Brahmagupta

— In indiantheory@yahoogroups.com, “rajchak1″ <rajchak1@…> wrote:
>
> The article “Resonance_brahmagupta.pdf” should be available under
> Files on the options bar at the left of the screen

> The article isn’t super-recent, but I thought it might be of interest.
>

I took a look at this article, and found a couple of amusing things.

The paper starts out by citing M. Atiyah. This is the same Atiyah who in 2005 claimed to have independently rediscovered my work published 11 years earlier in my book Time: Towards a Consistent Theory (Kluwer, 1994) and widely disseminated thereafter. Although Atiyah was immediately informed of my work, his claim to my work was AGAIN widely publicised through third parties (Notices of the AMS, 53(2006) pp. 674–678), in a blatant  “second oversight”. My prior work was eventually acknowledged only belatedly in an inconspicuous letter (Notices of the AMS, 54 (2007) p. 452) (both available online at the AMS site).  Although the Society for Scientific Values has in its recent post on its website only stated that three experts found my case against Atiyah to be prima facie valid, the situation is a lot worse than that, and I have put up some of the horrifying details on my website at http://ckraju.net/atiyah/atiyahcase.html since the AMS has completely suppressed my side of the story,  and prevented me from explaining my point of view despite a petition by a number of prominent Indian academics.
Although this paper on Brahmagupta was written well before these events, I find the paper procedurally incorrect in thinking that it is only through appeal to Western authority that Western biases can be corrected. This is a widespread attitude which urgently needs correction. I think it is precisely this sort of reliance on Western authority which is the source of the various distortions of history that one is now struggling to rectify, and such reliance on Western authority will no doubt generate many more such distortions in the future. If we rely on Western authority, why won’t they exploit this reliance to their advantage? (This happened e.g. also in the case of the false claims made by George Joseph and Dennis Almeida, regarding the transmission of the calculus and widely publicised through newspapers; see the correction of 25 Aug 07 in Hindustan Times at http://ckraju.net/Joseph/Almeida_Joseph.html.)

Let us try and understand the origin of the problem. While the ISI Calcutta has contributed greatly to the development of the NSSO which has been very useful to the country, I am not aware of a single result by a formal mathematician which similarly helped to improve the life of anyone in the country. The sole index of achievement for a formal mathematician is approval by a socially recognized authority who typically resides in the West. So formal mathematicians are helplessly tied to the West for their bread, butter, and jam. Under the circumstances, any history of Indian mathematics written by formal mathematicians (including those in the Wikipedia) should be taken with generous quantities of salt.

Secondly, a reference to the book by Bhanu Murthy (Wiley, 1992)  seems missing. That book has a full chapter on the cakravala method. (Bhanu Murthy worked with people like Gelfand and Harish Chandra.)  Of course, Bhanu Murthy too makes the same mistake of casting matters in a formalistic mould and speaking of lemmas and theorems, which Brahmagupta never had in mind. This has happened once again because of abject dependence on the West: Indian formal mathematicians have not shown the slightest evidence of any ability to critically examine the history and philosophy of the mathematics they do. Therefore, it does not strike them that formal mathematics is NOT universal, and that there might have been, and there might again be a fundamentally different way of doing mathematics. (Even if it does strike them, they have not dared articulate it, which is understandable given the existential conditions for their livelihood.)

Finally, the article does not mention the connection of Fermat’s challenge problem (related to “Pell’s” equation) with the solved exercise in Bhaskara II, which connection I have been pointing out for a decade to establish the transmisson of Indian mathematical texts to Europe in the 17th c. (My theory, developed in my book Cultural Foundations of Mathematics, is that pagan sources were then suppressed by Europeans on account of the Inquisition.)
C. K. Raju
P.S. I am copying this post to my blog at http://ckraju.net/wordpress/index.php.

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