The Indian Origins of the Calculus and its Transmission to Europe

[Sahasranama]

http://ckraju.net/papers/calculus_abstract_1.pdf

http://ckraju.net/papers/calculus_abstract_2.pdf

I have not read this yet, but it looks interesting.

C.K. Raju also published a book on the subject:

http://www.easternbookcorporation.co...chstring=14073

Another book on the subject:
http://www.easternbookcorporation.co...chstring=17101

[TatTvamAsi]

Excellent!

CK Raju is a genius and it is such a travesty that he is not more well-known around the world!

Highly recommend his articles and works.

Jai Hind!

[Sahasranama]

Yes, I was very excited to find his works. I will order his book soon.

Here's another paper about probability theory in ancient India.

http://ckraju.net/papers/Probability...ient-India.pdf

[Sahasranama]

Excellent!

CK Raju is a genius and it is such a travesty that he is not more well-known around the world!

Just looked at wikipedia for more information on him. It says:

He was awarded the Telesio-Galilei Academy Award in 2010.[3][5] The award was conferred on him, among other reasons, “for pointing out a mistake made by Einstein and correcting it.”

[sanjaya]

Uh...

I'm all for taking pride in accomplishments that truly are Indian. But I've read about the history of calculus, and I'm fairly convinced that it really was invented in England (or Germany, depending on whether or not you believe Newton). I read the first paragraph of this abstract, and he talks about methods of calculating sines using Taylor series. I'm sure someone in India came up with this. But if we're going to call this "inventing calculus," then we could just as well say that Archimedes invented calculus in Greece because he developed a method for calculating volumes of solids like the sphere, cone, etc.

The reason Sir Issac Newton and Gottfried Wilhelm von Leibniz are credited with inventing calculus is because they created a mathematical system with notations that would be usable by ordinary people. The difference between Newton's methods and those of Archimedes or Brahmagupta is that the latter two's are not easily reproduced by people of average intelligence. Any of us on this forum can take a class and learn Newton's calculus. We can't easily understand the works of these more ancient mathematicians and solve problems the way they did. The power of Newtonian and Leibniz formalism is that it is comprehensible, and that's why they traditionally receive the credit for inventing calculus.

[Sahasranama]

Thanks for your input, Sanjay. I did a research project in high school about the history of Calculus, at that time I wasn't aware that much about the Indian development in mathematics. European mathematics is based on platonic realism and on european/ islamic systems of logic which were often theologically motivated. This is a very shaky foundation. What C.K. Raju is saying is that the basic concept of calculus already existed in India, but when it came to Europe, it took 300 years for the mathematicians to understand it, because they had a different epistemological understanding of mathematics.

I do not know if C.K. Raju's zeroism is a better alternative. Indian philosophers had their own systems of logic, I think it's worth looking into those different theories from Indian philosophy like syadvada and shunyata and certain ideas from the vedas. Raju doesn't look like some cospiracy nutjob, he is a well respected scholar. He has recieved awards for noticing a mistake in Einstein's theories and correcting it. He has helped India build their first supercomputer. He has done 10 years of research into the history of math in Kerala and Rome, ironically some Britishers tried to appropiate his work. Therefore, I am not inclined to dismiss his ideas without further investigation.

The reason Sir Issac Newton and Gottfried Wilhelm von Leibniz are credited with inventing calculus is because they created a mathematical system with notations that would be usable by ordinary people. The difference between Newton's methods and those of Archimedes or Brahmagupta is that the latter two's are not easily reproduced by people of average intelligence. Any of us on this forum can take a class and learn Newton's calculus. We can't easily understand the works of these more ancient mathematicians and solve problems the way they did. The power of Newtonian and Leibniz formalism is that it is comprehensible, and that's why they traditionally receive the credit for inventing calculus.

They have definitely played their part in the history of mathematics. Indeed, anyone here can learn Newtonian calculus. Even a computer can learn it much better than a human being. The Indians probably had a better intuitive understanding of mathematical concepts. Testament to that in modern times is Ramanujan who surpassed any european in his intuitive understanding and who said he recieved inspiration from the godess of his family. When he came to England, he was introduced to academic formalism and the "civilised" way of life. He didn't really felt home in that environment and soon died of health problems. It's curious to notice that most europeans who tried to develop a more intuitive understanding of advanced mathematical concepts landed up in mental institutions. European mathematicians had nightmares of concepts like infitinity, they became schizophrenic just thinking about it. While in Hinduism and other eastern philosophies, paradoxes are an important part of the philosophical teachings.

ॐ पूर्णमदः पूर्णमिदं पूर्णात्पुर्णमुदच्यते
पूर्णश्य पूर्णमादाय पूर्णमेवावशिष्यते ॥
ॐ शान्तिः शान्तिः शान्तिः ॥

Om Puurnnamadah Puurnnamidam Puurnnaatpurnnamudacyate
Puurnnashya Puurnnamaadaaya Puurnnamevaavashissyate ||
Om Shaantih Shaantih Shaantih ||

Meaning:
That is Full, This also is Full, From Fullness comes that Fullness,
Taking Fullness from Fullness, Fullness indeed remains.
Om Peace, Peace, Peace.

Ishavasya Upanishad

[Eastern Mind]

Vannakkam: Calculus was a Godsend for me at about age 17. It was my mathematical limit (pun intended). A mathematical ego was crushed by it, for this mind didn't grasp. All had come easy up to that point. I don't care if it came from the Mayans, Argentina, India, Germany, or the Seychelles, just so long as my karma doesn't put me in a classroom hearing some dude spout off about its usefulness as I toil in sweat hearing naught but Greek.

Aum Namasivaya

[Sahasranama]

http://www.bbc.co.uk/programmes/p0038xb0

[Jainarayan]

Consider "convergent evolution (development)". Or cryptomnesia on Newton's part. I'm thinking convergent development. Ancient India produced a vast amount of mathematical, engineering, astronomical (not just jyotisha) and other sciences, theological, literary and philosophical achievements long before the west, even before the Greeks, when the west was still under Roman domination, then in the the Dark Ages. India was more prolific in these areas than even the Arab world was (which, at the risk of getting political is stuck in the 13th century regarding the aforementioned disciplines).

Btw, calculus, trig, algebra and that ilk make my brain explode like the Martians' brains in Mars Attacks!