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In NCERT textbook for class X mathematics, it is given that Baudhayan gave the relation between the hypotenuse square and sum of squares of the other sides of a right angled triangle. Is it true? From: NCERT Class X Mathematics Textbook

Research efforts:

  1. From Wikipedia (https://en.wikipedia.org/wiki/Baudhayana_sutras)

    The Baudhāyana Śulbasûtra is noted for containing several early mathematical results, including an approximation of the square root of 2 and the statement of the Pythagorean theorem.

    See also (https://en.wikipedia.org/wiki/Shulba_sutras).

  2. Facts Legend (https://factslegend.org/indian-mathematician-baudhayana-originally-discovered-pythagorean-theorem/)

  3. Sanskrit Magazine (https://www.sanskritimagazine.com/vedic_science/baudhayana-the-original-mathematician-behind-pythagoras-theorem/)
  4. PPArihar (https://pparihar.com/2014/08/31/baudhayana-pythagoras-theorem/)
  5. Simple web search [by duckduckwent, not googling :)] (https://duckduckgo.com/?q=baudhayan+pythagoras+theorem&t=ffab&atb=v192-1&ia=web)

As you can see, a lot of websites which support Baudhayan as original discoverer are either Indian or Hinduism oriented, so they may not be valid sources. The Wikipedia articles are not in this category, but an answer has asserted that Wikipedia is a major source of biased information about Indian science and mathematics.

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  • $\begingroup$ Have a look at Wikipedia's article on the Shulba Sutras for information about Indian mathematics during the late Vedic period. The Shulba Sutras contain instructions for the fire altar ritual, including needed geometry, such as the Pythagorean Theorem. Whether the geometry of the Sutras was developed by the Baudhayana school or records knowledge developed earlier is not certain, but the latter seems probable. It should also be said that the connection of Pythagoras to the theorem is tenuous and subject to much debate. $\endgroup$ – Will Orrick Jan 29 at 11:59
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    $\begingroup$ The textbook you have referenced claims only that Baudhayan stated the theorem, not that he proved it. Many cultures recorded their interest in Pythagorean triples, but it is believed that the Greeks were the first to prove the relationship. Proof appears to have been a uniquely Greek concept. $\endgroup$ – Nick Jan 29 at 18:57
  • $\begingroup$ @Nick Is there evidence of any culture's interest in Pythagorean triples independent of, or prior to, knowledge of the general rule? Perhaps that's not what you're suggesting, but I'm curious about why you specifically mentioned triples. $\endgroup$ – Will Orrick Jan 30 at 17:13
  • $\begingroup$ @WillOrrick For example, the papyrus Plimpton 322 , dated approximately 1800 BCE, shows that the Babylonians were interested in this relationship. $\endgroup$ – Nick Jan 30 at 17:54
  • $\begingroup$ @Nick But in the era of Plimpton 322 the Pythagorean rule was already known and used in solving geometric problems. Old Babylonian mathematicians had great facility with cut-and-paste geometry, and likely could "derive" the Pythagorean rule from more elementary geometric propositions. See, for example, IM 67118. I would see Plimpton 322 as an outgrowth of knowledge of the Pythagorean relation, rather than a precursor to it. $\endgroup$ – Will Orrick Jan 30 at 18:12
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The textbook you quoted is that of high school and probably written by high school/college teachers. Most of these side notes are often traditional hearsay. As a good scientist of future, do not trust whatever appears in books and Wikipedia should be your last resort to verify historical facts.

Are they all true? If yes, did they have any effect on other scientists whom we know today? And why Indians are then given less or no credit in books and articles?

Sorry to say but most of those ancient "inventions" are bogus. Wikipedia has become a major source of this non-sense. When someone tries to challenge that discovery, it is reverted. The problem with very old historical stuff is that there is no proof. Suppose a nation A claims today that they invented sines and cosines thousands of years ago. What is the proof? Is there any surviving manuscript? You see the problem with very old historical stuff including the origins of a certain concepts and giving due credit where it is due is one of the most difficult questions in history. Human history is often dependent on the author. You have to be critical when you read a rosy picture of any civilization.

Recently, there are series of rather ridiculous claims in History of Science and Mathematics, and even Physics that everything originated in ancient India. Claims range from invention of alegbraic formulae, sine, cosine, numbers, astronomy, distance between Earth and Sun, ancient air crafts, stem cell research and above all close relationship of German and Sanskrit. Usually Wikipedia and other dubious sources are quoted. BBC even made a report on it, sadly this is being propagated by some obscure university professors.

https://www.bbc.com/news/world-asia-india-46778879

However the easy question is what is the contribution of modern Indian scientists?

Some Indian scientists during the time of British made really major discoveries while working in India such as Sir Chandrashekhara Venkata Raman (Raman effect), Bose (physicist), Meghnad Saha (Ionization equation), Ramanujan and many others. Yes they faced difficulties in publishing in major journals and even faced inappropriate comments. However, later on they earned the respect from a majority of the scientists in the world.

An example is that of the interview of Arthur Compton's wife. She recalled her encounter with Raman as Ref: C. V. Raman and the Discovery of the Raman Effect, Phys. perspect. 4 (2002) 399–420,

" In an interview in 1968, although she could not at first remember Raman’s name, she stated: Anyway he [Raman] was very dark, just as black as could be, but he had a beautiful Scotch accent. He would be asking questions from the back of the hall, and it was so disconcerting to have this person, black as coal, with this beautiful Scotch accent. He was the one who said, ‘‘Compton, you answer questions well; you’re a good debater, but the truth isn’t in you.*’’

Today such labels would not be acceptable such as "black as coal" in any community.

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  • $\begingroup$ Thanks again. I see the question is closed because of 'asking a lot at a time', I will try to edit the question to suit the criteria. And the textbook is from NCERT, Indian government's institute for textbook. I wonder why they made the mistake. $\endgroup$ – J Arun Mani Jan 29 at 15:11
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    $\begingroup$ The question was closed because it was open ended not because you were asking a lot of time. Books are written by human beings. Even research papers have mistakes, textbooks have wrong info. So don't be surprised. Your NCERT books must be written by humans as well. What is sad is when these textbook writers say things without proof. Remember in science there is no authority. $\endgroup$ – M. Farooq Jan 29 at 15:32
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    $\begingroup$ The textbook excerpt in question is, however, more correct than wrong. There is a clear statement of the Pythagorean theorem and a list of Pythagorean triples in the Baudhayana Shulba Sutra. It's true that the 800 BCE date is highly uncertain--other sources say 800 BCE - 500 BCE. And it is speculative to refer to Baudhayana a "mathematician". He was the leader of a religious school about whom we know very little, and the mathematics in the Sutra may have originated elsewhere. $\endgroup$ – Will Orrick Jan 29 at 15:43
  • $\begingroup$ I would like to provide an alternative answer to this question, but since it doesn't seem that it is going to get reopened, I can only add a comment pointing to some helpful sources. Heath's translation of Euclid's Elements contains a discussion of the Pythagorean Theorem in the Shulba Sutras on pages 360-364. Wikipedia's article on the topic has links to Bürk's and Thibaut's translations of the Sutras, which is as close to the source as we're likely to get. $\endgroup$ – Will Orrick Feb 5 at 17:07
  • $\begingroup$ Unless you read Sanskrit, of course. $\endgroup$ – Will Orrick Feb 5 at 17:42

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