Srinivasa Ramanujan

Ramanujan’s early life is a story of hunger—for numbers, not merely for bread. Born in 1887 in Erode and raised in Kumbakonam, he encountered Carr’s Synopsis of Elementary Results in Pure Mathematics as a teenager, a compendium that listed theorems without proofs. From it, he learned to produce, test, and refine identities by intuition and computation rather than by the formal methods then current in Europe. His notebooks, begun in his youth, accumulated thousands of formulas: rapidly converging series for π, intricate continued fractions, congruences for the partition function p(n), expansions involving q‑series, and startling asymptotics. Lacking a degree and steady employment, he lived precariously; clerks and friends supported him as he pursued mathematics with monastic focus. In 1913 Ramanujan wrote a letter to G. H. Hardy, enclosing statements that seemed unbelievable and yet bore the signature of deep truth. Hardy, together with J. E. Littlewood, recognized brilliance beyond eccentricity and arranged for Ramanujan to come to Cambridge. There, they set about translating intuition into theorem: the Hardy–Ramanujan asymptotic for p(n); the circle method; work on highly composite numbers; and refinements across modular forms and zeta‑function territory. Hardy sometimes despaired at Ramanujan’s dislike of epsilon‑deltas, but he revered the imagination that could see a landscape of results before trails were cut. Cambridge during the war was spartan; vegetarian food was scarce; cold and illness worsened. Yet Ramanujan’s productivity remained astonishing. Election to the Royal Society and to a Trinity College fellowship followed, recognizing not only published work but promise. Returning to India in fragile health, Ramanujan continued to write. After his death in 1920, papers and notebooks left behind entered a long conversation with later generations. The “lost notebook,” found in the 1970s among papers at Trinity, revealed work near his death on what he called mock theta functions—objects that would, decades later, connect with harmonic Maass forms, modularity phenomena, and even string theory and black hole entropy via the theory of partitions. Ramanujan’s formulas, like crystalline structures glimpsed in fog, invited contemporary mathematicians to supply the proofs and frameworks that his circumstances denied him time to build. Culturally, Ramanujan became emblematic of raw genius. But the story, rightly told, also honors the infrastructure of care: Hardy’s letter answered, teachers who opened doors, patrons who found stipends. His career cautions against equating scholarship with credential, and it recommends an ethics of mentorship that risks faith in a stranger who sends breathtaking mathematics by post. In classrooms, Ramanujan’s series still inspire calculation; in research, his conjectures continue to seed new theorems. The notebooks remind us that discovery sometimes begins with a wild garden of identities tended by someone who loved numbers enough to live among them even when the world offered little else.