> Dr George Gheverghese Joseph from The University of Manchester says the 'Kerala School' identified the 'infinite series'- one of the basic components of calculus - in about 1350.
> The discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries.
Um, infinite series existed in the time of the ancient Greeks (even if they went out of their way to avoid using limits).
Here's the thing, though: phenomena can be rediscovered, with discoveries spaced even hundreds or thousands of years apart (e.g. Pythagorean theorem).
And, there's no strong evidence either way regarding Kerala school results 1) making their way to Europe in the 17th century or before, and 2) influencing results by Newton, Leibniz, and more.
But even if this is the case, Newton's line about standing on the shoulders of giants is apt -- there's no dispute here that he and Leibniz still had invaluable contributions that led to the development of calculus, or that they built on an existing foundation.
> Here's the thing, though: phenomena can be rediscovered, with discoveries spaced even hundreds or thousands of years apart (e.g. Pythagorean theorem).
I agree. We call it the Pythagorean theorem and not haltingproblem's great amazing proof ;) The earliest discoverer is given the credit as long as there is some evidence of the dissemination of the discovery.
The Kerala schools shows infinite series with limits and there is transmission as the article documents to Europe. Newton/Liebniz surely formalized and greatly advanced state of the art but what is the harm in giving credit to the Kerala school for the earlier discoveries.
(I've flipped the order of some statements, since I think it reads better this way.)
> there is transmission as the article documents to Europe
The article cites opportunity (Jesuit missionaries) and motive (Gregorian calendar reform), but there's no actual evidence that, say, Clavius actually brought back the full body of the Kerala school's work, or even anything that wasn't related to calendars.
"But wait," you might interject. "The article itself states: 'For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.'"
But this is an assertion, without any evidence in itself. For instance, gunpowder and paper both spread from China to the Middle East before making their way to Europe. The concept of zero (as a digit) is also widely acknowledged to have originated from India. And even these are just anecdotes, not to be taken as proof or refutation of a broader trend.
> The earliest discoverer is given the credit as long as there is some evidence of the dissemination of the discovery.
Unfortunately, that's not always the case, especially once the associated names become ingrained. Sometimes there's co-credit even for independent discoveries, something nothing.
- Chernoff bounds were actually named because of a notable paper that used them, even though Chernoff simply failed to credit Rubin because he thought it was a minor lemma (since it's an application of Markov's inequality).
- Floyd-Warshall is named after two independent discoverers, even though there's a third independent discoverer.
- Gaussian elimination was well-known (and present in textbooks) at the time that he said he used "common elimination".
- The Ising model was given to Ising by Lenz, his doctoral advisor.
(There are plenty of other instances, e.g. Cooley-Tukey FFT, Reynolds number, Schottky diode.)
Some other examples:
- Watson and Crick get most of the credit for discovering DNA's structure, even though they leaned heavily on Rosalind Franklin's work (she died from ovarian cancer, probably due to x-ray radiation).
The title brought a smile on my face. When we grew up there was no internet (I saw a computer when I was 21) but there was no shortage of memes in the air. Most loved meme run like this, “We, Indians, found x before y”.
In South India we loved football and the meme I cherished was this, “Maradona emigrated from kerala”.
When the internet came, I was frantically searching for the list of Indians who are at the top of everything. It took me a while to realise it was my own inferiority playing with me. The truth is painful but it liberates - a confession.
I have never seen anyone claim that Newton is the first to work with infinite series. In fact, finding the area under a curve the geometric way (finding quadratures) naturally leads to many series and in this case Newton himself is predated by many contemporaries and some ancients.
It arguably goes as far back as Eudoxus and his method of exhaustion. Archimedes basically reasoned about limits using synthetic geometry only.
The question here is not of precedence but rather source. This article does not appear to be about mutually independent and unconnected discoveries. Rather it raises the point that Kerala Mathematics was communicated to Europe and probably might have informed the mathematics there. If yes, and a huge IF, it is quiet intriguing and rewrites the history of mathematics. Atleast that is my reading of this article.
Yes, but this reminds me of the claims that 'Zheng He discovered America, since he could do that and there is no evidence he didnt.' a few years back. This also could rewrite history, but it didnt and I think it shdnt.
It is not about discoveries but the ability to stack them. Newton indeed stood on the shoulders of giants. But there is no reason to believe he was the first or the only one to come up with the core ideas of calculus. There probably was somebody in Kerala, Tobolsk or Nairobi thinking about these things but leaving no notes, using a rarer language etc. But Newton was the first, whose work was picked up by a wide body of researchers and rapidly developed further. For whatever reason (the Brits did not get there until much later) the Kerala school was not successful at sparking that uptake. Unfortunately the history is full of brilliant people who simply aren’t at the right spot at the right time. This is true in the west, too, by the way: the story of Scheele, for example
The problem with innovation here India is the level of bureacracy and their british era rules. As simple example would be drones, are limited to a flight of 15M height. Any serious drone type innovation required you to get a license and a permission before every flight from local police authorities.
The govt istelf cripples any innovation.
There was a sad incident where I don't remember the scientists name but he was shunned by the govt till the west recognised his research. Indians love to say we didn't first in our ancient books, but never question how west got ahead.
That dad in Goodness Gracious Me was right...everything is Indian. I do feel one day we will prove the Out of India theory. For now it remains Out of Africa.
Wow that is funny. I think that the world is still somewhat disconnected. How do you find prior research that happened on the other side of the world? There might not be good tools to do so, if we're stuck with simple keyword searching or something like that.
I think it's likely that ancient (or not-so-ancient but far from the roots of European civilization) scholars invented a lot of things before the so-called inventors. Many more than we'll ever know about.
I usually say something like "It's really dumb that we recognize the inventors of things, because if not for that person, someone else would have discovered it in a year, or a decade, or a hundred years, and those potential inventors get no credit" but in this case it might sound like a Westerner trying to downplay the accomplishments of non-Western scholars.
I tend to agree with You but think it probably goes much further back in time.
The article also mentions the fact that "Jesuits were in the area during that time."
It is well known that in the west during that time, the church kept a vast array of knowledge closely guarded from the general population, potentially a cause for the dark ages.
It is entirely possible that the Indian innovations were actually in fact passed to them from the Jesuits, only to be published by the Indian school and then eventually making its way back to the European masses.
And before that it's most likely the same discoveries were made by the Syrians and so on and so on...
To the west India is nothing but a cheap labor centre that is here for the service of the west with its thick accent and bad tech support. It’s difficult to change it, and you see it even persist in popular culture with the likes of Tim Ferriss glorifying this culture with books like “The four hour work week” asking people to outsource the trivial stuff to countries like India. Accuse them of it and they will evasively mollify the situation by talking about the rich culture(while thinking derisive thoughts about the ever-growing population) and yoga/meditation(while mentally smirking about how insignificant a contribution it is compared to their own). Nothing will change until we change fundamentally in our approach to viewing people.
But what is it representative of? The few who can afford to or the 1.3 billion? Until you can bring up the majority to a position where they wouldn’t have to rely on moving to cities like Bangalore and Delhi, there is no point in looking down at people whose wildest dream is to get a Govt Job(still the major job provider in India). You need startups and researcher centres at smaller towns, not everyone flocking to the same select seats in IITs and NITs(which is obviously not enough a number for so many kids that still want a good life) or to the same select cities. If you want to be in Thrissur and create a nation-wide startup you should be able to, but can you now?
Western-favoring narratives like the one in this article are so prevalent that they are even accepted in Eastern countries, in part because a small set of largely Western companies publish textbooks that are used globally.
> The discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries.
Um, infinite series existed in the time of the ancient Greeks (even if they went out of their way to avoid using limits).
An instance of Archimedes dealing with an infinite geometric series: https://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola
Here's the thing, though: phenomena can be rediscovered, with discoveries spaced even hundreds or thousands of years apart (e.g. Pythagorean theorem).
And, there's no strong evidence either way regarding Kerala school results 1) making their way to Europe in the 17th century or before, and 2) influencing results by Newton, Leibniz, and more.
But even if this is the case, Newton's line about standing on the shoulders of giants is apt -- there's no dispute here that he and Leibniz still had invaluable contributions that led to the development of calculus, or that they built on an existing foundation.