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.

Re:Umm, no.

[Anonymous Coward]

It's complicated, but the arguments for each can be summarized:

First known indication of knowledge of the relation for integer-sided triangles (Pythagorean triples) - 2,500 BC in Egypt
First known general statement of relation - ca. 1,800 BC in Mesopotamia
First known general statement of relation with respect to right triangles - ca. 800 BC in India
First known rigourous proof of the relation - ca. 1046 to 256 BC in China
(Pythagoras, who may or may not have had a proof - ca. 570 to 495 BC in Greece)

Fields Medal Winner, not just the politician

[billstewart]

I'll give the Indian politician the amount of credit it was due, along with mystical spacecraft flying to other planets and such. But this article by a guy who won the bloody Fields Medal not only deserves a lot more credibility before reading it, but also after - he talks about the discoveries of various parts of the idea in different parts of the world. And Indian and Arab mathematicians did contribute a huge amount to culture and civilization; you can't even claim they made zero contributions without using the zero they contributed,