Life and Work

S. Ramanujan to G.H. Hardy	17 April 1913

Madras Port Trust Accounts Department

Dear Sir,
I am in receipt of your letter of the 26th ultimo. I am a little pained to see what you have written at the suggestion of Mr. Littlewood. I am not in the least apprehensive of my method being utilised by others. On the contrary my method has been in my possession for the last eight years and I have not found anyone to appreciate the method. As I wrote in my last letter I have found a sympathetic friend in you and I am willing to place unreservedly in your possession what little I have. It was on account of the novelty of the method I have used that I am a little diffident even now to communicate my own way of arriving at the expressions I have already given. But still in this letter I have attempted to give a demonstration which would be acceptable to you all.
You speak of having written to me three long letters. But I have received only two. Your first communication to me and the letter of the 26th ultimo. I am anxious to know what your other communication contained. Very probably my not replying to you to what was contained in the letter not received by me made you write in the strain you have done at the suggestion of Mr. Littlewood. I was wondering why you never wrote anything about my personal question. Very probably the second communication contained something about it. I am glad to inform you that the local University has been pleased to grant me a scholarship of £60 per annum for two years and this was at the instance of Dr. Walker F.R.S. Head of the Meteorological Department in India to whom my thanks are due. The scholarship will help me a great deal for two years.
My knowledge of English being poor I find it difficult to collect my thoughts and put them in a form presentable to you. I have tried this time to give you a proof in connection with the expression I have for the distribution of primes. I do not agree with you when you say that my formula

is wrong and that it has been proved definitely that

is not of the order

My belief is that the expression I have given will be sufficient for practical purposes and if there are some terms which are omitted they will be terms of a very low order. I give as much as possible in the modern mathematical language a proof of the theorem on prime numbers and a continued fraction. I am delighted to hear that not only yourself but also other mathematicians at the very fountain head of mathematical knowledge are interesting themselves in my humble work. I request you to convey my thanks not only to your good self but also to Mr. Littlewood, Dr. Barnes, Mr. Berry and others who take an interest in me.

I am Yours very sincerely
S. Ramanujan