Hi Tim,
Thank you for sharing those first letters - I'd never seen them. There's quite a good British movie on Ramanujan which reminded me how very easily Hardy might simply have discarded Ramanujan's letter. It is to Hardy's credit that he did not. Not answering a letter is very easy: Schiller spent some years not answering Holderlin's letters after Holderlin went mad, though they knew each other.
I didn't know about Ramanujan's goddess, but I did know this anecdote about the number 1729:
https://www.ndtv.com/education/natio...number-2152767
Yup, Trinity collects mathematicians. I did my Ph.D. alongside Tim Gowers there, who won the Fields Medal in 1998.
Cheers,
John