Ramanujan's accounts of how he arrived at the proofs ("the Goddess revealed it to me"), reminds me of Paul Erdos's "theory", that "God" has a big book of all possible proofs, called "The Book"; and if you're a nice mathematician, once in a while He will open the book and reveal one to you. Taking up this thread, a couple of mathematicians compiled some of the most beautiful proofs and published them as "Proofs from The Book". http://www.amazon.com/Proofs-THE-BOOK-Martin-Aigner/dp/36420...
Ramanujan: Letters from an Indian Clerk:
Ramanujan asks the teacher, if there are zero people in the class and there are zero apples, will each person still get one apple?
I am not sure how old he was at that time but going by the topic, must have been in middle school. Amazing how his mind worked even at that young an age...
I believe the story was also mentioned in The Man Who Knew Infinity (but don't remember if the narrative is the same or not).
Edit: Looks like Google is displaying it only in India
(great book by the way - easy to read for even a non math person)
We can only marvel at (1) the human brain, the workings of which we know so little (as recent events in Newtown tragically reminded us in a very different way); and (2) mathematics, with which such a brain was able somehow to interact so fruitfully.
I think rearranging digits until the result has interesting properties is a dubious claim to fame. It evokes the pseudomathematics of numerology and is only one step away from nonsense like "The Bible Code".
Especially since "5 cubed" is respectable enough on its own.
The Hindu newspaper celebrates Ramanujan@125 here - http://www.thehindu.com/system/topicRoot/Ramanujan___125/
"But the alien climate and culture took a toll on his health. Ramanujan had always lived in a tropical climate and had his mother (later his wife) to cook for him: now he faced the English winter, and he had to do all his own cooking to adhere to his caste's strict dietary rules."
I'm not a maths person but this perked my interest - Anyone have more information?
The first term of the series (both Hardy&Ramanujan's and Rademacher's) is 1/(4 n sqrt(3)) exp(pi sqrt(2n/3)), which is already a good approximation in the sense that the ratio p(n)/this_approximation(n) tends to 1 as n gets large. This approximation theorem was conjectured by Ramanujan before he came to England, and proved by him and Hardy jointly.
You can find the actual formulae at http://en.wikipedia.org/wiki/Partition_%28number_theory%29#A... and more details at http://books.google.co.uk/books?id=Sp7z9sK7RNkC&pg=PA68&... .