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Math Science

Fields Medal Winner Manjul Bhargava On the Pythagorean Theorem Controversy 187

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.
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Fields Medal Winner Manjul Bhargava On the Pythagorean Theorem Controversy

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  • by Anonymous Coward on Sunday January 11, 2015 @04:11PM (#48788979)

    It could have been created in both places, it being a relatively simple law of mathematics that anyone pondering triangles is bound to discover soon enough.

    There are other examples of things being invented in two separate places at roughly the same time. Why the need for bragging rights? Let the evidence do that.

  • by SeaFox ( 739806 ) on Sunday January 11, 2015 @04:29PM (#48789075)

    Pythagorean theorem was discovered in India

    Nobody's going to change the name of it now, and there's no copyright royalties to be had on it.

    • by rabbin ( 2700077 )
      Agreed. The history of mathematics is interesting in itself, but should we as a society place so much emphasis on who was "first!"? It's simple chest thumping. Some may argue that it serves as a motivating factor, but I personally think that's a terrible idea as this is--in my experience with others at least--short lived and not very satisfying. Not to mention, just about every sensible person will find there are much better ways to feed that kind of impulse.

      Instead, teach the joy of doing mathematics
  • by onepoint ( 301486 ) on Sunday January 11, 2015 @04:31PM (#48789089) Homepage Journal

    He made a very good point, it's all about perspective.

    With that said, does it not sound like India reading a page from the book "stranger in a strange land"

    • by Anonymous Coward

      The only good point he made is that by mathematical standards the question is who proved the theorem. The rest of his interview is a pop-sci gobbledygook. Even a better question would be, "in what sense was it proved?" The first rigorous geometric theory was created by Euclid, who lived 200 years after Pythagoras. Did the Chinese have a theory, or did they just whip up some philosophical musings?

      • by swillden ( 191260 ) <shawn-ds@willden.org> on Monday January 12, 2015 @12:34AM (#48790909) Journal

        The only good point he made is that by mathematical standards the question is who proved the theorem.

        I disagree. Proofs aren't the only important element of mathematical creation/discovery. Conjectures are also crucial, and there are lots of important conjectures which are notable long before they're proved. The Pythagorean theorem is clearly one such, because it's extremely useful even if you can't prove it. For that matter, as noted by the article, the Egyptians found it very useful, and they not only didn't have a proof, they didn't even fully understand the relation. They merely knew that some certain combinations of proportions made right triangles... and then used that fact all over the place. The Babylonians also probably understood the principle, and the Pythagoreans likely learned it from them or the Egyptians.

        In addition, even a proof is irrelevant if it just gets lost, or buried. Communication of proofs, especially as part of a systematic theory is even more important and -- as you correctly noted -- that achievement is indisputably Greek. How much of it was due to the Pythagorean mystics and how much to Euclid is a matter of much debate; some historians of mathematics argue that the Pythagoreans discovered essentially everything in the first two books of Elements. Euclid's main achievement with respect to the theorem may well have been mostly just to record it and remove all of the references to beans and the rest of the Pythagorean mysticism. What the truth is we'll likely never know, but the Greeks attributed the knowledge of the theorem to Pythagoras, which I think is quite meaningful.

        All of these stages in the development, proof, formalization and dissemination of important ideas are crucial. The best point to be made here is that the question is inherently meaningless. Any attempt to pick an "origin" must fail because the theorem originated over millenia, and was likely independently discovered in different regions at different times. Even if it's a Chinese manuscript that contains the earliest proof, it seems unlikely that the Greeks got it from the Chinese, and it appears that the Chinese proof in question had little effect on history, Eastern or Western, while the Greek proof, alongside the rest of Elements, fundamentally shaped Western civilization.

        That last claim may seem a little too strong, but it's not. Greek Mathematics didn't so much influence Greek philosophy as create it, and Greek philosophy similarly founded Western philosophy as a whole.

        Plato's philosophy in particular, was essentially mathematical, and his notion of Forms, the central element of his ideas, is clearly an attempt to relate the pure, abstract beauty of geometry to the world as a whole, and to use it as a vehicle for understanding reality and man's relationship with it. Aristotle was, in many ways, the anti-Plato, but he also deeply honored mathematics. All of the rest of Western philosophy, including its deep influence on social and political structures, can be viewed, as Russell said, as a series of footnotes to Plato and Aristotle, they were that important. And a large part of the powerful influence of Greek ideas on Roman, medieval Christian, Renaissance and modern philosophy derived from the elegance and power of Greek mathematics. Although it wasn't often stated so clearly, the indisputable clarity and power of Greek mathematics impressed later generations and convinced them that the rest of Greek wisdom might well be equally profound.

        The Pythagorean version, as presented by Euclid, mattered.

        There may have been a half-dozen proofs of the Pythagorean theorem created, recorded and lost, in many locations around the world, perhaps long before Pythagoras. But none of them mattered. The one that did is the Greek proof, and the Greeks credited the Pythagoreans.

  • Chekov will probably be from India.

    Chekov: "Ah, yes - Quatro-triticale!"
    Kirk: "Does everyone know about this wheat but me?"
    Chekov: "Not everyone, Captain - it was an Indian inwention!"

    • Don't some Indian languages have the "w" sound but not the "v"? In that case, Chekov's accent would be correct (Russian has "v" but not "w").

  • Welcome to Indian/Hindu nationalism...government ministers often make outlandish claims about something having being invented in India.
    • Sure, the Hindu nationalist politician the other day who brought up the issue deserves your criticism, claiming that Indian mystics were flying to other planets centuries before the West was.

      But the Indian mathematician who won the Fields Medal, the mathematical equivalent of a Nobel Prize is the person were talking about today, and he gave a good discussion about what different aspects of the theorem were invented where and when. It was relatively short and sound-bitey, and there's a lot of history we r

      • by cusco ( 717999 )

        There seems to have been more communication between the different regions of Eurasia and Africa in ancient times than is generally realized. China traded as far away as Timbuktu, Marco Polo met Greek engineers in China, spices from India and Indonesia were used in Papal kitchens in the Vatican, tin from Britain was used in Greek bronze, African gold was used in Chinese coinage. Even jade from the Americas showed up in China and American pepper plants in Siam. If goods can travel then so can books and ide

  • by LostMyBeaver ( 1226054 ) on Sunday January 11, 2015 @05:40PM (#48789449)
    It was created by God and brought to Earth by his son Jesus and he's British!

    You heathen bastards!
  • The key to understanding why the whole debate is doubtable and nationalistic from the beginning, is to understand that general mathematics is a universal science.

    You cannot invent mathematics.

    (Remark: This should also be true with physics, these physics inventors haven't even their free energy device running so well it could power their cell phone.)

    Basic mathematics like pythagorean theorem is discovered,
    and Pythagoras didn't invent it, he discovered that just some basic relationships but he wrote down a un

    • You have to invent mathematics. It isn't a feature of the real world.

      Consider Euclid, for example. He has postulates, axioms, and definitions, and proceeds to deduce interesting things from these. He made things up: he knew of no physical examples of points or lines or circles, just approximations. He looked at real-life dots and almost-straight lines and almost-perfect circles, abstracted them, and ran with it.

      At that time, it was thought that geometry (earth-measure) was a description of reality,

  • According to The Fine Article, Indians have documentary evidence of knowledge of a few right triangles.

    The Pythagorean theorem states a universal truth about all right triangles.

    The difference is quite significant.

    And of course, the theorem predates Pythagoras - the Pythagoreans just projected a whole lot of mysticism onto the result.

    • Re:The theorem part (Score:5, Informative)

      by sconeu ( 64226 ) on Sunday January 11, 2015 @06:14PM (#48789617) Homepage Journal

      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
      • by Livius ( 318358 )

        It's not called a theorem without the proof.

      • The thing that Pythagoras can be most accurately given credit for was the idea that ALL triangles, not just triangles with sides of integer relation, abided by the formula. Realizing this effectively posited that irrational numbers could exist. Everybody before that just worked in "triples" of integers.

        The weird detail was that Pythagoras swore all his followers to secrecy about this fact, because he had a series of religious beliefs attached to integers and their ratios. He had at least one person kille

  • I'm thinking more along the lines of....what have you done for me lately? Shitty call centers.....got it.

    Spend less time on something that happens a long time ago and worry more about things like those call centers and your nifty new space program.

  • Uh-huh. (Score:2, Insightful)

    by fahrbot-bot ( 874524 )

    If someone else had discovered this theorem, it would have a different name -- unless there's an Indian named "Pythagoras" -- so checkmate Science Minister Harsh Vardhan.

  • In a nutshell... (Score:5, Interesting)

    by gwstuff ( 2067112 ) on Sunday January 11, 2015 @09:16PM (#48790347)

    -- In India there is an undeniable and strong tendency to construct narratives of how everything good in the world was discovered in India. All Indians don't share this perspective, in fact it is shared by a minority, but er, that amounts to 150 million people or something.

    -- This tendency is inward, not outward looking. This politician Harsh Vardhan is a fuck up, like a lot of Indian politicians. But generally this thinking is not directed at bragging to the rest of the world about how great India is, rather it is to nurse, heal, revive people's connections with their own trampled culture and history -- one that in recent times is increasingly being supplanted by a pseudo-western culture and western lifestyle. It's a way of telling people in India to give their intellectual heritage another chance.

    -- Honestly, most rational people don't give a damn about where the Pythagorus theorem was invented. I mean if it were an easily provable fact, then it might be an interesting piece of historical information, but given that it's ambiguous who cares, unless to stoke one's nationalist ego.

    -- The Princeton mathematician who won the Fields Medal... which is like a Nobel prize except that it's given once every 4 years... is a reference because of his grasp of mathematics, not because he's Indian. If you think of him as "some Indian guy trying to pocket a laurel for his fatherland" then that's a strong statement about you, not about him.

    • 1) I think pretty much every country is guilty of this "it came from here" thing; it's simple national chauvinism. Some more than others - Russia, US, France, India, and China all spring to mind as particularly prone.

      2) your last point is true; if anyone bothered to RTFA, he says essentially that it depends on your standard of evidence, really: if you're looking for the vaguest possible standard, then it probably was 'discovered' in Ancient Egypt. If you're ok with a partial standard, then India looks st

  • There's a saying that the credit for a discovery goes to the last person who finds it. This is a variation of Stigler's law:
    http://en.wikipedia.org/wiki/S... [wikipedia.org]

  • Isn't it very likely that something very basic like the pythagorean theorem was discovered more then once? Probably several times in the region we now call India.

    We know of the greeks because we got to copy their stuff before it was burned, but we burned thousands of equal amount of historical accounts, philosophy and science from other sources. We've had long-lasting cultures who mainly destroyed other cultures and all their records.

    We were just lucky the romans thought that the greeks were cool. If that h

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