Subject: Re: [HM] Who Ramanujan wrote to before Hardy
From: Richard Askey (askey@math.wisc.edu)
Date: Sun Mar 12 2000 - 02:23:30 EST
Dear John,
Please forward to the Historia-Math list, since I do not belong, but
read it occasionally.
Dinesh Maheshwari listed some of the people Ramanujan wrote to before
he wrote to Hardy. He listed
1. E W Middlemast
2. C L T Griffith
3. Founder Indian Mathematical Society
4. M J M Hill
5. Chief Accountant for the Madras Port Trust
6. E W Hobson
7. H F Baker
8. G H Hardy
Not all of these were written to. For example, S. Narayana Iyer, who
is 5, became a good friend of Ramanujan, and Ramanujan lived in Narayana
Iyer's for a while. There is a very interesting letter written
by Narayana Iyer's son about this, including a story of how his
father and Ramanujan used to work on mathematics together, scratching the
chalk and keeping others awake, and another one about Ramanujan getting
up in the middle of the night to write down formulas, which he said he
did in his sleep, and wrote down so he would not forget them. The son
also mentioned getting the book on Jacobian elliptic functions for
his father and Ramanuan, from the Madras university library. There is
no question that Narayana Iyer appreciated Ramanujan, but probably
could not judge how good Ramanujan really was. This is very hard to do
when someone is much better than you are. I have spent almost 25 years
doing mathematics somewhat related to that done by Ramanujan and cannot
say with any certainty how great he was. He is much much deeper than I
am, but I cannot tell by how much.
There are two letters from Hill, who clearly did not understand what
Ramanujan was doing. He gave good advice, read Bromwitch's book on
infinite series, but this does not seem to have been available in
Madras, and there is no indication that Ramanujan ever read it.
Hobson and Baker are likely the two mathematicians Hardy said had
been written to be Ramanujan and never answered. Hardy never mentioned
their names, but Littlewood mentioned two names to Ashis Nandy, who
gave them as Baker and Popson in his book "Alternative Sciences". This
is one of the most annoying books I have read, but this part of it
seems correct, except that there is no mathematician named Popson
at that time. Hobson is the obvious candidate, and he has been mentioned
by a few people as the second one Ramanujan wrote to. Neither Hobson
nor Baker had the right background to understand a letter like the
one Ramanujan wrote to Hardy. Surprisingly, at least in the case of
Hobson, there are connections between some of the mathematics in
Ramanujan's letter to Hardy and what Hobson had doe in spherical harmonics,
but this would not have been clear to anyone except possibly L.J. Rogers,
at that time. It would have been nice if either Hobson or Baker had
shared the letters they got with Hardy or Littlewood, but one can
understand why they did not appreciate the importance of the claims
Ramanujan made. Mathematics is not an easy subject and when you get
outside your area of firm knowledge, it is hard to judge quality.
We can only be thankful that Hardy was perceptive enough to appreciate
Ramanujan's work. We also thank Naranaya Iyer and a few others in
India who did what they could to help Ramanujan.
Dick Askey
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