Srinivasa Ramanujan · Mathematics
How a poor clerk in South India, working almost alone from a single crammer’s handbook, filled notebook after notebook with thousands of deep results - stated by intuition, almost never proved - that mathematicians are still mining a century later.
Srinivasa Ramanujan was born in 1887 into a poor Brahmin family in the town of Erode in South India and grew up in nearby Kumbakonam. Around the age of fifteen he came across a book that would shape his whole life: George Shoobridge Carr’s A Synopsis of Elementary Results in Pure and Applied Mathematics, a cramming aid for Cambridge examinations that lists some five thousand theorems one after another, terse, compressed, and largely without proof. Ramanujan devoured it and set about verifying and extending its results on his own, with almost no other books and no teacher who could follow him. He was so consumed by mathematics that he twice failed his college examinations, because he neglected every other subject. What Carr gave him was not just content but a style: mathematics as a stream of astonishing results, each a destination rather than a journey. Ramanujan would spend the rest of his life producing such results by the thousand.
Before he was thirty, Ramanujan had recorded his discoveries in a series of notebooks, writing in his own idiosyncratic notation and packing the pages with formulae on infinite series, continued fractions, integrals, and number theory. Across his life he produced nearly four thousand results, the great majority of them stated without any proof at all. These ‘notebooks of Srinivasa Ramanujan’ became one of the strangest treasures in mathematics: a private compendium of deep truths, some already known to Europe, many entirely new, and a few simply wrong, all jumbled together without the scaffolding that would let a reader see why they were true. Later mathematicians would devote entire careers to the notebooks. G. N. Watson and B. M. Wilson began proving the results in the 1930s, and decades later Bruce Berndt produced a multi-volume commentary that supplies proofs the notebooks omit. The pages are terse because Ramanujan trusted his own sight; the labour of justification he left, unknowingly, to the century that followed.
The most dramatic chapter of the notebooks came long after Ramanujan’s death. In the last year of his life, dying in India, he kept working and produced roughly a hundred loose sheets covered with more than six hundred formulae. These pages drifted into the effects of the mathematician G. N. Watson, and were nearly lost. In 1976 the American mathematician George Andrews, searching through a box of Watson’s papers in the Wren Library at Trinity College, Cambridge, recognised what he was holding: Ramanujan’s final work, unseen for half a century. The discovery of this ‘lost notebook’ was hailed as the mathematical equivalent of finding a lost symphony. Its contents, including the mysterious mock theta functions of his last letter, are still being unpacked today. Ramanujan died at thirty-two, but his handwriting has kept issuing new problems to the living for a hundred years.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned that Ramanujan was largely self-taught from Carr’s terse Synopsis , that his notebooks hold thousands of asserted results with few proofs, and that his ‘lost notebook’ was rediscovered in 1976. Explain, in your own words, what the notebooks contain and why proof-less genius is both a gift and a problem.
Leads to Pierre de Fermat.
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