Early Life in Kumbakonam
Ramanujan was born in Kumbakonam, a small town in Tamil Nadu, South India. His family was poor, and his early education was informal, conducted largely by his mother and other family members. As a child, he displayed an unusual fascination with mathematics. Unlike most prodigies who are nurtured by excellent teachers, Ramanujan largely taught himself through independent study of mathematical texts.
By age twelve, he had mastered trigonometry. By fifteen, he discovered the Euler-Mascheroni constant independently. His mathematical abilities were exceptional, yet he struggled academically in other subjects. He failed his college entrance exams and spent several years in relative obscurity, working odd jobs and pursuing mathematics privately.
Self-Education and Unconventional Genius
What made Ramanujan extraordinary was not formal training but an almost mystical intuition for mathematical relationships. He would fill notebooks with formulas and identities without proof, seemingly pulled from nowhere. When asked to explain his methods, he often could not articulate his reasoning—the answers simply appeared to him, he explained, as visions or intuitions.
This unconventional approach troubled some mathematicians who valued rigorous proof, but the formulas were almost invariably correct. Ramanujan possessed what can only be described as an intuitive grasp of the architecture of mathematics, an ability to see deep patterns and relationships that others could not perceive.
The Fateful Correspondence with G.H. Hardy
In 1913, at age twenty-five, Ramanujan did something remarkable: he wrote a letter to Godfrey Harold Hardy, one of the leading mathematicians of Cambridge University. The letter contained a summary of 120 theorems and identities Ramanujan had discovered. Hardy, who initially found the claims bewildering, soon recognized that he was looking at genuine mathematical genius.
Hardy later recalled that seeing Ramanujan's letter was one of the most remarkable events of his life. He described one specific formula as profound and unlike anything he had seen. Hardy recognized that Ramanujan's theorems, though often stated without proof, demonstrated a level of mathematical insight that appeared only once in a generation.
Cambridge Years and Collaboration with Hardy
Hardy convinced Ramanujan to come to Cambridge in 1914. The young Indian mathematician arrived in a country at war, facing culture shock, dietary restrictions due to his Brahmin beliefs, and the cold English climate. Yet he flourished intellectually, collaborating intensively with Hardy and producing extraordinary mathematical results.
Together with Hardy and J.E. Littlewood, Ramanujan worked on problems in analytic number theory, infinite series, and partitions. They co-authored several important papers. During his five years in Cambridge, despite persistent health problems, Ramanujan published over thirty papers and produced work that would occupy mathematicians for decades.
The Iconic Taxicab Number
One of the most famous anecdotes about Ramanujan exemplifies his extraordinary mathematical intuition. When Hardy visited him in the hospital near the end of his life, Hardy remarked that he had arrived in cab number 1729, which seemed an unpromising number. Ramanujan immediately replied that 1729 was actually fascinating—it was the smallest number that could be expressed as the sum of two cubes in two different ways: 1729 = 1³ + 12³ = 9³ + 10³.
Hardy had not noticed this property, but Ramanujan's instantaneous recognition of it exemplified his extraordinary mathematical vision. The number became known as the Hardy-Ramanujan number or the taxicab number, and it has since appeared in numerous mathematical contexts.
Work on Infinite Series and Partitions
Ramanujan made profound contributions to the theory of infinite series, discovering numerous identities and formulas. His work on the partition function—counting the ways a number can be expressed as a sum of smaller numbers—was particularly influential. He developed formulas for approximating partition numbers with extraordinary accuracy.
His series and identities have applications far beyond pure mathematics, appearing in quantum mechanics, physics, and other fields. Mathematicians continue to discover new applications and implications of Ramanujan's work more than a century after his death.
Illness, Death, and Legacy
Ramanujan's time in Cambridge was cut short by illness. He developed tuberculosis and other health problems, likely exacerbated by the English climate, dietary restrictions, and possibly contaminated food. In 1919, he returned to India, hoping to recover in his native climate. He died in Kumbakonam at age thirty-two, his life tragically brief but his mathematical legacy immense.
Today, Ramanujan is celebrated as one of the greatest mathematical minds of all time. Despite his lack of formal training, his contributions have proven foundational to multiple branches of mathematics. His life story—of a self-taught genius from rural India achieving recognition from the world's leading mathematicians—remains inspiring. The annual Ramanujan Prize is awarded by the International Centre for Theoretical Physics for outstanding research by a scientist under age forty from a developing country.