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Srinivasa Ramanujan
1887–1920 · Mathematician
A self-taught Indian mathematical genius whose intuitive insights into numbers produced thousands of results, many still being understood today.
“An equation for me has no meaning unless it expresses a thought of God.”
Why is this scientist famous?
Making extraordinary contributions to number theory, infinite series, and continued fractions, largely self-taught.
Ramanujan's ideas continue to influence modern number theory and mathematical physics, and mathematicians are still finding new connections with his work.
Srinivasa's story
Early Life
Born in Erode in southern India, Ramanujan showed an early genius for mathematics but struggled in every other subject. He failed college exams because he would not study anything except mathematics. He was largely self-taught. One especially important influence was G. S. Carr's Synopsis of Elementary Results in Pure and Applied Mathematics, which contained thousands of mathematical results for him to explore. Living in poverty, he worked as a clerk in the Madras Port Trust, filling notebooks with mathematical results in his spare time that he could not always prove but believed were true by intuition.
Reaching Cambridge
In 1913, Ramanujan wrote a letter to the Cambridge mathematician G. H. Hardy, containing a list of remarkable theorems and identities. Hardy initially thought it might be a hoax, but soon recognised its genius — he later called it the most singular event of his life. Hardy arranged for Ramanujan to come to Cambridge, and in April 1914 the self-taught clerk from Madras arrived at Trinity College.
The Hardy–Ramanujan Collaboration
During Ramanujan's years in Cambridge, he and Hardy produced important work in number theory, including major results on partitions and asymptotic formulas. Ramanujan was deeply religious and spoke of the goddess Namagiri as a source of inspiration for his mathematical ideas. Hardy respected this and worked to provide formal proofs for many of Ramanujan's insights.
Legacy
Ramanujan fell ill in England and returned to India in 1919, dying the following year at the age of 32. In January 1920, after returning to India, Ramanujan wrote his final letter to Hardy describing a remarkable collection of new functions that he called 'mock theta functions'. Their importance became increasingly clear through later twentieth- and twenty-first-century mathematics. His notebooks contain thousands of mathematical results. Most have since been proved or explained, while mathematicians continue to study their deeper connections and consequences. He became a Fellow of the Royal Society in 1918, one of the youngest ever elected, and his birthday is celebrated as National Mathematics Day in India.
What did they discover?
Partition Function Formula
With G. H. Hardy, developed a celebrated asymptotic formula for the partition function p(n), describing how rapidly the number of integer partitions grows.
Mock Theta Functions
In January 1920, after returning to India, Ramanujan wrote his final letter to Hardy describing a remarkable collection of new functions that he called 'mock theta functions'. Their importance became increasingly clear through later twentieth- and twenty-first-century mathematics.
Highly Composite Numbers
Studied numbers that have more divisors than any smaller positive integer, a concept he introduced.
Series for 1/π
Ramanujan discovered extraordinarily fast-converging infinite series involving 1/π. His formulas later became important in high-precision calculations of π.
Amazing facts
He was largely self-taught. One especially important influence was G. S. Carr's Synopsis of Elementary Results in Pure and Applied Mathematics, which contained thousands of mathematical results for him to explore.
Ramanujan was deeply religious and spoke of the goddess Namagiri as a source of inspiration for his mathematical ideas.
The number 1729 is called the Hardy–Ramanujan number — it is the smallest number expressible as the sum of two cubes in two different ways.
His notebooks contain thousands of mathematical results. Most have since been proved or explained, while mathematicians continue to study their deeper connections and consequences.
He became a Fellow of the Royal Society in 1918, one of the youngest ever elected.
His birthday, 22 December, is celebrated as National Mathematics Day in India.
Timeline
Born in Erode, Madras Presidency, India
Obtained a book on advanced mathematics and began filling notebooks with results
Began working as a clerk at the Madras Port Trust
Wrote his famous letter to G. H. Hardy at Cambridge
Arrived in London on 14 April, met by E. H. Neville; he travelled on to Cambridge several days later
Awarded a BA by Research from the University of Cambridge for work on highly composite numbers
Elected a Fellow of the Royal Society at the age of 30
Elected a Fellow of Trinity College, Cambridge
Returned to India in failing health
Died in Chetput, Madras, now Chennai, age 32
Awards & honours
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