sourced story
1913-1920 CEReputable source · 2 sourcesWell documented

Ramanujan Sends Hardy a Letter Full of Unproven Theorems

A self-taught clerk in Madras writes to Cambridge, and a skeptical professor decides the impossible-looking claims must be genuine

On the timeline · around 1913-1920 CE · Modern MathematicsModern MathematicsRamanujan Sends Hardy a Letter Full of Unproven Theorems185018751900192519501975

Quick facts

Ramanujan's dates
1887-1920
First letter to Hardy
January 1913
Hardy's reply
8 February 1913
Royal Society Fellowship
1918

What happened

Srinivasa Ramanujan, born in 1887 in Erode, India, had no university education and was largely self-taught from a single 1886 textbook of results, G.S. Carr's Synopsis of Pure Mathematics. In January 1913 he wrote to the Cambridge mathematician G.H. Hardy, introducing himself plainly, stating he had no university education but had undergone the ordinary school course, and enclosing pages of original theorems without proof. Hardy, initially suspicious the letter might be a hoax, spent hours working through the results with his colleague Littlewood and concluded the theorems must be genuine, since, as he put it, great mathematicians are commoner than thieves or humbugs of such extraordinary skill. Hardy replied on 8 February 1913 expressing keen interest and soon arranged for Ramanujan to come to Cambridge, where the two collaborated and wrote five joint papers. Hardy later said the limitations of Ramanujan's formal knowledge were as startling as its profundity, and that introducing him to new material typically produced an avalanche of original ideas rather than the standard textbook response. Ramanujan was elected a Fellow of the Royal Society in 1918 before returning to India in February 1919 in poor health; he died the following year, in 1920, at age 32.

Why it matters

Ramanujan's letter is one of the most famous unsolicited approaches in the history of mathematics precisely because it turned out to be genuine: an unaffiliated clerk with no formal training had independently rediscovered known results and produced entirely new ones, in a form so far outside normal mathematical training that two other mathematicians who received similar material beforehand failed to recognize its value. His collaboration with Hardy over the following years produced results in number theory and analysis still studied today, cut short by his early death.

How we know

Ramanujan's 1913 letter to Hardy and Hardy's own account of his reaction survive in Hardy's writings and in the mathematical correspondence between the two men, and Ramanujan's Cambridge career, including his Fellowship of the Royal Society and Trinity College, is documented in Cambridge's own institutional records.

Sources

See something wrong? . Corrections with a source get fixed fastest.

Part of a timelineHistory of Mathematics26 events · A number system built for taxes, a theorem older than the man it's named for, a proof too long for a margin, and an infinity too big to countView all →
Ramanujan Sends Hardy a Letter Full of Unproven Theorems · History of Mathematics · SourcedStory