidds: it's the same kind of question as hsm.stackexchange.com/questions/14835/… $\endgroup$– Mikhail KatzCommented Jun 17 at 8:02
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8$\begingroup$ In the (perhaps vain) hope this doesn't lead to some Reddit list of "Marxist Mathematicians," I have to point out that "Marxist" means different things to different groups at different periods in history. A Marxist mathematician in New York City in 1975 might be a completely different being, ideologically, from a Marxist mathematician in Moscow in 1931. If we're comparing this to the list of Nazis, bear in mind that National Socialism lasted nowhere near as long as Marxism has. $\endgroup$– RaydotCommented Jun 18 at 2:55
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$\begingroup$ Sofya Yanovskaya, tracked down Marx's mathematical manuscripts and arranged their first publication in Russian in 1933. $\endgroup$– nwrCommented Jun 19 at 3:10
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10 Answers
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This is a strange question. In Soviet Union, it was dangerous not to be a "marxist". Many mathematicians were members of the communist party, and you cannot be a member without being a marxist. Of course many of those mathematicians did not express marxist views in print, at least in mathematical publications, but to make this question meaningful, one can define precisely who is counted as "marxist". Member of the communist party? Or a person who expressed marxist views in publications? With both definitions, the list will be very long. Or you are asking about non-Soviet mathematicians?
Some examples of prominent mathematicians who expressed their marxist views in publications were A. D. Aleksandrov, Lyusternik and Sobolev. But these are just examples which immediately come to my mind. After the collapse of the communist party of Soviet Union, this information is rarely included on mathematicians biographies.
Here is a paper which confirms what I said: https://ui.adsabs.harvard.edu/abs/2008cpsu.rept.....G/abstract
The author tried to do some statistics, based on Soviet sources.
answered Jun 16 at 14:14
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4$\begingroup$ This seems to be a comment rather than an answer. I would disagree with your claim that one cannot be a member without being a marxist. Surely a distinction can be made between Pontryagin who was an enthusiastic one, and others who did it out of simple expediency. Similar situation existed in Germany in the 1930s, where certain mathematicians acted as they had to in order to retain their jobs, whereas others sincerely believed, such as Teichmueller and Vahlen. $\endgroup$ Commented Jun 16 at 14:31
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7$\begingroup$ @Mikhail Katz: Yes, this is an extended comment. On your second sentence, you have to specify what you mean by "marxist". To join a communist party, one had to confirm his marxist world view. Who "sincerely believed" and who did not is impossible to determine. $\endgroup$ Commented Jun 16 at 16:07
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7$\begingroup$ Hmm .... It seems to me that "impossible to determine" is probably too strong. Sure, if someone in the Soviet Union joined the Community Party in 1936, it's almost impossible to determine whether they were actually a Marxist, given that it wasn't practically possible to say otherwise unless they were willing to significantly risk their health and life. But at the other end of the scale, if someone in Russia joined the Bolsheviks in, say, 1906 or 1916, that would suggest to me that they were, at the very least, genuinely sympathetic to Marxism. $\endgroup$– AlexisCommented Jun 17 at 8:27
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1$\begingroup$ @AlexandreEremenko, Here Kutateladze writes: "Alexandrov hated all crooks, “marxism-borne” popes and inquisitors who used science for mean and greedy ends." This provides very little evidence that A. D. Alexandrov was a marxist. $\endgroup$ Commented Jun 17 at 13:07
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Lucio Lombardo-Radice wrote some important papers on finite geometry and combinatorics. In Italy he is best known for his work as a pedagogue and popularizer of mathematics in the working-class world (including on television). In the 1930s he came into contact with a group of young antifascists and clandestinely joined the Italian Communist Party (PCI). In 1939 he was unable to take up service as an assistant professor of analytical geometry because he was arrested and sentenced to four years' imprisonment as an opponent of the fascist regime; freed in 1941, he was arrested again and then released after a few months. He actively participated in the Roman resistance. After the war, he became a PCI leader and was a city councilor in the City of Rome from 1976 to 1981.
Ludovico Geymonat was one of the most important Italian philosophers, historians of philosophy amd mathematics, and epistemologists of the 20th century. In the 1930s he was an assistant professor of Algebraic Analysis at the University of Turin but refused to join the Fascist party, thus losing the possibility of an academic or state teaching career. In 1934 he went to Austria to study the neo-positivist philosophy of the Vienna Circle headed by Moritz Schlick. During World War II, under the battle name "Luca" he was a partisan in Piedmont in the 105th Carlo Pisacane Brigade and, after the Liberation, a communist alderman in the City of Turin from 1946 to 1949. Politically, he was initially close to the Italian Communist Party, from which he later distanced himself to join Democrazia Proletaria and later the movements that gave birth to the Communist Refoundation Party. During this political journey he participated in the founding, on February 11, 1987, of the Marxist Cultural Association in Rome and contributed to the journal Marxismo Oggi (Marxism Today). His epistemological work can be framed in the strand of neopositivism that he reworked from the perspective of the Marxist tradition (in particular regarding Galileo). As a mathematician he did some research on Picard's theorem and Carathéodory's theorem for harmonic functions. He also dealt with the foundations of probability.
Renato Caccioppoli was the son Sofia Bakunina (1870-1956), daughter of the Russian anarchist revolutionary and philosopher Michail Bakunin. His aunt was Maria Bakunin, a professor of chemistry at the University of Naples. Immediately after graduation, he became an assistant to Mauro Picone (a well-known fascist, by the way) in 1925. Picone immediately discovered his talents and pushed him into research in mathematical analysis. Over the next five years Caccioppoli published some 30 papers on topics developed completely independently that won him a ministerial prize for mathematics and in 1931, winning the competition at age 27, the chair of algebraic analysis at the University of Padua. In 1934 he returned to Naples to fill the chair of Group Theory; he then moved on to the chair of Higher Analysis and from 1943 to that of Mathematical Analysis. In May 1938 he gave a speech against Hitler and Mussolini on the occasion of the Nazi dictator's visit to Naples: together with his companion, Sara Mancuso, he paid an orchestra in a bar to play the Marseillaise, France's national anthem, after which he began to speak against fascism and nazism in the presence of OVRA agents (the secret police of the Kingdom of Italy). He was arrested again, but his aunt managed to get him released by convincing the authorities of her nephew's incapacity. Caccioppoli was thus interned, but continued his studies in Mathematics. After the war he approached the Italian Communist Party, although he did not take a party card. On February 15, 1947, he was admitted as a fellow at the Accademia dei Lincei, the same day his aunt Maria Bakunin was admitted.
Mario Fiorentini was an Italian partisan, secret agent and mathematician, for years a professor of geometry at the University of Ferrara. He was operative in numerous actions including the assault on the entrance to Regina Coeli prison and participated in the organization of the via Rasella attack. Already as a student he collaborated clandestinely with Giustizia e Libertà (Justice and Freedom) and the Communist Party. After July 25, 1943, with Antonello Trombadori, he formed a group of partisans known as Arditi del Popolo. On September 9, 1943, he took part in the battle against the Nazis at Porta San Paolo among the ranks of the Action Party adherents; in October he organized and placed himself under the command of the Antonio Gramsci GAP, assuming the battle name of "Giovanni". After the war, from 1964 he became involved in mathematical research, concentrating mainly on homological methods in commutative algebra and algebraic geometry, in close connection with the more advanced ideas of Grothendieck and his school. From November 1, 1971, he was full professor of higher geometry at the University of Ferrara. He died in 2022 at the age of 103.
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1$\begingroup$ I have some doubts about including Renato Caccioppoli on the list. He was certainly a mathematician, and his mother and grandfather were communist, and he was an anti-fascist, but apparently not really a communist or marxist. $\endgroup$ Commented Jun 16 at 13:48
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3$\begingroup$ There are definite sources that after World War II he was a supporter of the Communist Party. The most obvious one is the testimony of the 11th president of the Italian republic, Giorgio Napolitano, as well as a leading exponent of the Italian Communist Party: "I also remember the electoral rallies that Renato Caccioppoli used to hold in Naples for the Communist Party, even though he was not a member of the Party; [contd] $\endgroup$– user6530Commented Jun 16 at 14:12
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3$\begingroup$ rallies that he would hold with a taste for going against the tide, and that he would ask to be held in the most difficult squares for the Communist Party in the center of Naples, in middle and upper middle class neighborhoods. Renato Caccioppoli was known and appreciated there, and it was there that he would expose himself to these trials, that he would launch these challenges, these provocations. There, that's how I remember Renato Caccioppoli, [contd] $\endgroup$– user6530Commented Jun 16 at 14:13
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3$\begingroup$ and I also remember evenings with him, and what it meant, for us young people, to meet him at the Caffè Gambrinus, in Via Chiaia, or in a pizzeria, what the conversation with him was and what, moreover, was also the poignant spectacle of a deeply troubled man, of a man on his way to a tragic destiny." see radiof2.unina.it/in-ricordo-di-renato-caccioppoli $\endgroup$– user6530Commented Jun 16 at 14:13
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2$\begingroup$ I can confirm what user6530 says about Caccioppoli, there are many sources in Italian that say that Caccioppoli was active in the Communist Party, and it is well known in Naples, I have also personal testimonies, as my mother was at the university of Naples when Caccioppoli was there, and she knew him and his aunt Bakunin, who was her teacher, as she studied biology. $\endgroup$ Commented Jun 16 at 15:19
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I've got the impression that Lawvere was; cf. e.g. this:
In this talk, he will show how science is corrupted to pseudo-science under imperialism, and how Lenin's "Materialism and Empirio-Criticism" serves as a guide to science and mathematics under the two superpowers.
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1$\begingroup$ Amazing. I wasn't aware of this. Are you sure this is not a hoax/joke? $\endgroup$ Commented Jun 16 at 8:47
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3$\begingroup$ I don't have any particular reason to believe it's a hoax/joke. As noted in this reddit discussion, Lawvere references Mao's "On Contradiction" in his paper "Quantifiers and Sheaves", published in 1970, and see also this math.SE comment about Lawvere's category-theoretic interpretation of Hegel. $\endgroup$– AlexisCommented Jun 16 at 9:53
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7$\begingroup$ I first met Bill Lawvere circa 2011 via a mutual colleague, Harvey Friedman. Lawvere openly discussed being a communist, as well as the intricacies of "Moa-ism" versus "Stalin-ism". $\endgroup$ Commented Jun 17 at 8:29
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7$\begingroup$ Moa-ism is a mere emu-lation of communism. I think you meant Maoism. :-) $\endgroup$ Commented Jun 17 at 14:18
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Dirk Struik (1894–2000), author of some well-known math history and differential geometry books, was a devout Marxist (see for example Wikipedia and an obituary in MAA News).
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José Luis Massera (Uruguayan mathematician, 1915-2002). Here's an article about him where his Marxism is explicitly stated.
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1$\begingroup$ Interestingly that article claims he kept his Marxian views separate from his mathematics (if I read it correctly). $\endgroup$– mdeweyCommented Jun 17 at 16:05
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There are several Dutch mathematicians who were outspoken Marxists. Most well-known is probably Dutch-American mathematician Dirk Jan Struik (1894-2000), Professor of mathematics at MIT, who was a member of the Communist Party of the Netherlands (CPH) while he was a student in Leiden. After he had moved to MIT, he was barred from returning as visiting professor to Leiden because of these Marxist beliefs. He was also targeted during the McCarthy era. You can really notice his Marxist philosophy in his historical writings.
Mathematician and philosopher Gerrit Mannoury (1867-1956), Professor of mathematics at the University of Amsterdam was a member of the Social Democratic Workers' Party (SDAP) and later the CPH, where he was kicked out because of his support for Trotski.
Jan Burgers (1895-1981), Professor of Fluid Dynamics and Applied Mathematics at the University of Maryland and one-time secretary general of the International Union of Theoretical and Applied Mathematics, was also a member of the CPH. He was barred from working in the US during the early 1950s because of his membership but was later allowed to work at the University of Maryland after they accepted he was only a "follower" and not an active participant of the party.
Finally there's the Dutch econometrist and Nobel Memorial Prize winner Jan Tinbergen (1903-1994), who studied mathematics in Leiden and was a member of the SDAP. However, by then, it was mainly revisionist and no longer overtly Marxist. His research in statistical analysis was heavily influenced be his belief in scientific socialism and a planned economy.
To read more on these mathematicians and how they combined Marxism and science, check out the paper: Gerard Alberts, "On Connecting Socialism and Mathematics: Dirk Struik, Jan Burgers, and Jan Tinbergen", Historica Mathematica 21 (1194): 280-305. doi:10.1006/hmat.1994.1026
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$\begingroup$ But which of these were mathematicians? I notice that Historia Mathematica has an older tradition than I would have ever suspected. $\endgroup$ Commented Jun 18 at 11:11
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2$\begingroup$ Struik was professor of mathematics at MIT, Mannoury was professor of mathematics at the UvA, Burgers was secretary general of the IUTAM, Tinbergen was trained as mathematician. You can decide for yourself what qualifies as being mathematician and how many of these were mathematicians. $\endgroup$– cktaiCommented Jun 18 at 11:14
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An obvious one to mention is Karl Marx himself. Wikipedia has an article about his mathematical writings:
The mathematical manuscripts of Karl Marx are a manuscript collection of Karl Marx's mathematical notes where he attempted to derive the foundations of infinitesimal calculus from first principles.
The notes that Marx took have been collected into four independent treatises: On the Concept of the Derived Function, On the Differential, On the History of Differential Calculus, and Taylor's Theorem, MacLaurin's Theorem, and Lagrange's Theory of Derived Functions, along with several notes, additional drafts, and supplements to these four treatises. These treatises attempt to construct a rigorous foundation for calculus and use historical materialism to analyze the history of mathematics.
Marx's contributions to mathematics did not have any impact on the historical development of calculus, and he was unaware of many more recent developments in the field at the time, such as the work of Cauchy. However, his work in some ways anticipated, but did not influence, some later developments in 20th century mathematics.
According to a 1977 article Karl Marx and the foundations of differential calculus by Hubert C. Kennedy: (pp. 315-316)
While Marx' analysis of the derivative and differential had no immediate effect on the historical development of mathematics, Engels' claim that Marx made "independent discoveries" is certainly justified. It is interesting to note that Marx' operational definition of the differential anticipated 20th century developments in mathematics, and there is another aspect of the differential, that seems to have been seen by Marx, that has become a standard part of modern textbooks─the concept of the differential as the principle part of an increment.
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1$\begingroup$ Marx was not a mathematician by any stretch of the imagination, and had an infamously poor understanding of mathematics. $\endgroup$ Commented Jun 17 at 3:07
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3$\begingroup$ "his work in some ways anticipated ${\ldots}$ some later developments in 20th century mathematics" : I would be interested in seeing some evidence for such a claim. Do you have any? $\endgroup$ Commented Jun 17 at 11:33
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$\begingroup$ @MikhailKatz: I am quite sure they meant the claim that Marx invented a precursor to the nonstandard analysis: J.Dauben, Marx, Mao and mathematics: the politics of infinitesimals. Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Doc. Math. 1998, Extra Vol. III, 799–809. $\endgroup$ Commented Jun 17 at 12:36
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2$\begingroup$ @MoisheKohan, Dauben makes no such claim in his article, which is not surprising because he is a competent scholar. Such claims may have been made by Maoists in China, but that's another story. $\endgroup$ Commented Jun 17 at 12:40
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2$\begingroup$ @MikhailKatz I've edited to add a quote from Wikipedia's source for that claim. By my understanding, Marx objected to one definition of differentiation via infinitessimals, and came up with his own definition to resolve what he considered to be the problem; as far as I know, his definition was at least valid. FWIW, I have no opinion on whether Marx discovered or rediscovered any novel or valuable mathematical ideas; I don't think somebody has to do original research, or even good mathematics, before we count them as a mathematician. $\endgroup$– kaya3Commented Jun 17 at 18:04
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While German Nazi mathematicians like Bieberbach and Teichmüller are notorious and well-known, it seems much harder to find proponents from the opposite side of the political spectrum. However, during the German Weimar Republic, left wing parties like the German Communist Party (KPD) had a large following, so by the laws of probability some of its members or sympathisers should have been mathematicians. One person that came up through a Google search was the mathematical statistician Emil Julius Gumbel, one of the founders of extreme value statistics. Whether he was a marxist or a socialist is open to debate, but he joined the Independent Social Democratic Party of Germany (USPD) in 1917 which according to Wikipedia adhered to centrist marxism. Initially, it also "hosted" the Spartakusbund which later separated and morphed into the KPD. According to the biographical information here, in 1932, hence a year before the Nazis came to power, Gumbel
was the first professor dismissed from his chair because of Nazi pressure.
The same source says:
His admiration for the Soviet Union was stoked by a year-long sabbatical in Moscow (1925-1926), which he spent editing the mathematical notes of Karl Marx and Friedrich Engels.
There is also an ongoing exhibition (in German) about Gumbel, prepared by the Technical University of Munich, which states that he prepared an edition of Marx's mathematical papers (mentioned by several OPs here) which, however, was never published.
The sources given make it abundantly clear that the Nazis hated his guts. Luckily, he managed to escape to France and later the US before they could get hold of him.
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$\begingroup$ Do you have any more specific information on Gumbel's sabbatical in Moscow, and on his editing of the said mathematical notes? $\endgroup$ Commented Jun 19 at 13:13
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$\begingroup$ No, sorry - I only know what's in the linked documents. $\endgroup$ Commented Jun 19 at 13:18
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$\begingroup$ Having said this, the cited biographical information is from the Leo Baeck Institute and entitled "A Guide to the Microfilm Edition of the Emil J. Gumbel Collection: Political Papers of an Anti-Nazi Scholar in Weimar and Exile, 1914–1966" (also linked on Gumbel's Wiki page). There's the odd chance that they also have his edition of Marx's notes. $\endgroup$ Commented Jun 19 at 13:54
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$\begingroup$ The Emil J. Gumbel Collection has indeed been digitised. The "Marx edition" is not part of it (as my cursory search suggests), although Gumbel mentions it in his autobiographical sketch from 1928. $\endgroup$ Commented Jun 19 at 14:22
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I am not sure how “Marxist” is being defined but Chandler Davis was certainly a “leftist.”
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Jean van Heijenoort appears to qualify -- and have had a rather colourful life: he was a historian of mathematical logic who, amongst others, spent much of his last decade at Stanford University. Earlier in his life, he was a personal secretary and bodyguard to Leon Trotsky (1932--39), as well as one of Frida Kahlo's lovers (!).
