UNIVERSITY OF LONDON, UNIVERSITY COLLEGE
Telephone No.
3979 Central
Gower Street, London, W.C.,
3-12-1912
Dear Professor Griffith,
Your letter of the 12th Nov., reached me a day or two ago, and I write now in order not to miss the mail.

I am sorry that the twenty years, which have passed since you were with me, prevent me from remembering anything about you but your name.

As soon as I can get more time I will look into Mr. Ramanujan’s paper about the Bernoulli’s Numbers, but I cannot do this during term time.

One thing however is clear.

Mr. Ramanujan has fallen into the pitfalls of the very difficult subject of Divergent series.
Otherwise he could not have go the erroneous results you send me
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All the 3 series have infinity for their sums. The book which will be most useful to him is Bromwich’s Theory of Infinite Series, published by the Cambridge University Press (or Macmillan).

Next as to the publication of papers, if Mr. Ramanujan will write out his ideas carefully and clearly on some one subject and send them to the Secretary and clearly on some one subject and sen them to the Secretary of the London Mathematical Society, London W.C, his paper will be referred to a Mathematician, who is an expert in the particular department of Mathematics with which his paper deals. If it is found to be new and worthy of publication, it will be printed in the Proceedings of the Society at the expense of the Society and 25 free copies will be sent to the author.

But he should be very careful with his Mss. It should be very clearly written, and should be free from errors; and he should not use symbols which he does not explain (e.g. in his printed paper he should have explained on page what the symbols C1,C2,C3 & c... mean; §12 to which he refers on p.5 does not apparently exist. He passes from §11 to §13.

What you say about him personally is very interesting and I hope something may come of his work.

I will write later when I have had more time to look into his paper.

I remain,
With kind regards,
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Yours sinerely,
M.J.M. Hill

 

"with this letter in mind", Ramanujan wrote in his second letter to Hardy, dated Feb. 27, 1913:

“If I had given you my methods of proof I am sure you will follow the London Professor [Hill]. But as a fact, I did not give him any proof but made some assertions as the following under my new theory. I told him that the sum of an infinite no. of terms of the series: under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on hi simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. You may ask how you can accept results based upon wrong premises. What I tell you is this: Verify the results I give and if they agree with your results, got by treating on the groove in which the present day mathematicians move, you should at least grant that there may be some truths in my fundamental basis”. So what I now want at this stage is for eminent professors like you to recognize that there is some worth in me. I am already a half starving man. To preserve my brains I want food and this now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university or from the Government.

"...You may judge me hard that I am silent on the methods of proof. I have to re-iterate that I may be misunderstood if I give in a short compass the lines on which I proceed. It is not on account of my unwillingness on my part but because I fear I shall not be able to explain everything in a letter. I do not mean that the methods should be buried with me. I shall have them published if my results are recognized by eminent men like you".