His discovery (albeit not identified as such) contributed to laying the foundation for work in string theory and he had no clue.
I recently bought Leonard Susskind's "The Theoretical Minimum"  so I could better understand theoretical physics. The explanations are short and clear, but I'm starting to realize that I learn a lot better when I know the historical context in which these concepts developed (or why they were needed). Feynman does this in his lectures and it really helps.
I might really enjoy these podcasts.
FYI, the three notebooks are available in PDF form here: http://www.math.tifr.res.in/~publ/ramanujan.html. This warms my heart.
ics@kafka-mbp:~ ls -l ~/Projects | grep Ramanujan
drwxr-xr-x 3 ics staff 102 Nov 6 16:54 RamanujanManuscripts
There's a joke in Dr Who where the 11th Doctor (Matt Smith) gives a proof of Fermat's Last Theorem to geniuses on earth in order to convince them he can prevent annihilation by the Atraxi. He basically gives them "Fermat’s Theorem. The proof. And I mean the real one. Never been seen before. Poor old Fermat got killed in a duel before he could write it down. My fault. I slept in."
That always makes me wonder - was there and is there indeed a better, shorter and more elegant proof than the one we have?
Who knows, maybe Ramanujan was on his way to developing one!
Galois died in a duel at 20, writing down his mathematical testament the night before he died and scribbling in the margins 'I have no time'.
> "He was a whiz with formulas and I think [his aim was] to construct those near counter-examples to Fermat's last theorem. So he developed a theory to find these near misses, without recognizing that the machine he was building, those formulas that he was writing down, would be useful for anyone, ever, in the future."
OMG, that is ridiculously romantic, and the linked bio of Hardy is amazing. Please tell me there is a book or play or movie about Hardy, maybe along the lines of the one Tom Stoppard wrote about Hardy's contemporary A E Housman.
If you want more romance and mathematics, read about Galois.
Notice that Ono says that only a few people knew about this stuff. Another way of saying the same thing (the more usual way in my opinion) is that "this was already known by the experts".
I believe in this regard he was unlike Euler, who used to go down wrong paths but explain why he was doing something and why he backed out to go down the right path (apparently Gauss looked down on this, but Gauss wasn't blind and doing it all in his head).
There is a new biopic about Ramanujan. I wonder if anyone on HN knows when it will be released in the US. So far it seems it is only at film festivals.
what a great investigation
The article does make a very interesting point I had never considered: Mathematics as machines. Which absolutely makes sense when you see it from the point of view of input-processing-output.
The more general problem is known as Waring's problem. For example, every integer is the sum of 19 fourth powers. Of course special families of integers require fewer fourth powers.