New Delhi: Albert Einstein was a fraud who never really understood relativity. Euclid never existed; he was an invention of the Church. And modern mathematics is religious propaganda of the West that stole calculus from Indian ‘ganita’ without understanding it. These were some of the claims made by Indian mathematician C.K. Raju (69) at a lecture at Delhi-based think tank Vivekananda International Foundation (VIF), Thursday.
His evangelism, however, found few takers among his peers. “I have been trying to speak about this topic in public for 10 years, without any success,” he said at the start of his lecture, blaming the lack of endorsement on fear of and unwillingness to accept new ideas.
According to him, while non-experts do not understand the technicalities, experts at top institutes fear they will lose their jobs if they accept his theories. “They are scared of new ideas,” he said.
In a sparsely populated conference room, with barely 40 people in attendance, the talk began with chants of ‘Om’ and Sanskrit shlokas. Most of the attendees were from Vivekananda International Foundation, while some in the audience included retired defence employees and lawyers. Throughout the lecture, the audience quietly nodded along with Raju. There was no mathematician in the audience to question any of his claims.
At the end of the lecture, one attendee asked him what he thought of Einstein, to which Raju responded by claiming that the theoretical physicist was ‘simply a clerk at the patent office who stole ideas from others’. “My stated position for the last 30 years is that Einstein did not discover the theory of relativity. He was a clerk at the patent office and understood legality of ideas. So his bright idea was copying from the frontline of scientists,” he said.
Responding to another question about what can be done to spread more awareness about ‘ganita’, Raju said that he will continue to try to reach out to authorities to get them to make ‘ganita’ a part of school curriculum.
According to Raju, ancient Indian mathematics – which he referred to as ‘ganita’ – is superior to what he dubbed as ‘Western ethnomathematics’.
“The West stole calculus from India without really understanding any of it. They added the concept of real numbers, because of which calculus became so difficult and complicated,” Raju said at the lecture titled ‘Practical Ganita vs Religious Mathematical’.
“Ganita is practical. Whereas mathematics is religious. How can something that is religious be taught as a compulsory subject in our schools,” he asked.
C.K. Raju is an honorary professor at the Indian Institute of Education in Pune. His talk is summarised in a blog post on Medium written earlier this month.
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‘Creating a false dichotomy’ — peers refute C.K. Raju’s claims
Mathematicians ThePrint spoke to rejected Raju’s arguments and refuted his claims. For one, his belief that real numbers have no practical application does not hold any water, they said.
“For the very practical problem of finding the length of the diagonal of a square or rectangle (or for that matter, finding the length of all sides of a right-angled triangle) knowledge of square roots of any natural number is essential,” said Sitabhra Sinha, a researcher at the Institute of Mathematical Sciences in Chennai.
On Raju’s claim that western mathematics should be rejected owing to its purportedly religious origins, Sinha pointed out that ancient Indians were trying to figure out square roots in Sulbasutras — ancient texts that delve into dimensions of fire altars used for rituals. He cited the works of Indian mathematicians and astronomers like Aryabhata (476–550 CE), who is thought to have been the first to discover an approximation of pi (62832/20000 = 3.1416) — a number essential in calculating the area of circle.
“If he (Raju) thinks real numbers are useless, then he should also conclude that much of classical Indian mathematics, which was obsessed with estimating pi more and more accurately, was useless,” said Sinha.
Raju also claimed that Euclid — an ancient Greek mathematician, who is considered the “father of geometry” — did not actually exist. According to Raju, the Church ‘invented’ Euclid and his book to further its own politics.
“In the case of Euclid, the Arabs had already translated it from Greek by the 8th century, so it certainly cannot be a creation of the mediaeval Christian Church. Also, there are references to Euclid’s elements in the works of Heron from 1st century CE, among others,” said Sinha.
On the subject of Euclid, Amritanshu Prasad, a researcher at Chennai’s Institute of Mathematical Sciences, told ThePrint, “From what little I’ve seen of ancient Indian texts, mostly from second-hand accounts, such as P.P. Divakaran’s beautiful book The Mathematics of India, and ancient European texts — Euclid’s Elements remains readable even today — I feel that Professor Raju is creating a false dichotomy.”
1+1=2
In his address at the VIF lecture, C.K. Raju also went on to claim that mathematics prohibits empirical proofs — accepting a solution based solely on observations.
To support his hypothesis, he presented the examples of proving 1+1=2. While empirically this is an obvious statement, Raju claimed that British mathematician Bertrand Russell “took over 380 pages to prove the same”.
This, however, is not all Russell and his former teacher A. N. Whitehead set out to do in their work Principia Mathematica. Considered the landmark work in formal logic, the 2,000-page book is devoted to showing how truths of mathematics could be derived from logic.
By proving 1+1=2, without assuming anything to be obvious — while tedious and impractical — proved that all of mathematics is based on logic.
Prasad explained that there are some simple underlying common principles that are used to arrive at answers to all mathematical problems. He added that Italian mathematician Giuseppe Peano set down these principles as a simple set of axioms for arithmetic in 1889 and “we continue to use these today, almost unchanged”.
“Nobody finds 1+1=2 difficult to understand, East or West. There is no prohibition on empirical reasoning in any country. Throughout the world, school students are taught arithmetic empirically. Mostly only those planning to work in highly sophisticated mathematical reasoning are made to learn logical foundations of mathematics,” he said.
‘Great step backward’
Raju also claimed that he reached out to the National Council of Educational Research and Training (NCERT) several times, and that his requests to ‘correct’ Indian school textbooks were declined.
“Raju is advocating that we reject ‘European’ tradition and return to ‘Indian’ methods. What he doesn’t tell you is that Indian (Chinese, Persian, and many other) ideas contributed deeply to what he calls European mathematics, and continue to do so,” said Prasad.
This, Prasad termed a “beautiful achievement” of the human intellect that led to tremendous technological advancement. He added, “To reject it and revert to a small subset of these ideas — those that Raju considers truly Indian — that are mostly somewhat old — brilliant and glorious as they may be — would be a great step backward.”
Note: An earlier version of this report identified Sitabhra Sinha as a researcher at the Indian Institute of Mathematics. The error is regretted.
(Edited by Amrtansh Arora)
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