There's a lot more to calculus than infinite series.... Also by the time Newton came along most of calculus had been discovered. Newton was the one who saw the big picture & showed that it was all part of the same theory.

Yeah I was sure Archimedes was calculating areas and volumes using principles of integration. Not sure if he was aware of differential calculus though.

This was in the papers yesterday. But I don't think is 'news' as such, since I have read about this school and its work on calculus at Wikipedia of all places, more than a year ago.

The method of exhaustion was created by Euxodus, not Archimedes, and since the Greeks didn't have the concept of a limit it's not the same thing as calculus. Not as we know it & not as Netwon or Leibniz knew it.

Whenever I here a statement to the effect of "[Insert Western innovation] was really discovered in India," I get a little concerned that the source is just another nutjob. There are whacko nationalist groups in India which claim that airplanes and spacecraft were invented by Indians millenia (yes, thousands of years) before they ever appeared in the West. I'm Indian, and even I think such beliefs are insane!

However, it looks like this might be a more credible story. I am aware that the Greeks had a mathematical technique similar to integral calculus. But I wonder if they ever conceived of adding infinite sums of finite numbers. Anyone know something about this?

I think it's interesting to learn of historical advances in mathematics and physics... wherever and whenever they occurred... and why the development propagated or didn't. There are certainly cases where one wonders what would have happened "if they only knew that..." or "if they could have only written down..."

This shouldn't take away from the advances that we celebrate and build upon today.

I find it very useful to teach that method as part of a calculus course as it aids in the understanding of what follows. It may not be what we know today but it certainly was the foundation of what we know.

I like this thought. How information propagates is one issue. Information propagation is not as much of a problem now as it was a long time ago. It has been a thought of mine that the small number of alphabetical characters in European languages helped to propagate information more readily than in areas of the world where there are 100s or 1000s of characters. Thus early mass production of acedemic material was first accomplished in Europe.

Another issue is "who created calculus". If Newton did not know of the India calculus then he "created" it as much as they did. Otherwise we probably need to attribute the creation of all concepts to alien races on other worlds who discovered the methods a long long time ago in galaxies far far away.

It does not diminish the discoverers in anyway. To be the first to develop a method in an area where there is ignorance of the knowledge known in other areas is still a feat in itself.

One question I have is, did Newton or Leibniz know of India's efforts? My guess would be that they did not.

More likely I see this scenario. Algebra as I learned in the 70s was developed in the Muslim world. However, as I understand it Muslims have been in India a long time. They could have learned directly from India about Algebra. Therefore the original knowledge source for Algebra should be rightly attributed to India.

The concept of 'calculus' is really no big deal, since it can simply be seen as a transformation of an expression as certain small terms are reduced to the point of minimal significance.

Anyone working with infinitesimals would want to find a way to knock out all the clumsy 'other' terms.

In practice, it can be envisaged as sliding two curves closer & closer together until they operate at the same point. It remains a transform, & it is often much easier to reverse away from the zero (singularity) limit into discrete space & work from there. This is, after all, what we do in many numerical schemes.

It's not magic, or given from some higher power - it's logical & a neat trick.