SRINIVASA RAMANUJAN was a mathematician like no other. He had almost no formal training yet produced some of the most stunning mathematical results of all time.
This month marks the 100th anniversary of Ramanujan’s death. Yet his extraordinary ideas and remarkable life story are still highly influential in mathematics, including in inspiring both of us to pursue mathematical research.
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Ramanujan was born in 1887 and became obsessed with mathematics as a teen. He spent so much time making original discoveries in mathematics that he flunked out of college – twice!
In 1913, he sent a now-legendary letter to G. H. Hardy, a mathematician at the University of Cambridge. In pages upon pages of dense formulae, Ramanujan seemed to report from a parallel universe. He later said he saw the equations in his dreams.
The formulae lacked explanations. Some were well known, yet presented as original results; some claims were impossible but displayed a wildly creative flair; and some formulae were so breathtaking that Hardy wrote: “They must be true because, if they were not true, no one would have had the imagination to invent them.” Hardy was beyond intrigued, and invited Ramanujan to join him in Cambridge.
When Ramanujan arrived in the UK, Europe was at the edge of war, and seismic shifts were taking place in the spheres of art, music, literature and civil rights.
Over the next five years, Ramanujan and Hardy would introduce a host of groundbreaking ideas in the field of number theory. From advances in our knowledge of partitions – ways to split up numbers, which is surprisingly complicated – to the powerful circle method that is now a ubiquitous tool for mathematicians and physicists, the pair’s results sent shock waves through mathematics.
For his advances, Ramanujan became the first mathematician from India , in 1918.
Ramanujan returned to India in 1919 a national hero, but he was in failing health, diagnosed with tuberculosis, which is now believed to have been a misdiagnosis. Reunited with his family and wife, the 32-year-old number theorist made his most profound discovery, even as his health worsened.
In a letter to Hardy dated 12 January 1920, Ramanujan sketched details of an enigmatic, previously undreamed-of theory of “mock theta functions” – strangely symmetric equations. Before Hardy could reply, he received the news that Ramanujan had died.
In the century since Ramanujan’s final letter to Hardy, mathematicians have stretched their collective mind to understand the underlying theories he didn’t write down. In probing the consequences of Ramanujan’s work, Jean-Pierre Serre and Pierre Deligne discovered Galois representations, and the latter was awarded a Fields medal – a sort of maths Nobel prize.
Work in this direction sparked a chain reaction of advances in 20th-century mathematics, culminating in the 1995 proof by Andrew Wiles and Richard Taylor of the almost 400-year-old conjecture known as Fermat’s last theorem.
The sphere of Ramanujan’s influence continues to expand: modern fields building on his formulae range from signal processing to black hole physics. It is only in the 21st century that his mock theta functions have come to be understood and appear to describe stringy black holes.
Contemporary mathematicians are still fleshing out the details of the theories in Ramanujan’s dreams.
