|
|
HARDY TO RAMANUJAN
(EXCERPTS)
VERY
REMARKABLE WORK DONE
|
Trinity College
Cambridge
26 March 1913.
|
| Dear
Mr. Ramanujan, |
Since I wrote to you last .I have heard from Mr. Littlewood
to whom I sent your last letter to me, and I have considered
further some of your results.
|
The
theory of divergent series leads, as a rule, to correct
results. The important exceptions to the general rule lie
in the theory of prime numbers, the most difficult of all
branches of pure mathematics. If, as seems to me probable,
it has led you here into mistakes, my view that what you
have done is very remarkable would not in any way be shaken:
the results you give concerning continued fractions and
Elliptic functions are enough in themselves to show it (assuming
as I am quite willing to do, that they are correct).
|
Mr. Littlewood suggested to me also that your unwillingness
to give proofs was probably due to apprehensions as to the
use I might make of your results. Let me put the matter quite
plainly to you. You have in your possession now 3 long letters
of mine,. in which I speak quite plainly about what you have
proved or claim to be able to prove. I have shown your letters
to Mr. Littlewood, Dr. Barnes, Mr. Berry, and other mathematicians.
Surely it is obvious that, if I were to attempt to make any
illegitimate use of your results nothing would be easier for
you than to expose me. You will, I am sure, excuse my stating
the case with such bluntness. I should not do so if I were
not genuinely anxious to see what can be done to give you
a better chance of making the best use of your obvious mathematical
gifts.
|
What
I should like above all is a definite proof of some of your
results concerning continued fractions. . . . and I am quite
sure that the wisest thing you can do, in your own interests,
is to let me have one as soon as possible.
|
I
am
Yours very sincerely
G. H. Hardy. |
|
|
|