Srinivasa Ramanujan:
The Self-Taught Genius Who Rewrote Mathematics
In January 1913, a 25-year-old clerk from Madras wrote a letter to G.H. Hardy, one of the most eminent mathematicians in Britain. The letter contained 120 mathematical theorems — many of which Hardy had never seen, some of which he thought might be wrong, and several of which he could not prove himself. He wrote back within weeks.
Srinivasa Ramanujan had no university degree. He had failed his college exams twice — because he was so absorbed in mathematics that he neglected every other subject. He had taught himself almost everything he knew from a single borrowed book: A Synopsis of Elementary Results in Pure and Applied Mathematics by G.S. Carr — a compilation of 5,000 theorems with almost no proofs.
Between 1914 and 1919, working with Hardy at Cambridge, Ramanujan produced results in number theory, infinite series, and continued fractions that are still being explored and proved by mathematicians today — more than 100 years after his death at age 32.
Hardy's Assessment
G.H. Hardy later devised a "mathematical ability" scale where he placed mathematicians from 0 to 100. He gave himself a score of 25. He gave David Hilbert — perhaps the greatest formal mathematician of the 20th century — 80. He gave Ramanujan 100.
"I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class."
— G.H. Hardy, on reading Ramanujan's 1913 letter
The Taxicab Number: 1729
When Hardy visited Ramanujan in hospital, he mentioned he had arrived in a taxi numbered 1729 — "a rather dull number." Ramanujan replied immediately: "No, Hardy, it is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."
1729 = 1³ + 12³ = 9³ + 10³
1729 is now called the Hardy–Ramanujan number. The story illustrates something extraordinary about Ramanujan's mind: he did not compute; he knew. Numbers were his personal acquaintances, and he knew their properties the way you know the faces of people you grew up with.
Ramanujan's Legacy in Modern Mathematics
• His formula for π converges so rapidly that it is used in modern supercomputer calculations of π to billions of decimal places
• His work on the partition function (how many ways can a number be expressed as sums?) led directly to modern analytic number theory
• His mock theta functions, which he described in his final letter from his deathbed, were not fully understood until the 1980s — and led to new discoveries in string theory
• Three Ramanujan notebooks (unpublished during his lifetime) contain thousands of results that have kept mathematicians busy for a century
Source: Robert Kanigel, The Man Who Knew Infinity, Washington Square Press (1991)
"Ramanujan's subsequent career was one of the most extraordinary in the history of mathematics. He was, in the simplest terms, a genius."
— G.H. Hardy, Ramanujan: Twelve Lectures, Cambridge University Press (1940)
Sources
- • Robert Kanigel, The Man Who Knew Infinity, Washington Square Press (1991)
- • G.H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Cambridge University Press (1940)
- • Bruce Berndt, Ramanujan's Notebooks, Springer (5 volumes, 1985–1998)
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