A film, The Man Who Knew Infinity, is now showing about the mathematician Srinavasa Ramanujan.
The film is far from a documentary, but sketches some of the extraordinary facts in Ramanujan’s life. He grew up in a poor family in India, near Madras, and learned most of his mathematics from an old textbook he picked up in at school. Because he paid little attention to other school subjects, he was unable to get into university. He had to seek work as a clerk, but was known around Madras as a mathematician and had some of his work published.
He wrote to mathematicians in England, and in 1913 got a reply from G H Hardy, one of the leading number-theorists of the day. Hardy arranged for Ramanujan to come to Cambridge, on a scholarship granted by the University of Madras.
Hardy and Ramanujan collaborated on many advances in number theory. But Ramanujan fell ill. After he recovered partially, he returned to India in 1919, but relapsed and died in 1920. He left notebooks full of work – mostly conjectures without full proofs – which mathematicians continued to study for decades afterwards.
The film gives little idea of what Ramanujan’s mathematics was about, but here is a short article by Tim Gowers explaining Ramanujan’s contribution to the theory of partitions, which features in the film.
And here’s a (long: 34-minute) mathematical video explaining Ramanujan’s bizarre equation:
1 + 2 + 3 + 4 + …. = −1/12
And a shorter one explaining the same equation: