Marx and mathematics-5:
The relevance for Marxism

C. K. Raju

To recapitulate, Europeans stole the calculus from India, and claimed its “discovery” on their infamous doctrine of discovery. On the epistemic test, thieves, like students who cheat in an exam, fail to fully understand what they copy, regardless of how much they are glorified. Hence, Newton and Leibniz and others failed to understand calculus, particularly the notion of derivative and how to sum an infinite series. This explains the mystery of discovery sans understanding. Further, while some Europeans in the 19th c may have used terms like limits, it is wrong to retrospectively superpose the current meanings of those words, for there was no coherent account then of formal real numbers needed for limits. Therefore, in the 19th c., it is but natural that a clear thinker like Marx too failed to understand these notions.

So what difference does it make if Marx never understood the calculus? For this, we need to shift our focus a bit. Apart from the issue of Marx’s understanding of mathematics there is also the more important but completely neglected issue of the Marxist understanding of mathematics.

Post-revolutionary societies
Marx did not theorise much about post-revolutionary societies. But the planned economy was extremely successful and catapulted Russia from the poorest nation in Europe to a superpower in a short span of time. True, planning faced problems then because of the slow speed of data collection, which is irrelevant today in the days of instant big data. Likewise, China’s present-day economic prosperity and military might is indubitable. In India, though a similar model of a planned economy—the Feldman model called the Mahalanobis model here—was used, Nehru’s aim was different, to give invisible subsidies1 to private capital in order to build capitalism in India, and it succeeded in that aim. Basically, planning (whatever its aim) results in better performance to achieve that aim, in the economy as in other things.

But despite the economic and military success of the planned socialist economies, the Soviet system collapsed. Why? I believe that to understand this, we need to go beyond the usual cliches of internal corruption etc. and look at the failure to theorize adequately, even after the fact. First, as many people have noticed, contrary to Marx’s expectation that a revolution would first take place in a society where the productive forces were most highly developed, the actual revolutions took place in the most backward and “feudal” agricultural societies like Russia, China, Vietnam, and Cuba where the productive forces were least developed on Marxist theory, but there was a high incidence of poverty. However, there is another less-noticed feature common to these revolutions. They took place in societies which were also educationally “backward”.

Macaulay’s recommendation for the British poor
But after the revolutions, all these societies came under intense international pressure. The only way they had to meet that pressure was to use science and technology to rapidly develop their military power and economy. This required widespread science education, and the only model of science education available then was the Western model of education, a model declared as essential to science education by Macaulay in his infamous minute on education.

But all failed to notice a critical issue: Western education, in Marx’s/Macaulay’s time, was entirely owned by the church, and had been so owned for centuries. It is a great folly to imagine that this education was designed by the church to benefit the educated, as even so many Marxists do to this day, when they simplistically demand “education” for all, without bothering about the content of that “education”. But the opponents of Marxism understood this dimension of education.

The Communist Manifesto begins by asserting that “a spectre is haunting Europe”. However, Marxists have ignored what the European aristocracy did to exorcise that spectre. Remarkably, (“Lord”) Macaulay, in a speech in British parliament, shortly before the Communist Manifesto, raised exactly that spectre and proposed education as the best counter-revolutionary measure to exorcise this spectre.2

Note that, in the British context, Macaulay’s claim (that education would stop revolution) was completely different from his claim in India that Indians needed Western education for science. But the two claims are obviously linked, because both involved the same system of church education. To reiterate, the same Macaulay who said that Indians needed Western education for science, also said that the British poor should be given state-sponsored, free education solely to PREVENT a revolution from taking place in Britain. Why? Because, according to him, “the state is not a hangman”, and failed in its duty if it only hanged people after a revolt, and much destruction of property; it must work to prevent that from happening. And, Macaulay opined, the cheapest means to prevent revolt was (Western) education. (This is a subtler version of the common claim today that “development” will prevent revolt.) Macaulay hence demanded state-sponsored, free education for the poor, just as Marxists do today. What an ironical agreement between counter-revolutionaries and professed revolutionaries!

Western education meant church education then. I must reiterate that not only mission schools, but all the “respected” big universities, such as Oxford, Cambridge, and Paris, were set up by the church and kept under its thumb for centuries. And the fact is (whether a correlation or a cause) that Macaulay was right: wherever this education penetrated, whether in Britain or India, there was no revolution. The spectre of revolution was successfully exorcised by “education”.

However, while Marx dismissed Macaulay as a Whig historian, Marxists never thought it worthwhile to discuss this education as a counter-revolutionary measure. They stick to the dogmatic line that “education is progressive”, even if was suggested by Macaulay against a revolution, and even if it is church education, and teaches superstitions. Hence, Marxists have never demanded a change in it or a re-examination of the content of education, especially not as regards math or science. This was a major mistake.

Because of its counter-revolutionary potential, church education imported for science created a “schism in the soul” in post-revolutionary societies. Was this responsible also for their collapse? Without going into numerous particulars, the point is simply this. The post-revolutionary societies were put in a paradoxical situation: to save the revolution, they needed science for which they needed church education which was counter-revolutionary, and propagandised those it “educated”.

Propaganda through science and science education
Western education certainly permits a variety of Christian superstitions to be slipped into the minds of the “educated”, eventually creating a huge internal dissonance. No one suspected science and mathematics could be a vehicle for superstition, but the effect is manifest. The most comic and easy example of superstitions in science is Pervez Hoodbhoy, a Pakistani physicist, who has been arguing for decades, exactly like traditional Christian propagandists against Islam, that the Christian superstition about God’s “eternal laws of nature” is essential to science.3 (For the manner in which this is still used as part of Christian propaganda today, see these minutes.4 ) Incidentally, the same claim was also made by Steven Weinberg a Nobel prize winner in physics.5 (The two claims are connected.) But the Christian superstitions in formal mathematics are much harder to spot and remove.

Perhaps another example will help. During the Cold War, the “respected” journal Nature relentlessly wrote propagandist pro-West and anti-Soviet editorials in every issue. The objective was clear, “if you want our science, you must take the political propaganda with it,” though in that case, the propaganda was up-front, and not dangerously hidden.

The church understood this tactic long ago, that propaganda, to be palatable, must be mixed with something of recognizable value. This is like mixing poison with something agreeable. This is one reason why it is church institutions which brought science to the colonised. This simple fact is totally contrary to the story that science and the church are at war, but the colonised avoid the facts staring them in the face and go by the story (mostly the 500 year old story of Galileo, without checking the facts even in that one case). The fact is manifest: the best undergraduate colleges for science in India, such as St Stephen’s, or Madras Christian College (whose products dominate TIFR and, consequently, Indian math education6 ) etc. are still church institutions. Why would the church help to disseminate science worldwide if science was at war with the church?

But manifest facts slip from the minds of the church educated as easily as water off a duck’s back. They stick to the story. And a story can be indefinitely defended. As I teach in my course on the History and Philosophy of Science, any silly theory can be defended against any facts, for any length of time, by piling on the hypotheses. (A common current example from science is the hypotheses of dark matter, and its peculiar distribution as a halo, used to explain away the manifest failure of Newtonian gravitation for the galaxy.7 ) In a word, stories can be saved from contrary facts by piling on a thousand more stories. One lie can be saved by telling a thousand more, this must be understood as a strategy for preserving lies, not as an old proverb against telling lies.

Metaphysics and superstitions through math
Mathematics is needed for science. And Western formal mathematics, taught today, is founded on the superstitious belief that prohibiting the use of facts is what makes formal math “superior” to normal mathematics or other indigenous systems of mathematics. This claim of superiority is like racist claims of superiority: it has never been debated. Prohibiting facts was a belief so very convenient to the church (for all its dogmas are contrary to facts), but such prohibition of facts is of negative value to science. So, formal math should NOT be used for science.

Because of its divorce from the empirical, formal mathematics is pure metaphysics in the Popperian sense, as also admitted by Russell when he said “[formal] mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”8 Why should this be the best basis of science? But people, indoctrinated to mimic the West from childhood, swallow the story all the same, and believe there is some magical value in formal math

In practice formal math forces blind reliance on authority, which reliance the church cements by spreading ignorance of mathematics, through education, even at the level of why 1+1=2 (in formal real numbers). That widespread ignorance of math is another undeniable fact. The ignorant cannot change the system. But the church indoctrination makes the colonised feel pretty happy with their state of ignorance in math and they don’t want any change in the education system, especially as regards math and science, though it came specifically for that reason. They believe, as the church wants them to do, that they are bad in math because they are personally inferior.

Reliance on metaphysical axioms instead of facts also allows political prejudices to be slipped in easily. This is very clear in the case of economics, say Arrow’s impossibility theorem which got the Nobel prize.9 But exactly how does that happen in calculus? Through axioms about infinity related to church dogmas of eternity.10 Briefly, calculus is used to formulate the “laws of physics”, and if formal real numbers are used for calculus, that metaphysics forces beliefs about time and eternity to be aligned to church dogmas about “linear” apocalyptic time.

Stephen Hawking’s creationism (singularity theory) was only meant to drive the point home: that church superstitions can be recast as scientific truths. But when I first addressed these issues in informal meetings on science and society in Delhi university in the 1990’s I found many Marxists who were fans of Stephen Hawking, and had bought his popular book (though no one admitted to having read it!). Even the general relativists understood very little of Hawking’s singularity theory, as became apparent in a later public debate with Roger Penrose.11

The remedy
So what is the remedy? Can the colonised (or future revolutions) be saved from this poisonous mixture of truths and untruths in Western math and science, coupled with widespread ignorance? The remedy obviously is to decolonise education, particularly mathematics and science. Marxists who have never demanded it, should do so now. Decolonisation does NOT mean wholesale rejection of everything “Western” as so many prejudiced people often jump to caricature.12 It does not mean that if only because so much of the Western history of science is false, and what is declared “Western”, such as calculus (or the Copernican model, due to Ibn Shatir), is not Western in origin.

Anyway, decolonisation actually means being critical; it means understanding and getting rid of the church superstitions in mathematics and science. Why should anyone object to this agenda? It seems clear that only an inferior sort of science can be based on a form of mathematics which prohibits facts. If there is any genuine doubt on this issue, it should be resolved by a critical and public comparison between the two different philosophies of mathematics, of normal mathematics vs formal mathematics, a comparison which was never done, leave alone publicly debated. And any attempt to do so today is widely censored.13 Formal mathematicians have been persistently refusing to carry out such a comparison publicly,14 preferring to exert authority from behind closed doors to continue to fool the common people who are ignorant of math. And the colonised trust those “experts” implicitly!

The ignorance results in a belief that there is no alternative to imitation of the West. Church education also typically instils the fear that failure to follow the rituals, or failure to imitate the West, will result in some sort of apocalypse. These superstitious fears are completely unfounded: to reiterate, most advanced technological applications, such as NASA calculating the trajectory of a rocket, are all done on computers, and computers cannot work with real numbers. (Computers use what are called floating point numbers, which are quite different, and do not even obey the associative law for addition.15 ) That is practical applications, including artificial intelligence, use normal mathematics not formal mathematics. In fact, calculation of rocket trajectories involves numerical solution of differential equations, in a way which is perhaps slightly more efficient than what was done by Aryabhata and his followers, but based on the same principles.

Anyway, if future revolutions are to succeed, Marxists must clearly understand that accepting church superstitions (in both math and science) is not a precondition to do science. They must see that this acceptance of church education is strongly counter-revolutionary, as Macaulay correctly thought. To the contrary, science and math need to be reformed, and ripped away from church superstitions, and Western false history, especially about the axiomatic inferiority of everything non-Western.

Decolonisation of math and science is a precondition to sustain a successful revolution.

Notes & References
1  C. K. Raju, “Kosambi the Mathematician,” Economic and Political Weekly 44, no. 20 (May 16, 2009): 33–45, Also,
2  T. B. Macaulay, Speech to the House of Commons, 18 April 1847, vol. IV, Speeches of Lord Macaulay, n.d.,; C. K. Raju, “Education and Counter-Revolution,” Frontier Weekly 46), no. 7, Aug 25-31 (2013),
3  C. K. Raju, “Islam and Science,” in Islam and Multiculturalism: Islam, Modern Science, and Technology, ed. Asia-Europe Institute University of Malaya and Japan Organization for Islamic Area Studies Waseda University, 2013, 1–14,
4  “Minutes of a Discussion in the Philosophy Department of the Universiti Sains Malaysia,”,
5  Steven Weinberg. “A Deadly Certitude.” In Lake Views: This World and the Universe, 216–217. Cambridge, Mass.: Harvard University Press, 2009.
6  “Kosambi the mathematician”, cited above.
7  C. K. Raju, “Functional Differential Equations. 4: Retarded Gravitation,” Physics Education (India) 31, no. 2 (June 2015),
8  Bertrand Russell, “Mathematics and the Metaphysicians,” in Mysticism and Logic and Other Essays (London: Longmans, Green, and Co., 1918), 74–96.
9  C. K. Raju, The Eleven Pictures of Time: The Physics, Philosophy and Politics of Time Beliefs (Sage, 2003) chap. 10, “Time as money".
10  C. K. Raju, “Eternity and Infinity: The Western Misunderstanding of Indian Mathematics and Its Consequences for Science Today,” American Philosophical Association Newsletter on Asian and Asian American Philosophers and Philosophies 14, no. 2 (2015): 27–33.
11  C. K. Raju, “Penrose’s Theory of the Mind: A Rebuttal,” in Debate with Roger Penrose, in: Matter of the Mind, India International Centre (New Delhi, 1997).
12  C. K. Raju, “Be Critical, Choose What Is Best,” The Sun, Malaysia, August 29, 2011
13  C. K. Raju, Mathematics, Decolonisation and Censorship, 2017,
14  “Conversation with a Formal Mathematician,”
15  C. K. Raju, “Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhāṣā,” Philosophy East and West 51, no. 3 (2001): 325–362

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Sep 13, 2020

Prof. C. K. Raju

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