From: devkumar@ccwf.cc.utexas.edu (Devakumar Sreevijayan)
Newsgroups: alt.culture.kerala
Subject: Re: "This is knowledge for the soul" and Math in Mediaeval Kerala
Date: 17 Dec 92 09:35:39 GMT
Organization: The University of Texas at Austin, Austin TX

In article <Bz7ztE.Lty.1@cs.cmu.edu> pjn+@cs.cmu.edu (P J Narayanan) writes:
>
>This song, however, reflects (copies ?) KumAran AsAn's
>darshanam of a cemetery (shmashAnam) as the ultimate center
>of spiritual learning. Asan expressed it in his kr~ti
>PrarOdanam, a vilApakAvyam lamenting the death of
>kErala pANini A. R. rAjarAja varma. The relevant shLOkam is:
>
>
>kaShTam! sThAnavalippamO prabhuthayO sajjAthiyO vamsamO
>puShTashrI thanudhATiyO cheRuthuminngOrilla ghOrAnalan
>spaShTam mAnuShagarvamokkeyiviTepukkasthamikkunnithin-
>ngiShTanmAr piriyunnu hA! iviTamAnAdhyAthmavidyAlayam.


             The cemetary as the ground of true spiritual awakening, where
one contemplates the transitory nature of all existence, is a classical 
Buddhist concept. Indeed, the patron saint of Tibetan Vajrayana Buddhism,
Milarepa, is said to have sat upon a corpse in meditation until he became
enlightened. It is interesting to note AsAn's Buddhist connection, especially
as author of Karuna, which, if I  remember right, features a Buddhist Bhikshu.
            I have been very interested in Buddhism lately, and I am curious
whether Buddhism was a force in Kerala at all. Does anyone have any historical
pointers? I realize that Buddhism did exist in Kerala at one time and that the
community gradually got subsumed within the larger Hindu fold or converted.
But, are there any physical traces (ruins of vihAra's for example) left        
in Kerala?  And while we are on the subject, could someone recommend good 
books on Kerala history, particularly of Mediaeval and Ancient Kerala?
            
            On a tangent, I was reading Roger Kanigel's book on Ramanujan
earlier this semester, and he kept referring to the "brilliant mathematicians
of Kerala", while committing the unpardonable sin of omitting references. I
was all agog trying to figure out who these people were, who had continued
and advanced the tradition of Bhaskara, AryaBhatta, and others who we are
familiar with. The other day, while browsing in the Univ CoOp, I chanced 
upon a rather nice book in the Math section entitled "The Crest of the
Peacock: Non-European Roots of Mathematics", by George Ghevarghese (yes,
thats how it is spelt) Joseph, a Penguin paperback. It had a whole section
on Kerala Mathematics (8 pages), and a wealth of references. I dug out
some of the references and am considering writing a short article based
on them for this net, if there is interest. Apparently, the beginnings
of Calculus (the subject of Analysis, really) has its beginnings in 
IrinjAlakuda, where a person by name of Madhava (c. 1340-1425, of Sangamagrama,
which was IrinjAlakuda in the old days), derived the infinite series expansions
for the Inverse Tangent, the Sine, the Cosine and other Trig functions. 
Other mathematicians mentioned include Nilakantha (c. 1445-1545),
Putumana Somayaji (c. 1660-1740), Sankara Varman, Jyeshtadeva (c. 1550 A.D.),
Sankara Variar (c. 1500-60), et al. These discoveries push back the dates on 
such familiar (to those with a Math background) themes like the Taylor and
Gregory series, the power series expansions of Sine and Cosine attributed to
such giants as Leibniz and Newton by a couple of centuries. 
             Is it my own colossal ignorance, or are you folks also unaware
of these people?  I bought the book, needless to say, and would highly 
recommend it, in this forum and elsewhere. While a title such as "non-european
roots' might raise PC-sensitive eyebrows in Academia, I believe the book
(such as I  have read) presents a balanced and well-reasoned perspective that
calls into question, without sounding hoarse, the Eurocentric (I hate using
the word, but it is descriptive) viewpoints of such renowned historians of
Mathematics like Morris Kline and Carl Boyer (whose weighty tome graces
my bookshelf and is singular in its silence about these Kerala Mathematicians
and their achievements, while only too hastily subscribing to Al-Biruni's
view that Indian Mathematics was 'a mixture of common pebbles and costly
pearls').                         
              The author, G.G. Joseph, was born in Kerala, but spent most
of his life outside India, in such diverse places as Papua New Guinea and Kenya.
He attended University in England, where he now lives and works at the 
University of Manchester. 

Dev

Formerly of EranAkuLam  
Newsgroups: alt.culture.kerala