Does no one remember Indian Contribution to Mathematics – Part 2
Some of you may have read an article I wrote more than two years ago, titled: “Does no one remember the Hindu contribution to Mathematics?”
I stumbled across a related piece recently: “Indians predated Newton ‘discovery’ by 250 years”
Dr George Joseph at the University of Manchester suggests in his latest research that the “Kerala school” identified the ‘infinite series’- one of the basic components of calculus – in about 1350 – hundreds of years before Newton.
His team also revealed that the Kerala School “discovered what amounted to the Pi series and used it to calculate Pi correct to 9, 10 and later 17 decimal places”.
The story also mentions:
“…there is strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.
That knowledge, they (the researchers) argue, may have eventually been passed on to Newton himself.”
Dr Joseph is the author of “‘The Crest of the Peacock: the Non-European Roots of Mathematics”
The discovery does not suggest that Newton’s accomplishments were any less commendable but as Dr Joseph says: “…other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus- infinite series.”
Related Posts:
Does no one remember the Hindu contribution to Mathematics? for some more links on Kerala School, pl. see comment #2 to this post.
Does no one remember the Indian contribution to Technology? and
May be of interest.
India: Father of Mathematics
By Suresh Soni
Later on, many mathematicians like Aryabhatta, Bhaskaracharya, Shridhar, etc. were seen in the country. Of them Bhaskara-charya wrote Siddhanth Shiromani in 1150. This great book has four parts: (1) Leelavati, (2) Algebra, (3) Goladhyaya, and (4) Graha Ganit.
In his book Bhaskaracharya, Shri Gunakar Muley writes that Bhaskaracharya has acknowledged the basic eight works of mathematics:
1. Addition
2. Subtraction
3. Multiplication
4. Division
5. Square
6. Square Root
7. Cube
8. Cube root.
All these mathematical calculations were prevalent in India for thousands of years. However, Bhaskaracharya tells Leelavati a strange thing, “At the root of all these calculations there are only two basic calculations—rise and fall or increase and decrease. Addition is increasing and subtraction is decreasing. The entire mathematics permeates from these two basic acts.”
Read more at this site:
http://www.organiser.org/dynamic/modules.php?name=Content&pa=showpage&pid=198&page=18
Thanks Bharat.
I will have a look at the article.
Dear Shantanu,
In this context, I have recently posted a prize-winning essay by my son. It had attracted some enlightening comments from people like Shri Karigar. Karigarji has also provided a link to a beautiful PPT.
May I invite you to have a look at it.
The link is
http://kartha-pes.sulekha.com/blog/post/2007/08/kerala-legacy-to-world-mathematics.htm
Dr. Kartha
Dear Dr Kartha: Thank you for sharing your son’s essay with all of us and thanks also for the link. I had a look at it…Truly impressive
Shantanu,
Don’t miss this really wonderful presentation by Dr. Rajeev:
The Pre-History of Calculus in Medieval Kerala.
It also has some interesting information about lifestyles of of namboothiris and how they maintained their dominations! (slide 32).
Some more material here
As he rightly concludes about Calculus:
Knowledge possibly transferred to Europe by Jesuit missionaries. Shrouded in mystery. Church records hold the key to unlocking this mystery.
Thanks for the link KK. Will have a look.
There is growing research done on Bhaskara, a mathematician who lived near Kaladi , Kochi, Kerala. He is supposed to have developed the theory of differential equations. I am told that Western mathematicians/reserachers are doing further reserach on his contributions.
One of my mathematician friends in Notre DAme University confirmed this.
Information age will bring out the suppressed truth and Bharatiy Rushi/Munis (Sages) and their discoveries will be highlighted not only by Bharatiy but by whole world.
Information age belongs to the only environment friendly race in the world and that is Bharatiy.
Jai Bharat!
A. Mathematics
1. Zero – Most Powerful Tool – India invented the Zero, without which there would be no binary system. No computers! Counting would be clumsy and cumbersome! The earliest recorded date, an inscription of Zero on Sankheda Copper Plate was found in Gujarat, India (585 – 586 CE). In Brahma-Phuta Siddhanta of Brahmagupta (7th century CE), the Zero is lucidly explained and was rendered into Arabic books around 770 CE. From there it was carried to Europe in the 8th century. However, the concept of Zero is referred to as Shunya in the early, Sanskrit texts of 4th century BCE and clearly explained in Pingala’s Chandah Sutra of the 2nd century.
B. Geometry
1. Invention of Geometry – The word Geometry seems to have emerged from the Indian word ‘Gyaamiti’ which means measuring the Earth. And the word Trigonometry is similar to ‘Trikonamiti’ meaning measuring triangular forms. Euclid is credited with the invention of Geometry in 300 BCE while the concept of Geometry in India emerged in 1,000 BCE, from the practice of making fire altars in square and rectangular shapes. The treatise of Surya Siddhanta (4th century CE) describes amazing details of Trigonometry which were introduced to Europe 1,200 years later in the 16th century by Briggs.
2. The Value of PI (n) In India – The ratio of the circumference and the diameter of a circle is known as Pi which gives its value as 3.1428571. The old Sanskrit text Baudhyana Shulba Sutra of 6th century BCE mentions this ratio as approximately equal to 3. Aryabhatta in 499 CE worked out the value of Pi to the fourth decimal place as 3.1416. Centuries later, in 825 CE Arab mathematician Mohammed Ibna Musa says that “This value has been given by the Hindus (Indians).â€
3. Pythagoras’ Theorem or Baudhayana’s Theorem? – The so-called Pythagoras’ Theorem – the square of the hypotenuse of a right-angled triangle equals the sum of the square of the two sides – was worked out earlier by Baudhayana in Baudhayana Sulba Sutra. He describes: “The area produced by the diagonal of a rectangle is equal to the sum of the area produced by it on two sides.â€
C. Mathematics
1. 100 BCE The Decimal System Flourished in India – “It was India that gave us the ingenious method of expressing all numbers by means of ten symbols (Decimal System)… a profound and important idea which escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.â€
extract from Understanding Hinduism by
(Shri Swaminarayan Mandir, Neasden, London).
Courtesy and Copyright Swaminarayan Aksharpith.
Even if all the claims for India’s genius in mathematics are established, what really counts in the world is whether Indian mathematics is a force in the world today. That is different from Indian mathematicians established in research institutions abroad. No one can say with confidence that the Indian research effort is as strong as it should be but neither is it in any sense so poor that we should be so lacking in confidence that we have to grope around in the distant past to nail down the achievements of our ancestors.
India has linked none of the theorems with individuals that are found in found in the ancient world of Greece and Rome which have been the other significant centers of mathematical achievements. To take an example, there is some suggestion that Leibniz discovered calculus before Newton but Newton is remembered because he published his research first. I have not seen the French people raise any issue about it because without doubt Newton as one of the giants of all time. Neither is Euclid thought of any less of because he did not author the theorems which are identified with him but the assembly of them provided great minds that followed to build on them. Einstein himself has expressed his gratitude to Euclid.
There is no doubt that the zero is one of the greatest innovations of all time. To build our confidence on has beens can so easily be shattered if it was established that the idea came from elsewhere. Egypt has even been touted. I am afraid that while Indian mathematics has wallowed in self-satisfaction, the challenges thrown up by Euclid were overcome by the West in modern times. There is no reason to doubt the greatness of our ancient past, but to dwell on it to the exclusion of the future is a fruitless exercise.
There is no reason to doubt the greatness of our ancient past, but to dwell on it to the exclusion of the future is a fruitless exercise.That is the key.
@”Dr George Joseph at the University of Manchester suggests in his latest research that the “Kerala school†identified the ‘infinite series’- one of the basic components of calculus – in about 1350 – hundreds of years before Newton.”
There is more to George Joseph story than to this.
Read http://ckraju.net/Joseph/Almeida_Joseph.html
One of the 2 researcher had to resign from his univ. job for this
@Sid
“Sid said:
There is no reason to doubt the greatness of our ancient past, but to dwell on it to the exclusion of the future is a fruitless exercise.
That is the key”
The important thing to remember is that english colonialist hisotrians from the 1800 tried to denigrate ” the greatness of our ancient past – contribution to S& T” by Indians ( to the extent, some even ‘doctored’ texts).
Only few Indian historians have tried to reveal this.
In this context, It would be good to remember the story of how “The Hindu” employed their “eminent historians” (during an election year) to disprove Indian contribution to S & T.
What is clear that India with its tradition of learning was bound to have had significant achievements as revealed in these discussions. When the British established their rule were hardly likely to exercise their choice to showcase Hindu achievements if they did not add anything to the sum of learning they already possessed. The West had no qualms about acknowledging their debt to Greece and Egypt on Mathematics. If India had produced something new rather than only confirmed already established (albeit later) mathematics, no doubt a debt a gratitude would be in order. The discovery of calculus can even be discerned from the Indian work. What Newton did was discover tool calculus for the solution of the problem on gravity. The mathematicians of the West had no need of Indian mathematics for this reason. Einstein in the same way developed tensor calculus to establish on general relativity.
Khandu Sir,
Please try to read more before you spout out such inanities.
Your statements about Einstein is wrong
“The mathematicians of the West had no need of Indian mathematics for this reason. Einstein in the same way developed tensor calculus to establish on general relativity.”
read what Prof.C.K Raju says about Einstein (http://ckraju.net/)
http://michaelsantomauro.blogspot.com/2010/06/einstein-false-god-of-science-copied.html
“The West had no qualms about acknowledging their debt to Greece and Egypt on Mathematics”
Its a pity that you have not read Bankim Chandra Chatterji’s views regarding this.
” Neither is Euclid thought of any less of because he did not author the theorems which are identified with him but the assembly of them provided great minds that followed to build on them. Einstein himself has expressed his gratitude to Euclid. ”
I am really surprised with the ease with you get lapped on to some of western fictions.
Read http://ckraju.net/blog/?p=16
“Mischievous Eurocentrism 2: Euclid
Euclid is one of the pillars of the story that mathematics originated in Greece. But Euclid is a fake. Ask yourself: do you really know of any evidence of Euclid?
A few years ago, the late David Fowler, an authority on Greek mathematics, candidly and publicly admitted in response to my post, on the Historia Matematica discussion list, that “nothing†is known about Euclid.
The racist element of the Euclid story is brought out by Indian school texts which display images of Euclid (and various other “Greek†mathematicians) as Caucasian stereotypes. Note that even these sources now admit that Euclid was from Alexandria in Africa. So how did they determine the color of Euclid’s skin? Such racist images from “reputed†Internet history sites like McAndrews lend a concrete reality to “Euclid†in the minds of young children. This conditions them lifelong to look askance at anyone who questions the existence of Euclid. This is the crux of propaganda–to make a large number of people believe something without evidence, and to make them believe that anything to the contrary is absurd.
More recently, on the Philomathes list, some people again started talking about this mythical Euclid using the terminology of “Euclid’s division algorithm†found also in many mathematics texts. This lacks elementary commonsense. How could an algorithm have developed with the clumsy Greek notation for numbers? Just try doing even a trivial sum like adding 17 and 23 in Greek numerical notation! So, I again reminded people that there was no evidence that Euclid even existed, and no non-textual evidence that Greeks ever used algorithms (and no evidence from any early texts).
One of the discussants pompously responded that he didn’t care whether or not Euclid existed, and that he was referring to the book with Euclid’s name in front of it, and the algorithm inside it.
I asked for the whereabouts of such a book. Thus, the fact is that Euclid is NOT mentioned in Greek manuscripts of the Elements until the 18th c. which mention only Theon (an opponent of the church like his daughter Hypatia, and her successor Proclus).
Since “Euclid†is mentioned only in post-12th c. Latin manuscripts, the most moderate hypothesis is that “Euclid†was a translation mistake for the Arabic “uclidesâ€, meaning “key to geometryâ€. The Latin manuscripts of “Euclid†up to the 15th c. are all derived from Arabic, where ucli = key, while des = geometry.”
@Sandeep S
Thank you for your very learned response. I cannot fully respond as fully as I would like in my short reply.
Wikipedia cites documentary evidence of Euclid’s existence with a fragment of his Elements dated to 100 AD. This is well before the Arabs under Islam about 750 AD was presumed to have rescued his work. The Coptic Christians have Jesus with a very deep tan and in Europe he is fair skinned. I would not read any racist intent on either of the races.
The theorems in Euclid no doubt were known to India but any systematic recording of history is lacking which is not the case with Greece. There is grasp of calculus hundreds of years before it was discovered in the West. It does not seem to have found use for anything but astronomy. Newton’s calculus came about from his study of gravity. This had immediate application in gunnery and brought into being the industrial revolution. India was helpless against the industrial might of the Western powers. A course of study in calculus in any English high school syllabus is replete with applications to many types of problems. The calculus in Newton’s papers are not recognizable in the calculus that is taught today because notations have evolved for the better. That is even more true of the Mathematics of Kerala School. A study of the originals would be tedious for anyone but a specialist in the history of Mathematics.
I do not see the same lack of confidence that I am seeing in my Indian counterparts. The Japanese and Chinese have no problems in borrowing the best from the West. A genius has no difficulty in the search to rediscover mathematics. Examinations further hone these skills. Rote learning obviously does not do not.
Einstein made his discoveries a century ago on knowledge and tools that was available to him at the time. Knowledge has greatly advanced since then. Others that have followed since have put him in the shade. Gell-Mann and Feynmann just to name two. Professor Raju has done some interesting research which challenges some of Einstein’s premises, notably with his work on functional differential equations. This work advances the frontiers of knowledge which is what research should be all about. There is also room for history which is certainly in poor shape in India.
@Khandu patel
“Wikipedia cites documentary evidence of Euclid’s existence with a fragment of his Elements dated to 100 AD”
Didn’t you read Prof.Raju’s “explanation” of “documentary” evidence of elements.
For your benefit. Please read it once more-
“More recently, on the Philomathes list, some people again started talking about this mythical Euclid using the terminology of “Euclid’s division algorithm†found also in many mathematics texts. This lacks elementary commonsense. How could an algorithm have developed with the clumsy Greek notation for numbers? Just try doing even a trivial sum like adding 17 and 23 in Greek numerical notation! So, I again reminded people that there was no evidence that Euclid even existed, and no non-textual evidence that Greeks ever used algorithms (and no evidence from any early texts).
One of the discussants pompously responded that he didn’t care whether or not Euclid existed, and that he was referring to the book with Euclid’s name in front of it, and the algorithm inside it.
I asked for the whereabouts of such a book. Thus, the fact is that Euclid is NOT mentioned in Greek manuscripts of the Elements until the 18th c. which mention only Theon (an opponent of the church like his daughter Hypatia, and her successor Proclus).
Since “Euclid†is mentioned only in post-12th c. Latin manuscripts, the most moderate hypothesis is that “Euclid†was a translation mistake for the Arabic “uclidesâ€, meaning “key to geometryâ€. The Latin manuscripts of “Euclid†up to the 15th c. are all derived from Arabic, where ucli = key, while des = geometry.â€
Funny to see how you are clinging on to Wikipedia for documentary of Euclid’s existence.
” Professor Raju has done some interesting research which challenges some of Einstein’s premises, notably with his work on functional differential equations.”
Khandu Sir,
You are one of a kind to draw such a nice conclusion of Prof. Raju’s work.
@Sandeep S and Shantanu
Since you believe in presenting the true picture of India and countering a lie at its source, here is some food for thought – in line with the misinformation being spread about the contribution of India to mathematics and Science.
The links is – http://www.cosmicfingerprints.com/blog/faq/#designer
Here the following is written by the author of the blog-
“Science got started in ancient China; in ancient Egypt and Greece and Rome; and in Islam. But it never went anywhere. In those cultures, it sputtered and coughed and died.
Why?
Because those cultures did not have a theology to support it.”
Since this is mainly a Christian theology site, with a pretty good traffic, I think you should counter this lie with your expertise and exposure in this knowledge. It will give a good exposure to the hidden facts about India’s science legacy, and to an audience which is the most “misinformed”, and will set the record straight.
Thanks for the link and the tip-off Gyan. I will have a look.
Please also read: http://indianrealist.wordpress.com/2009/01/26/how-jesuits-took-calculus-from-india-to-europe/
and this link to Prof CK Raju’s work,
The Infinitesimal Calculus:
How and Why it Was Imported into Europe by C. K. Raju
Someone does remember!
See this extraordinary 35-tweet thread on ‘The discovery of elegant solutions of indeterminate equations by ancient Hindus ….
The author believes …It would not be an exaggeration to state that it formed the very foundation of modern number theory as we know today.