Indian Philosophy and Mathematics

[S Krishna]

Dr Antreas Hatzipola asks:
>
>1. Which was the role of the Indian Philosophy (Brahmanism)
>in great S. Ramanujan's Mathematics?


AFAIK, Ramanujan was a deeply religious person who brought in his family
diety, nAmagiri,( the consort of narasimha in nAmakkal) into
every mathematical discussion...one of his early feats( not an original
idea, but a mathematical feat) was to reel off the Mc Laurin expansions
for complex functions without the benefit of paper and pencil: i.e.
something like the Mc Laurin series expansion of
(e**2x)*cos(2x)*tan(3x)...... Asked how he managed it, his reply would
be : "nAmagiri said so"/"nAmagiri appeared to me in my dream and wrote
it on a blackboard"( The last statement also occurs in some of his
theorems in number theory)

  I don't think ( based on my perusal of "The Man who knew Infinity",
"The collected letters and papers of Ramanujan" and S.R.Ranganathan's
book on Ramanujan) that he directly used  Hindu philosophy in any of his
mathematical theories. There are references to his talking about the
mystical significance of certain series e.g.N= (2**n) -1; for n=1
, we get N=1 i.e. God, for n=2, we get N=3 i.e. the trinity, n=3, N=7
(saptarsi) etc etc. but this seems to be a simple interpretation instead
of any new mathematical truth.


>
>2. Are there influences of Indian Philosophies on Modern Mathematical
Theories/inventions?

I am not a  mathematician professionally, but have a very healthy
interest in mathematics and specially in number theory. As a result of
perusing papers,I have therefore seen very few SPECIFIC MENTIONS of
Hindu philosophy in papers/books. The only place where I've directly
seen a mention is in the autobiography("Across 50 years"), of the late
Sir S.V.Ramamurti, a ICS officer who was an amateur mathematician. He
claims that he developed some concept in number theory thru Hindu
philosophy(details not stated) and showed it( or rather, barged into the
office of :-) Albert Einstein and tried to get Einstein to read it;
Einstein went thru it once or twice and returned it as being a little
too complex for him to understand and being outside his field of
expertise.

  I am speculating here, but there COULD be some related work ( in this
context)by one Dr Erakkal Chandy George Sudarshan, a prof at UT Austin,
AFAIK. I remember reading in a newspaper report some 7-8 years ago that
he was deeply influenced by Hinduism in both his personal
and professional life; but then newspapers aren't the best sources for
scientific research.

Hoping to help,
Krishna



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