I have been looking at Marx's notes to himself, late in life, on the calculus. Marx relied on an out-of-date textbook, J. L. Boucherlat's 1828 Elementary Treatise on the Differential and Integral Calculus, as well as other out-of-date primary texts.
The foundations of calculus were a mess at that time. Marx was totally correct about that. Echoing Bishop Berkeley, Marx finds that the mathematicians were operating with fractions of the form 0/0. He tried to make sense out of this.
Unbeknownst to Marx, the foundations were being relaid in his day. I will mention the epsilon-delta definition of a limit, the construction of the real numbers as Dedekind cuts, and Cantor's set theory. I suppose Fourier series goes into this story. Marx never knew about any of this.
Some, sympathetic to Marx, argue that he treated the derivative as an operator.
Some mathematicians have been Marxist and socialists. These views have influenced their activities in developing mathematics, at least to the extent of the settings in which they did their mathematics. For this post, I am not going to sort through mathematicians in the Soviet Union or in China. I limit myself to a few in the United States.
- I know little of Chandler Davis' mathematical work. He lived from 1926 to 2022. The University of Michigan fired him in 1954 for refusing to cooperate with the oppression being practiced by the House UnAmerican Committee (HUAC). He went to jail for six months and then into exile into Canada.
- F. William Lawver was an expert in category theory, including its use to describe Hegelian dialectics. He was dismissed in 1971 partly for his political activities.
- David Schweickart has written a number of books outlining how socialism might be implemented. He is both a philosopher and a mathematician. I am not sure that he is a Marxist.
- I know of Stephen Smale principally through his horseshoe map, which is a canonical model for dynamical systems. He won the Fields Medal and denounced the United States for invading Vietnam.
- Dirk Jan Struik (1894-2000) could not get a job in Holland, partly due to his political commitments. He ended up at MIT. Struik co-founded and taught at the Samuels Adams School, one of several institutions set up to teach workers. These, of course, were illegally shut down by the government. HUAC went after Struik himself, and MIT chose the route of cowardice. He applied Marxist ideas to the sociology of mathematics, a field he helped create. He co-founded Science and Society. He also praised Marx's work on the foundations of calculus.
I will not be surprised if others know of more examples.
https://arxiv.org/abs/2606.01739
ReplyDeleteI distrust efforts to justify mathematicians from centuries ago with non-standard analysis. I see the connection. I do not understand model theory, though.
Deletehttps://worldmarxistreview.org/index.php/wmr/article/view/151
ReplyDeleteThanks. I did not know that arguments over Marx's take on calculus were so current.
DeleteMATHEMATICAL MARXISM. I am Nikolai Mokushev, a professor of mathematics from Russia. I am a graduate of the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University.
ReplyDeleteThe author has built a mathematical model of Marx’s CAPITAL (parts).
The book is titled “Marx’s Capital Is Thermodynamics.” It was published in Russia in English.
This is a new direction in Marxism — MATHEMATICAL MARXISM.
The results are as follows.
1. A fundamental constant of value has been introduced.
2. Marx’s CAPITAL turned out to be thermodynamics in political economy.
3. The law of value turned out to be the Mendeleev–Clapeyron equation from gas theory.
4. The local law of value holds in the tangent space only for an isobaric process.
5. The problem has been solved: “What is used to measure consumer value?” This problem has remained unsolved for 150 years.
The author's theorem. The total consumer value is the ENTROPY OF the MARKET
MARX'S CALCULATION SCHEMES
Marx's calculation schemes are cosmological equations.
They describe the movement of the entire global capital. The Hilbert-Einstein cosmological equations in general relativity describe the motion and shape of the entire universe.
So, Marx’s calculation schemes play an equally important role in political economy. They describe the movement of the entire capitalist universe.
But Marx presented them in an abstract form. And it is not at all easy to turn them into concrete mathematical and economic equations.The first person who tried to do this was the economist Leontief. An American of Russian origin. And he received the Nobel Prize thanks to Marx.
But he said thank you to Marx.
But Leontief did it wrong. And his equations turned out to be not fundamental, but engineering-oriented.
The author of the book did it right; everything was done exactly according to Marx. And now it is possible to organize economic calculations based on Marx’s CAPITAL. But mathematicians and physicists are needed. The work must be continued.Marx believed that the mathematical model of CAPITAL could predict the date and scale of a new global crisis. But Marx’s CAPITAL is a very complex book.
We need young mathematicians and physicists to build a complete mathematical model of Marx’s CAPITAL. And then we will need to incorporate the economic data of global monopolies into this model.ABOUT MARX
The book CAPITAL is the greatest scientific work in the entire history of humanity. Marx’s Capital is more complex than quantum mechanics and the theory of relativity combined. In the book, I showed that it is quite possible to build a quantum model of Marx’s Capital.
. “Capital” by Marx is a book for the new Gausses and the new Hilbert. Only young, brilliant physicists and mathematicians will be able to fully study Marx’s great work.And then the young geniuses will tell humanity: Marx’s book shows the path to the salvation of humanity.. Humanity is not yet ready for Marx.
MATHEMATIZED DIALECTICS OF HEGEL. The author studied abstract dialectical pairs of categories A–B, C–D. The author introduced a multiplication operation for such pairs of categories. The author’s goal is to derive the theorems of Hegel and Marx using an algebraic method.
Friends! I hope that there will be mathematicians and physicists who will continue the work. They will be able to build a complete mathematical model of the world economy based on Marx’s book.
And my task is to make it easier for new young mathematicians and physicists who will take on this titanic task. Nikolai Mokushev.