Fields Medal Winner Manjul Bhargava On the Pythagorean Theorem Controversy

prajendran writes There were a lot of controversies generated at the Indian Science Congress earlier this month, including claims of ancient aircraft in India, the use of plastic surgery there, and ways to divine underground water sources using herbal paste on the feet. One argument that could be tested using some form of evidence was the assertion by Science Minister Harsh Vardhan that the Pythagorean theorem was discovered in India. Manjul Bhargava, a Princeton University professor of mathematics and a Fields Medal winner describes why the question is not defined well.

Comments

Re:Umm, no.

[crunchygranola]

The nice Indian mathematician does bring up some nice cogent and logical things.

But he also leaves out some points which are fairly damning to the argument that the Indians had much to do with this. Many/most non-Indian historians of mathematics seem to believe that the key Indian document here was very likely based on earlier (non-Indian) traditions. In other words, it was just a copy of stuff from Mesopotamia.

I'll quote the wikipedia article on the Theorem (which in turn supplies full quotes from the scholarly document if you hate wikipedia):

"Van der Waerden believed that "it was certainly based on earlier traditions". Boyer (1991) thinks the elements found in the ulba-stram may be of Mesopotamian derivation."

That makes any claims that India "discovered" the theorem really really weak by any definition I would think.

I have actually read Van der Waerden's books on Mespotamian mathematics and astronomy (I have copies of them at hand). His "belief" is not evidence of any kind. He is simply supposing, without any supporting evidence.

And Boyer, who wrote his history of mathematics 50 years ago (1991 is a reprint, he died in 1976), was no expert in ancient mathematics. He has been called the "Gibbon of Mathematics" which is a very good analogy, since Gibbon's work represents a compilation of everything known and believed about the Romans, written from the perspective of an 18th century European, complete with moral interpretations drawn from contemporary cultural viewpoints. It was a work that says at least as much about Gibbon and Europe of the time, as it does about the Romans. Similarly Boyer's beliefs represent the assumptions of a western scholar trained in the 1930s.

No one has yet shown any evidence at all that the suryas actually draw from Mesopotamian sources. Saying it doesn't make it true.