Eliminating the myth, fraud, and superstition in formal math

C. K. Raju

*Indian Institute
of Advanced Study
Rashtrapati Nivas, Shimla
171005
*ckr@ckraju.net

**Abstract:**
Many people laugh at the thought of decolonising mathematics. What is
there to decolonise in 1+1=2 they ask? They have in mind the
kindergarten images of 1 orange and 1 orange making 2 oranges. This
is an empirical proof accepted in normal math. However, most people
are unaware that colonialism changed math teaching from normal to
formal math,^{1}
which prohibits such empirical proofs,^{2}
and demands axiomatic proofs instead.

This makes formal
math extraordinarily difficult without adding an iota to practical
value, as in the 378 pages needed by Russell and Whitehead to prove
1+1=2 in their *Principia*,
which proof adds
nothing to the practical value of arithmetic in a grocer’s
shop. Going a step further, no one has yet met my
Cape Town challenge to prove 1+1=2 in formal real numbers, from first
principles, *without*
assuming
*any* result from axiomatic set theory. “Real”
numbers are declared essential to calculus, though the practical
value of calculus (in calculating, say, rocket trajectories) today
involves computers, which use floating-point numbers and *cannot*
represent metaphysical “real” numbers. (See footnote 2.)

The widespread
ignorance of current math facilitates the imposition of formal math,
by declaring it (normatively) universal, or epistemically “superior”.
This is supported not by any reasoned debate, or critical
comparison, but by (a) the *fraudulent* claim that such
deductive/axiomatic proofs avoiding the empirical (a church
technique) are actually found in
“Euclid’s” Elements;^{3}
(b) the *myth* that the book’s author was (a White, male)
called Euclid who intended such proofs;^{4}
and (c) the *superstition* that deductive proofs are “superior”
since infallible. Actually, deductive proofs are *more*
fallible, and manifestly inferior to empirical proofs.^{5}

Though formal proofs are epistemically inferior, this method of
reasoning without facts was glorified since it was politically useful
to the church (and its theology of reason, as in Aquinas’ proof
about angels on a pin^{6}).
Even today, formal math enables politics (including church
superstitions) to be smuggled into “science” as in the
creationism of Stephen Hawking’s singularity theory,^{7}
which mimics Augustine.

Decolonisation of
math seeks to eliminate the fraud, myth, and superstition associated
with formal math, and reverts to simple, utilitarian, normal math
with a philosophy of accepting inexactitude, called zeroism.^{8}
Reverting to normal math makes math easy. It *enhances* practical value, and enables students to
solve harder practical problems, as has been demonstrated in teaching
experiments, across the last decade, in three countries, teaching
calculus at university level,^{9}
and geometry at school level.^{10}

However,
decolonisation of math results in the complete crash of the long myth
of Western intellectual/racist superiority. But Western thinkers have
been unable to respond intellectually to the critique, in public debate, in the last
two decades. Hence, amusingly, various entities from an Oxford
philosophy journal, to racist newspapers in South Africa, to an MIT
science magazine, and the American Mathematical Society^{11}
are repeatedly making scurrilous ad hominem attacks in complete
desperation, to avoid loss of power and influence through
decolonisation of math.

C. K. Raju holds a PhD from the Indian Statistical Institute, Kolkata, preceded by an MSc in mathematics and a BSc (Hons) physics from Mumbai. He initially taught and researched in formal math (advanced functional analysis and applications to relativity and quantum field theory) for several years. Later, he was responsible for porting large applications (space, oil etc.) on India’s first supercomputer, Param, and that experience led him to abandon formal math.

He has authored
numerous research papers and several acclaimed books. In *Cultural
Foundations of Mathematics* (Pearson Longman, 2007) he compiled
evidence for the development of calculus in India (with a different
philosophy, now called zeroism) and its transmission to Europe in
the 16^{th} c., where it was not properly understood. In
*Time: Towards a Consistent Theory *(Kluwer, 1994) he earlier
explained why Newtonian physics failed for *theoretical*
reasons, and was replaced by relativity (by Poincare), because Newton
(failing to understand the Indian calculus) had made time
metaphysical. He went on to outline a new physics, using functional
differential equations, forced after relativity, but which Einstein
failed to understand. In the *Eleven Pictures of Time* (Sage,
2003) he proposed a new way to relate science and religion through
time. He has developed and taught decolonised courses on math, and
the history and philosophy of science. His shorter books include *Is
Science Western in Origin?* (Multiversity 2010), *Ending
Academic Imperialism* (Citizens International, 2011) and *Euclid
and Jesus* (Multiversity, 2012).

He has wide-ranging
interests: he has headed India’s largest computer science
department, been editor of the *Journal of Indian Council of
Philosophical Research* and Vice-President of the Indian Social
Science Academy. He has received several awards. Currently he is an
Honorary Professor of the Indian Institute of Education, and Tagore
Fellow at the Indian Institute of Advanced Study.

Web, Writings and talks, Press, Videos.

**References**

1 *How
Colonial Education Changed Our Math Teaching | C.K. Raju*, 2020.
https://www.youtube.com/watch?v=Rm6d-bUmmGg.
*Sulba Sutra Geometry: Can We Teach It in Schools Today? | C.K.
Raju*, 2020. https://www.youtube.com/watch?v=rLI_UU6dfnE.

2 C.
K. Raju, “Computers, Mathematics Education, and the
Alternative Epistemology of the Calculus in the YuktiBhâsâ”,”
*Philosophy
East and West*
51,
no. 3 (2001): 325–362. http://ckraju.net/papers/Hawaii.pdf.
Abstract at http://www.ckraju.net/papers/Hawaii-abstract.pdf.

3 C.
K. Raju, *Euclid
and Jesus: How and Why the Church Changed Mathematics and
Christianity across Two Religious Wars*
(Penang:
Multiversity and Citizens International, 2012).

4 C.
K. Raju, “To Decolonise Math Stand up to Its False History and
Bad Philosophy,” *Conversation*,
October 24, 2016, CENSORED after publication; reproduced in C. K.
Raju, “Was Euclid A Black Woman? Sorting Through The False
History And Bad Philosophy Of Mathematics | Science 2.0,”
October 24, 2016,
https://www.science20.com/the_conversation/was_euclid_a_black_woman_sorting_through_the_false_history_and_bad_philosophy_of_mathematics-180581;
also reproduced in C. K. Raju, “Black Thoughts Matter:
Decolonized Math, Academic Censorship, and the ‘Pythagorean’
Proposition,” *Journal
of Black Studies*
48,
no. 3 (2017) 256–78; and in C. K. Raju, “To Decolonise
Math Stand up to Its False History and Bad Philosophy,” in
*Rhodes
Must Fall: The Struggle to Decolonise the Racist Heart of Empire*
(London:
Zed Books, 2018), 265–70; see, also
C.
K. Raju, *Mathematics,
Decolonisation and Censorship*,
2017,
https://kafila.online/2017/06/25/mathematics-and-censorship-c-k-raju/.

5 C.
K. Raju, “Decolonising Mathematics,” *AlterNation*
25,
no. 2 (2018): 12–43b,
https://doi.org/10.29086/2519-5476/2018/v25n2a2
(free
access).

6*Summa
Theologica*, First Part, Q. 52, article 3.
http://www.newadvent.org/summa/1052.htm#article3.

7 C.
K. Raju, *The Eleven Pictures of Time: The Physics, Philosophy and
Politics of Time Beliefs.* Sage, 2003. Also, “The Christian
Propaganda in Stephen Hawking’s Work.” *DNA India*,
January 16, 2011, sec. Lifestyle.
https://www.dnaindia.com/lifestyle/review-the-christian-propaganda-in-stephen-hawking-s-work-1495047.
And, “Decolonising mathematics: how and why it makes science
better”,
http://www.ckraju.net/papers/palestine-extended-summary.pdf,
abstracts of two invited talks at Palestine Technical University,
aborted by Israel’s refusal to grant a visa. Also, “The
politics of creationism from John Philoponus to Stephen Hawking”,
http://www.ckraju.net/papers/Berlin-2020-abstract.html,

8 C.
K. Raju, *Cultural
Foundations of Mathematics: The Nature of Mathematical Proof and the
Transmission of the Calculus from India to Europe in the 16th c. CE*
(Pearson
Longman, 2007); C. K. Raju, “Zeroism,” in *Encyclopedia
of Non-Western Science, Technology and Medicine*
(Springer,
2016), 4604–4610,
http://ckraju.net/papers/Springer/zeroism-springer-f.pdf.

9 C.
K. Raju, “Teaching Mathematics with a Different Philosophy. 1:
Formal Mathematics as Biased Metaphysics,” *Science
and Culture*
77,
no. 7–8 (2011): 274–279, arXiv:1312.2099; C. K. Raju,
“Teaching Mathematics with a Different Philosophy. 2: Calculus
without Limits,” *Science
and Culture*
7,
no. 7–8 (2011): 280–285, arXiv:1312.2100. See, also,
“Calculus
without limits”, CUTS, Sarnath, Calculus
without limits, CISSC, Tehran, “Calculus
for social science”,
Ambedkar University, Delhi, “Calculus
without limits”, SGT University, Delhi,
Institute lecture and
workshop, IIT: BHU, etc.

10 E.g.
poster at http://ckraju.net/geometry/Rajju-Ganit-poster.pdf.
Also, C. K. Raju, *Rajju Ganita: String geometry for class IX*,
to appear.

11 “Plagiarism by Ex-President of the Royal Society. 1: The Facts”; 2: The Cover-up by the American Mathematical Society”; 3: Lessons for Decolonisation,”.