Remembering Ramanujan

Sunday 26^th April 2020 marks the 100th anniversary of the death of world-renowned mathematician Srinivasa Ramanujan, who was born in the city of Erode, in India in 1887. Ramanujan’s extraordinary aptitude for mathematics led to him gaining and then losing a scholarship to the prestigious Government Arts College in Kumbakonam – he focused so much on mathematics that he neglected his other subjects and failed his exams. He continued to research independently and was eventually appointed as a researcher at the University of Madras, where he met several prominent Indian mathematicians who recognised his talent, but were concerned by his lack of formal training in mathematics.

Srinivasa Ramanujan, copy of a passport photo 1913 (Add.Ms.a/94/7)

With the help of his friends, Ramanujan began contacting British mathematicians in 1913. His breakthrough came when he presented his work to G.H. Hardy, who was then a lecturer in mathematics at Trinity College, Cambridge. Hardy was initially sceptical that such impressive work could have been produced by an unknown and untrained mathematician. He recognised that Ramanujan had an intellect “of altogether exceptional originality and power.”^[1] Hardy and his colleague E.H. Neville spent over a year trying to persuade Ramanujan to accept an invitation to study at Cambridge, as his devout Hindu upbringing made him reluctant to travel abroad. Ramanujan arrived in Cambridge in the spring of 1914 and moved into rooms in Whewell’s Court. He was awarded a Bachelor of Science degree by research (now known as a PhD) in 1916. The first part of his final thesis was published in the journal of the London Mathematical Society, and he joined the society a year later. In May 1918 he was elected a Fellow of the Royal Society and in October 1918 was the first Indian to be appointed as a Fellow of Trinity College, Cambridge.

Letter from Ramanujan to G. H. Hardy (Add.Ms.a.94/2/3)

Hardy and Ramanujan often clashed due to the stark differences in their working style. Ramanujan was deeply religious and relied on his intuition and insights, which he saw as ‘divine inspiration,’ to make breakthroughs. Hardy, a fervent atheist, struggled to convince Ramanujan of the importance of proof and rigour in his work. Despite this, the two mathematicians collaborated successfully for five years. Their names have been given to several of the formulae they discovered – notably the Hardy-Ramanujan theorem and the Hardy-Ramanujan asymptotic formula.

Letter from G H Hardy to Ramanujan (Add.Ms.a/94/16/1)

Ramanujan suffered from ill health throughout his life, which was exacerbated by rationing during World War I as well as the difficulties of observing Hindu dietary requirements in England. He was diagnosed with tuberculosis and severe vitamin deficiencies, and returned to India in 1919. He died a year later, aged only 32. More recent analysis suggests that his death was due to a condition called hepatic amoebiasis, a parasitic infection of the liver caused by earlier bouts of dysentery. After his death, Hardy and other colleagues began the process of ‘editing’ Ramanujan’s notebooks: they examined each claim in turn, either citing proofs where the theorem was already known or attempting to provide proofs of their own.

In 1976 a visiting researcher to the Wren Library named George Andrews sent waves of excitement across the mathematical world when he re-discovered around 138 sheets of paper among the effects of G.N. Watson, a mathematician who had spent several years working on Ramanujan’s formulae and editing his notebooks. Known as the ‘lost notebook’, these loose papers contain much of the research he completed in the last two years of his life, on topics such as q-series and mock theta functions, which were integral to later research into black holes. In true form, all of the formulae in Ramanujan’s ‘lost notebook’ – over six hundred in total – were recorded without proofs.

A sheet from the ‘Lost Notebook’ (Add Ms a/94/15/65)

Ramanujan’s papers have been digitised and can be viewed in the Wren Digital Library.

^[1]  https://www.nature.com/articles/105494a0.pdf