Sunday, January 11, 2015

Pythagoras or Baudhayana?

The Indian Science Congress Association, together with the University of Mumbai, recently arranged the 102nd Indian Science Congress 2015, at the University's Kalina campus in Mumbai.  The objective of the congress was to provide a platform for challengers to connect with creators to inspire future possibilities and bring them to life.  The event was inaugurated by the Union Minister for Science and Technology, Sri Harsh Vardhan on 3rd January, 2015.  While delivering the inaugural speech, drawing attention to ancient Indian sciences, he said, "Our scientists discovered the Pythagoras theorem but we sophistically gave its credit to Greeks.  We all know we knew "Beej Ganit" much before the Arabs, but very selflessly allowed it to be called Algebra."  This was enough to kindle a debate on the issue. Two groups dutifully endorsed and opposed what the minister said. Even as one of the groups was ridiculing the statement, Sri Shashi Tharoor, former Union Minister, endorsed the minister's observation, albeit in guarded language. The debate about Algebra and Geometry in particular, and Mathematics and Science in general, begs for deeper understanding and civilized behavior.  But it has unfortunately turned out to be "Pythagoras v/s Baudhayana".

Who was this Baudhayana?  What was his contribution to Mathematics?  When and where did he live?  Is there any truth in the claims that he was the original author or finder of the theorem?  These questions demand some consideration to understand the whole issue in proper perspective.

Baudhayana is believed to have lived during the 8th century before Christ (800 BC) in the area between present Eastern Uttar Pradesh and Bihar.  He is said to belong to the Krishna Yajurveda Taittariya shakha (branch).  Some also claim that he belonged to Shukla Yajurveda shakha.  He is respected and remembered even today.  The third "New Moon Day" (Amavasya in the month of Jyeshta) of the lunar calendar is known by his name as "Baudhayana Amavasya".  His Baudhayana Sutras are well known and a source of valuable knowledge to mankind. Apastamba, another sutrakara (author of sutras or formulae) who lived around 600 BC has improved on the sutras of Baudhayana.  Sutras are appendices to the Vedic texts and provide rules for constructions of altars for Havans and Yagnas, the sacred rituals. These sutras give the formulae and do not give proof in detail as is given in modern mathematical books.  Most of the ancient texts are in the form of formulae for easy remembering and passing on the knowledge to the next generations. This is to be understood in the context of the times when paper and printing was not available and the most prominent source of learning was in face-to-face interaction of the "Teacher and the Disciple", as per the "Guru-shishya parampara".

Baudhayana is known for many valuable contributions and three of them are outstanding gifts to sources of knowledge.  In addition to the issue in question (Pythagoras theorem), he has given an approximation of the square root of 2 and finding a circle whose area is equal to that of a given square.  This is something like reverse of squaring a circle.  In his sutras, Baudhayana uses the example of a rope and states that "A rope stretched along the length of the diagonal produces an area which the vertical and horizontal lines make together".   This content is the same as the Pythagoras theorem and hence the claims that he was the founder of the theorem.

Pythagoras is believed to have lived in the 6th century BC (570-495 BC), about two centuries later.  He has made invaluable contributions to philosophy and religion. There are claims that Pythagoras was given credit to the theorem known by his name, three centuries later and Euclid is also credited for this theorem.  Who is the original author or finder of this theorem?  Mysore University has recently come out with a software that can find plagiarism and ensure quality research output by Ph D students. Unfortunately, this software cannot be used to settle the issue between Baudhayana, Pythagoras and Euclid!

The solution for the problem is in the Indian way understanding of sources of knowledge itself. Ancient indian philosophy believes that many strands of truth always exist in the universe and there is nothing called invention as such.  These ever existing truths are found by somebody and the entire mankind benefits from them.  While it is only fair that the first finder should be given credit for his efforts, all the arguments about the first finder only succeed in diverting the spotlight from the basic issue, which is the essence of the truth.  While debating such issues, it is pertinent to remember the following possibilities:
  • Same truth could have been found by more than one person at the same time, without knowing about other's efforts.
  • Same truth could have been found by more than one person at different times, without knowing about each other, especially in ancient times when flow of information was not as easy as today.
  • A seed found by an earlier person might have been developed by a later person adding more dimensions and clarity.
Now that the issue has come to sharper focus, what can be the future course of action? Continuing the arguments with lot of heat is not the answer at all. A clinical study of all the available information without prejudice and due respect to all the past greats and arriving at a conclusion acceptable to all, can be the first step. Respecting all streams of knowledge irrespective of the source is the second. Showing gratitude to all those who have contributed accumulation of knowledge over the years and gifted to us, is the third.

At the beginning of the famous Bruce Lee movie "Enter the Dragon", there is a scene in which Bruce Lee is teaching martial arts to a young student.  Lee points his finger to the moon and tells the student to look at the full moon in the sky, in all his glory.  The boy keeps looking at the finger.  Lee hits the boy on his head and advises him, "Do not look at the finger; look at the moon.  Otherwise you will miss all the beauty of the moon!" 

This argument of Pythagoras v/s Baudhayana is very similar to looking at the finger and missing all the beauty of the full moon in the clear sky.       


  1. Excellent observation and interpretation, Sir.

  2. I am delighted to read your article. I am amazed, how you collect these interesting details.Keep up the good work. I closely follow all your articles.

  3. Rabindranath Tagore wrote about the futility of argument on the country of origin of an idea or product, "......Whatever we understand and enjoy in human products instantly becomes ours, wherever they might have their origin. I am proud of my humanity when I can acknowledge the poets and artists of other countries as my own. Let me feel with unalloyed gladness that all the great glories of man are mine."

  4. Thank you for putting the entire debate in such a lucid picture and ending with such wise notes. But I should mention here that the debate is more due to the media trying to hog attention than the scientific society itself. I remember reading in some other source that most European/Western Scientific Society have acknowledged the contribution of Ancient Indian Scholars to the field of knowledge in many spheres including Algebra and Geometry and Calculus. While the Ancient Knowledge may have travelled West, the Science as we understand today is vastly developed by the West. So this debate is actually uncalled for and should rest at this point.