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:India? I don't think so...

[fustakrakich]

Pythagoras hacked Sony to suppress the truth

Pythagoras imposed his quasi-religious philosophies... about never urinating towards the sun...

when Pythagoras’s student Hippasus tried to calculate the value of [square root of] 2, he found that it was not possible to express it as a fraction, thereby indicating the potential existence of a whole new world of numbers, the irrational numbers (numbers that can not be expressed as simple fractions of integers). This discovery rather shattered the elegant mathematical world built up by Pythagoras and his followers, and the existence of a number that could not be expressed as the ratio of two of God's creations (which is how they thought of the integers) jeopardized the cult's entire belief system.

Poor Hippasus was apparently drowned by the secretive Pythagoreans for broadcasting this important discovery to the outside world.

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)

Re:The theorem part

[sconeu]

That's not how I RTFA'ed. I saw it as

• * Egypt had (undocumented) knowledge of a few right triangles
• * Mespotamia had documented knowledge of many right triangles, -- including large ones, which would indicate knowledge of the theorem
• * India has the first documented statement of the theorem
• * China has the first documented proof of the theorem

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,