“Is math racist?” asked a recent article in USA Today, the largest circulated newspaper in USA. The headline was widely mocked following which the paper changed it, and clarified that the article was about math education being racist.
Clearly, EVERYBODY in US thinks math (per se) can NOT be racist: after all, where is the racism in 1+1=2? Nonetheless, this article argues to the contrary— that math per se is racist, not merely math education or math history (which, of course, is racist). But let us begin with the easier aspect of racism in math history.
Contrary to false history, the West, starting from the (White) Greeks and the Romans, was traditionally a laggard in math. Greeks and Romans were backward even in elementary arithmetic of fractions compared to (Black) Egyptians.
The USA Today article talked only about the way students of color are taught math. But there is the wider issue of the racism inherent in the stock terminology of the “Pythagorean theorem”, taught to all students. That terminology slyly teaches all students that Blacks were intrinsically inferior in math. Thus, that terminology is justified by claiming that (White) Greeks did a “superior” kind of geometry compared to (Black) Egyptians. (Actually, (White) Greeks were laggards in math, and lacked knowledge of even elementary fractions as found in the Ahmes (Rhind) papyrus.) But, as regards geometry, as this earlier article[1] explained, that claim of superiority is blatantly false: there are no axiomatic proofs in the “Euclid” book.
Yet another subtler question arises: are axiomatic proofs really “superior”? Also, since axiomatic proofs did not originate with the “Euclid” book (in which they are not found) how exactly did they originate? When and why?
As this previous article explained,[2] axiomatic proofs originated during the Crusades, as part of the church political requirement for a Christian version of the Islamic theology of reason (aql-i-kalam). Though the church wanted reason, it could not reason in the normal way (“I see smoke, therefore, there is a fire”). This normal reasoning starts from observations (“I see smoke”) or facts. The church could not use normal reasoning since facts were contrary to most church dogmas. Therefore, the church invented axiomatic reasoning, or the method of reasoning from assumptions (or axioms) instead of facts, and prohibiting the use of facts. That explains the when and why of axiomatic proofs.
Typical of the church, it declared anything politically convenient to itself as “superior”. Accordingly, this medieval method of axiomatic reasoning was declared “superior”, and is still believed to be. Hence, most “modern math” is based on the axiomatic method. However, as the previous article explained, there is nothing practically, epistemically, or aesthetically superior about axiomatic reasoning (or axiomatic math). That is just a Crusading superstition embedded in the foundations of “modern math”.
But all this has to do with the church. Where is the racism?
A broader understanding of racism
As already explained, in this earlier article,[3] racism, or the silly belief that Whites are superior to Blacks, itself began with the church assertion that Christians are superior to non-Christians. This led to the related assertion (bull Romanus Pontifex) that Blacks could be enslaved, since they were non-Christian. Assertions of White superiority came later, after slavery of Blacks.
Specifically, racism is not limited to colour prejudice, but is all about assertions of “superiority”. To successfully eradicate racism (in the sense of assertions of White superiority), one must understand its relation to other assertions of superiority: the religious prejudice which preceded it (which asserted Christian superiority) and the colonial prejudice which followed it (which asserted Western superiority). That is, racism started with the church proclamations of the religious superiority of Christians, which was the basis of slavery.
But after the large-scale conversion of Blacks following the transatlantic slave trade, slavery could no longer be justified on that belief in religious superiority. Hence, it mutated into a belief in White superiority, to preserve the profits from slavery and the slave trade. Specifically, the belief in Christian superiority mutated to the belief in White superiority using the Biblical curse of Ham, or the curse of Kam, which asserted Blacks were black since inferior Christians. (Therefore, they could still be enslaved.)
Still later, the profits of colonialism (since 1757) hugely overshadowed the profits of slavery,[4] especially for Britain (whose profits from slavery had declined sharply after American independence, 1776). Further, on the Aryan race conjecture[5] (1786), it came to be believed (no evidence needed, as usual) that the colonized were of the same race as the colonizer. Therefore, the belief in White superiority further mutated into the belief in Western (civilizational) superiority, to preserve the profits of colonialism. (So, the West could pretend it was only spreading its “superior” “civilization”, not committing vast genocides and looting people to steal wealth it could not honestly create.)
The one constant in all this was the assertion of superiority, which always applied to the same group of humans, no matter how they were variously labelled, whether as Christians, or Whites, or West.[6] In parallel, the same glorified early Greeks were ascribed different labels from “friends of Christians”, to Whites, to Westerners.
So far as math is concerned, the claim was, as we saw, that “Greeks” did a “superior” geometry, and the fantasized “Greeks” were successively regarded as “friends of Christians”, then Whites, then Westerners. As we saw, the sole basis of that purported superiority of Greeks in math was the mythical claim that they used “superior” axiomatic proof, which is, alas, not even found in “Euclid”!
That is, a first indication of the racism of axiomatic math (per se) lies in the assertion that axiomatic proof is “superior”. Is this assertion of superiority anything more than another silly church superstition, exactly like the church assertion that (curse of Ham) that Whites are “superior” Christians? As we saw, axiomatic math is not practically, epistemically or aesthetically superior. (However, most people don’t easily understand this.)
Regardless, one might object that in case of the assertion of Christian/White/Western superiority, those assertions enabled one group of human beings (differently labelled as Christians/Whites/Westerners) to dominate over another group (non-Christians/non-Whites/non-Westerners). How does the assertion of the superiority of axiomatic math enable one group of humans to dominate others?
Let us examine it.
What then is the real value of axiomatic math?
If formal math fails to add practical, epistemic or aesthetic value, to normal math, what is its value? Why not openly revert to normal math, which is what is actually used in practice? Why continue with the confusing mixture of useless formal math and useful normal math?
The answer may be quite unexpected, but brings us to the crux of the thesis that axiomatic math is racist.
Axiomatic math is politically valuable today to Christians/Whites/Westerners whom it puts in charge of mathematical knowledge. Let us understand how that happens.
First, recall, from the previous article, that axiomatic math prohibits the empirical hence converts math to metaphysics. In metaphysics authority is the sole way to decide truth. That is, converting math to metaphysics, as Russell[7] realized he did, makes mathematical “truth” authority-dependent. This insidious consequence of doing mathematics axiomatically has gone unnoticed and uncommented. This actuality is in stark contrast to the widely prevalent naive view that mathematical theorems are universal truths.
Specifically, the truth of most mathematical axioms or theorems cannot be decided by checking whether they are true in the real world. For example, the plausible-seeming “axiom of choice” (a principle of transfinite induction), commonly used in current math, cannot be empirically checked for an arbitrary collection of infinite sets to which it is supposed to apply. Likewise, on the Banach-Tarski theorem,[8] a consequence of set theory, a ball of gold can be subdivided into a finite number of pieces which can be reassembled (without stretching) to create two balls of gold identical to the first. This is obviously false in the real world (but still true as a mathematical theorem).
That is, since the empirical is excluded from axiomatic math, there is no way to decide “mathematical” truth (of metaphysical axioms or theorems) based on one’s experience, or common sense, any more than the validity of the medieval theology of immaculate conception can be so decided.
The next question is: which authority decides mathematical truth? After colonialism (i.e., in “post-colonial” times) the locus of mathematical authority is among Whites/West (and those they approve).
Western ethnomathematics, incorporating the church theological way of axiomatic reasoning, was globalised during colonialism. This globalisation was not done with a specific plan to ensure White/Western dominance. Presumably, it was done just because of the silly racist/religious belief that church methods of reasoning, attributed to the Greeks, were “superior”. (Church propaganda always has been “we are superior, imitate us”.) However, the sustained racist belief in the superiority of Western ethnomathematics naturally had the racist consequence of making White/Western mathematicians socially dominant in math.
This is, just as the religious/racist belief in the superiority of Christians/Whites led to the denigration and enslavement of Blacks, so also the religious/racist/colonial belief in the “superiority” of church/colonial math led to the mental subordination/enslavement of the whole world, through colonial education. Math is, today, a compulsory subject in schools.
The current social dominance of the West in math is not due to any historical Western achievements in math. To reiterate, contrary to false history, the West, starting from the Greeks and the Romans, was traditionally a laggard in math. Greeks and Romans were backward even in elementary arithmetic. Elementary fractions were introduced in the European curriculum only in the late 16th c., but were known to Black Egyptians, and taught by Ahmes the scribe (Rhind papyrus), 3000 years earlier.
Due to ignorance of fractions Greeks and Romans had such a bad calendar (since stating the duration of the year requires fractions of days). This bad (Roman) calendar was adopted as the official Christian calendar in the Council of Nicaea (4th c.). It used the primitive system of leap years, a practice continued in the reformed Gregorian calendar. Leap years are a very inferior substitute for precise fractions, for they get the duration of the year right only on a 1000-year average, and not from year to year/
Likewise, the stories that Newton and Leibniz discovered calculus are bunkum. The domination of math by the West started with the attempts to understand the stolen Indian calculus using axiomatic real numbers, which eventually led to set theory and “modern math” or present-day math, which is cast in the axiomatic mould.
This social dominance of the West is reflected in the contents of present-day math. That is, this is no longer about racism in math history or math education, it is about racism in math per se. Thus, the content of axiomatic math has two components: axioms and theorems. Both are tightly controlled by Whites/Westerners.
Thus, the axioms of formal mathematics are, in principle, perfectly arbitrary (Russell: “we take any hypothesis that seems amusing”). However, all the axioms of formal math, as used in the math actually taught today, are all exclusively laid down by Westerners. For example, calculus is taught using real numbers whose axioms were laid down by Dedekind. Real numbers are constructed (and most math assumes) axiomatic set theory whose axioms were laid down by von Neumann, Bernays and Gödel, or Zermelo, Skolem, and Fraenkel in the 1930’s.
It is NOT necessary to teach calculus using real numbers. Even within axiomatic mathematics, calculus could be taught in another way, using non-Archimedean arithmetic, the way calculus originated in India.[9] This makes calculus very easy. But because the West controls math, to teach such (semi-decolonised) calculus, even with another set of axioms, first requires the permission of Western mathematicians.
That requirement of prior permission is the equivalent of the bonds of slavery and colonialism. On this analogy, decolonization of math is about breaking the Western stranglehold on math, by its conversion to metaphysics, and its spread by church/colonial education. One cannot breakaway by “prior permission”, any more than slavery or colonialism could be abolished by prior permission.
In a free society, as opposed to a racist or colonised one, what math to teach would be decided by educated public debate, and the usefulness of math to society. But Western mathematicians absolutely and persistently refuse to participate in any public debate on the philosophy of math. Reason? They know the arguments defending Western ethnomath are weak, and they currently rule all mathematics. And they have the inquisitional method of deciding truth secretively (“secretive peer review”), so they can do just what they like behind that veil of secrecy. For public discourse, they can always resort to the high Western “scholarship” of abuse and lies so ably demonstrated by scholars from leading Institutions (see previous article for details).
The West controls not only the axioms, but also similarly controls the theorems of math (to decide whether a theorem has been validly proved, whether it is “interesting”). (This is not to mention how theorems are named so as to glorify the West.) Theorems too need Western social approval, for the proposed proof may be wrong (fallible). As an example a Japanese claims to have proved the abc conjecture. But this has not been socially approved by the West (Japanese are only “Honorary Whites”!) hence the claim is treated as false! Another example, is how to judge the “value” of a failed/incomplete attempt to prove the Riemann hypotheses.[10] What Socrates thought of as the eternal truth of mathematics, have been reduced to a farcical process of mere social approval in a dystopian society.
To reiterate, the Western social approval process for math involves a highly secretive and opaque process under the control of editors who may well be dishonest. For example, Andy Magid, the editor of the Notices of the American Mathematical Society dishonestly helped to cover up the plagiarism from my published book by the “top” mathematician Michel Atiyah, on the centenary of Einstein’s special relativity paper.[11] Magid misused his editorial powers to suppress my response.[12] What is interesting is that not a single mathematician from the American Mathematical Society stood up against this clear violation of ethics: mathematicians understand the repressive Inquisitional nature of their society. Because of secretive refereeing there is ample play for further subjectivity in what exactly is “amusing” and what is “interesting” and what is not! That is the Western mathematicians are dictatorial rulers of axiomatic mathematics.
That is, the West has total control over formal mathematics, both its axioms and theorems. Under such conditions, it will never approve of any change because that would leave Westerners with egg all over the face, such as admitting that the West stole the calculus,[13] suppressed the evidence of its theft for centuries [14]. What is suppressed till today is the failure of the West to understand the knowledge it had stolen, so that there is a better way to teach calculus.[15] For this change for the better to happen the totalitarian rule of the West over math must be broken.
The difficulty of axiomatic math
Western rule over axiomatic math is strengthened by the fact that axiomatic math makes the easiest things like 1+1=2 excessively difficult. This difficulty makes most people ignorant, hence makes them fear math and forces total reliance on authority.
Thus, we have seen the difficulty in the axiomatic proof of 1+1=2. Compare it to simple normal math which involves the empirical observation that 1 apple and 1 apple make 2 apples, a math that any child in kindergarten can understand. But, almost nobody can understand Bertrand Russell’s 378 page proof of 1+1 = 2.
In fact, there are additional complexities. 1+1=2 is an ambiguous statement in axiomatic mathematics. There is no unique number 1. The real number 1 is not the same entity as the cardinal number or the natural number 1. Failing to understand this, the senior mathematician who participated in the Cape Town debate on Decolonizing Science,[16] triumphantly claimed that Peano’s axioms could be used to prove 1+1 = 2. Pitiably, Peano’s axioms do not apply to real numbers (and my question pertained to the real number 1). The senior mathematician, sunk in his South African sense of White superiority never properly learnt even 1+1=2 in axiomatic math, and was too dishonest to admit his mistake.
The axioms of axiomatic set theory (as distinct from naive set theory[17]) do apply to real numbers, but that makes the proof of 1+1 = 2 in real numbers, from first principles (without assuming any result from set theory). extraordinarily complex. So complex, that I offered a prize of ₹1 million in India’s leading University, JNU for a proof of this from first principles.[18] But no one accepted the challenge.
This extreme difficulty adds to the political value of axiomatic mathematics. Lots of people complain that math is difficult. They usually blame themselves or their teachers, never the subject, though, if students and teachers were at fault the same problem would arise with other subjects. though quite clearly it does not: no subject other than math has such a fearful reputation. And axiomatic math IS undeniably difficult, as we just saw, even in the case of 1+1=2.
This difficulty (of axiomatic math) has political value because it makes most people afraid of math, and ignorant of it. Fear of math makes people reluctant to apply their mind: they mindlessly trust the designated social authorities in math — the colonially educated formal mathematician. Fear of math makes people dependent on socially designated “experts”.
The church understood that value of fear long ago, hence implanted fear of God and ignorance of Latin and Greek (sources of Bible) so that the church will was done here on earth (as it never will be in heaven!). The point is, fear and ignorance of anything works, it does not have to be God. The church made people believe they needed God for their future lives, to avoid burning in hell forever. People really do need math for science and future technology.
The question is which math do people need for science and technology? Normal math (which accepts the empirical) or formal math? The two are conflated, though the relation between the two is as exploitative as the master-slave relation on American plantations. Normal math is like the slave, and really does all the practical and useful work; useless formal math is like the master, claims superiority by staying aloof from the empirical (adding metaphysics) and grabbing all the credit, the way the master grabbed all profits from the slave’s work while ill treating the slave, both by using the racist claim of superiority.
In other words, for applications to science and technology, what is needed is normal math; formal or axiomatic math and its complex metaphysics are entirely irrelevant.
The power of the formal mathematician
But who decides which math to teach? The Western/formal mathematician has the sole prerogative to do so, because church education and Western ethnomathematics incorporating the church way of reasoning was globalised during colonialism.
To reiterate, most people, being scared of math, are afraid to apply common sense any more than they dared to apply common sense to church theology. They passively accept the authority of the formal mathematician.
This category of “most people” also includes decision makers such as most Vice Chancellors of universities. Tell them about an alternative way to do math easily (“decolonised math”) and they might be excited. But they will say, “we will consult with our mathematics department and get back”. There is no chance of a favorable response. The math departments almost always has only formal mathematicians who veto it, since they are allowed to judge in secret.
In short, formal mathematicians have a global stranglehold on math education, even if they contribute nothing useful or beautiful to math, they get paid a useful salary for their idle metaphysics and gatekeeping. The one thing absolutely taboo is a public debate on Western ethnomathematics, for that will result in its collapse.
The axioms of present-day math all involve a metaphysics of infinity. Noticeably, these fantasies about infinity are remarkably analogous to church fantasies about eternity.[19] People who thought medieval church theology has ended should think again. It has expanded! We now have the whole world of formal mathematicians exploring fantasies, not about angels but about eternity and infinity! Modern math has revived medieval metaphysics.
To summarise, the theorems of math are NOT some universal truths, but mere socially approved relative truth, relative to these Western socially approved fantasies (metaphysical axioms) about infinity.
Effect on science
Because mathematics is central to knowledge, control of math allows control of various branches of knowledge, such a physics, statistics, economics, etc.
As already stated there is a remarkable resemblance of these mathematical fantasies (metaphysical axioms) about infinity to church (politicised) fantasies of eternity.[20] Hence, this control over (axiomatic) math enables manipulation of science at the highest level, as in Stephen’s Hawking’s creationist claims.
All that is needed are signs of social approval, as in the recent Nobel prize to Roger Penrose.[21] The common people who understand not a word of the underlying math, avidly believe all that is said as “scientific truth”, as avidly as medieval Europeans believed the church. Likewise, in economics we have Arrow’s impossibility theorem.[22] This means that through control of “mathematical truth”, West can control various branches of knowledge. At least what is perceived as truth. That is a terrific propagandist advantage.
Summary and Conclusions
We already saw in the first article in this series that the racist terminology of “Pythagorean theorem” is supported by the claim that “Greeks” did a superior kind of mathematics. But there are NO axiomatic proofs in the “Euclid” book.
Nevertheless, when this fact was exposed by Bertrand Russell and David Hilbert, they along with most European mathematicians, still accepted the polemic of superiority of axiomatic proofs. (This was at the peak of colonialism.) Hence, they (and other mathematicians) soon converted most mathematics to axiomatic mathematics, also called “modern math”.
Despite boasts of rigor, as we saw in the preceding article, axiomatic mathematics is NOT superior in terms of practical, epistemic, or aesthetic value. However, axiomatic mathematics is 100% metaphysics. Consequently, “modern math” has restored the uselessness and ugliness of medieval theology. The difference is that, through math, the whole world is now involved in the silly games of medieval theological proofs.
In metaphysics, the only way to decide truth is by authority. And, Western mathematicians control the content of axiomatic mathematics, as currently taught and practiced, both its axioms and its theorems. During colonial times this Western ethnomathematics was globalized, using the polemic if its superiority, which was never critically examined by the colonised.
That is, the assertion of the superiority of Western ethnomathematics has resulted in the West dominating mathematics, and deciding its content. Assertions of superiority, resulting in domination by Christians/Whites/Westerners is the core of racism. Hence, mathematics per se is racist.
Because axiomatic mathematics is excessively difficult, most people are reduced to ignorance of math. Hence, people naively feel that before any change the prior permission of Western mathematician is necessary. Of course, neither slavery nor colonialism was abolished by prior permission. In mathematics, this “prior permission” involves a peculiar secretive process of review. The editors ensure this will never go against the grain of the community.
Decolonization of mathematics requires overthrowing the authority of the Western mathematician. Hence, such secretive processes must never be allowed. Instead, those who object to the change should be asked (or compelled) to publicly debate their objections. So far, my experience has been that all mathematicians run scared from any sort of public debate, because they understand the innate weaknesses of axiomatic mathematics (and even their knowledge of formal mathematics is rarely sound).
Control of mathematical knowledge enables control of knowledge in allied fields (such as physics, economics, statistics). This control is misused at the highest levels, as in Stephen Hawking’s creationism, the recent Nobel prize to Penrose, or Arrow’s impossibility theorem.
References
[1] “Racism in the math classroom: “Pythagorean theorem” and the two myths of “Euclid”, https://medium.com/@c_k_raju/racism-in-the-math-classroom-pythagorean-theorem-and-the-two-myths-of-euclid-c83da308bda4.
[2] “The church origins of (axiomatic) math”, https://medium.com/@c_k_raju/the-church-origins-of-axiomatic-math-e08036dbe29d.
[3] C. K. Raju, ‘“Euclid” Must Fall: The “Pythagorean” “Theorem” and The Rant Of Racist and Civilizational Superiority — Part 1’, Arụmarụka: Journal of Conversational Thinking 1, no. 1 (2021): 127–55. http://ckraju.net/papers/AJCT-Euclid-must-fall-Part-1.pdf.
[4] Eric A. Williams, Capitalism and Slavery (University of North Carolina Press, Chapel Hill, 1944).
[5] W. Jones, ‘The Third Anniversary Discourse, Delivered 2d February, 1786: On the Hindus”’, in The Works of Sit William Jones, vol. 1 (London: G. G. and J. Robinson, 1799), 19–34.
[6] The definition of “West” on the religio-historic theories of Toynbee and the military strategy of Huntington’s “soft power”, reverts to that religious connection, in the search for world power, after the Cold War. Arnold Toynbee, A Study of History (Oxford University Press, 1957); Samuel P. Huntington, The Clash of Civilizations and the Remaking of World Order (Viking, New Delhi, 1997).
[7] Bertrand Russell, ‘Mathematics and the Metaphysicians’, in Mysticism and Logic and Other Essays (London: Longmans, Green, and Co., 1918), 74–96.
[8] http://ckraju.net/sgt/technical-presentations-faculty/ckr-sgt-tech-presentation-2.pdf.
[9] C. K. Raju, ‘California, Indian Calculus and the Technology Race. 2: Don’t Cancel the Calculus, Make It Easy!’, Boloji.Com, 24 December 2021, https://www.boloji.com/articles/52950/california-indian-calculus-and.
[10] Such as those of B. Bagchi, see C. K. Raju, ‘Kosambi the Mathematician’, Economic and Political Weekly 44, no. 20 (16 May 2009): 33–45, https://www.epw.in/journal/2009/20/special-articles/kosambi-mathematician.html.
[11] See the belated acknowledgment in Notices of the American Mathematical Society54(4) (2007) p. 472. http://ckraju.net/atiyah/Belated_mention_NoticesApril2007.pdf. More details, http://ckraju.net/atiyah/atiyahcase.html. For the latest in this continuing cover-up act by AMS, see, “Plagiarism by ex-president of the Royal Society. 2: The cover-up by the American Mathematical Society”, http://ckraju.net/blog/?p=184, and “Part 1: The facts”, http://ckraju.net/blog/?p=183. Noticeably this is a collective phenomenon. Ordinary member of the AMS failed to publicly condemn the actions of the AMS.
[12] http://ckraju.net/atiyah/petition/Atiyah-press-release.html.
[13] C. K. Raju, ‘California, Indian Calculus and the Technology Race. 1: The Indian Origin of Calculus and Its Transmission to Europe’, Boloji.Com, 11 December 2021, https://www.boloji.com/articles/52924/california-indian-calculus.
[14] M. D. Srinivas, “Emergence of a New Era in the History of Indian Mathematics”, Bhavana 6(3) https://bhavana.org.in/emergence-of-a-new-era-in-the-history-of-indian-mathematics/.
[15] Raju, ‘California, Indian Calculus and the Technology Race. 2: Don’t Cancel the Calculus, Make It Easy!’
[16] Decolonising Science Panel Discussion: Part 1 (University of Cape Town, 2017), https://youtu.be/ckbzKfRIi6Q.
[17] Paul R. Halmos, Naive Set Theory, 1960.
[18] “Statistics for social sciences and humanities: should we teach it using formal math or normal math?” starting at https://youtu.be/A9Og1k-Z5O4?t=662. http://ckraju.net/papers/presentations/statistics-jnu.html#slide-org948751a.
[19] 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. http://ckraju.net/papers/Eternity-and-infinity-Pages-from-APA.pdf.
[20] Raju.
[21] C. K. Raju, ‘A Singular Nobel?’, Mainstream 59, no. 7 (30 January 2021), http://www.mainstreamweekly.net/article10406.html.
[22] Discussed in more detail in C. K. Raju, The Eleven Pictures of Time: The Physics, Philosophy and Politics of Time Beliefs (Sage, 2003).
