G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician who made his mark in number theory and mathematical analysis, and also gave his name to the Hardy–Weinberg principle, a cornerstone of population genetics. He is best remembered by non-mathematicians for his 1940 essay *A Mathematician's Apology*, which is widely regarded as a superb window into how a working mathematician thinks. The novelist Graham Greene placed it alongside the notebooks of Henry James as "the best account of what it was like to be a creative artist."

From 1914 onward, Hardy served as mentor to the Indian mathematician Srinivasa Ramanujan, a partnership that became legendary. Hardy quickly saw that Ramanujan’s untrained mind was extraordinary, and the two became close collaborators. When the young Paul Erdős once asked Hardy what his greatest contribution to mathematics was, Hardy answered without hesitation that it was discovering Ramanujan. He rated mathematical ability on a scale where his own was 25, his colleague Littlewood’s was 30, Hilbert’s was 80, and Ramanujan’s was 100. In a lecture, Hardy called his association with Ramanujan “the one romantic incident in my life.”

Hardy was born on 7 February 1877 in Cranleigh, Surrey, into a teaching family. His father worked as Bursar and Art Master at Cranleigh School; his mother had been a senior mistress at Lincoln Training College. Both parents had a mathematical bent, though neither had attended university. Hardy and his sister Gertrude “Gertie” Emily Hardy (1878–1963) were raised by their educationally progressive parents in a typical Victorian nursery with a nurse. As a small child, he argued with his nurse about Santa Claus and the effectiveness of prayer, and he read aloud to his sister from *Don Quixote*, *Gulliver’s Travels*, and *Robinson Crusoe*. His mathematical talent showed early: at age two he wrote numbers up to the millions, and in church he amused himself by factorising hymn numbers. After attending Cranleigh School, he won a scholarship to Winchester College for his mathematics. In 1896 he entered Trinity College, Cambridge. His first tutor, Robert Rumsey Webb, left him unsatisfied, and he briefly considered switching to history. He then studied under Augustus Love, who advised him to read Camille Jordan’s *Cours d’analyse*—a book that, Hardy later said, first showed him “what mathematics really meant.” After just two years of preparation with coach Robert Alfred Herman, he placed fourth in the Mathematics Tripos. Later in life, he tried to abolish the Tripos system, believing it had become an end in itself rather than a means to genuine learning. At Cambridge he joined the Cambridge Apostles, an elite secret society. Hardy credited his independent study of Jordan’s *Cours d’analyse* as his most important influence, introducing him to the more rigorous mathematical tradition of continental Europe. He passed part II of the Tripos in 1900 and was elected to a Prize Fellowship at Trinity College that same year. In 1903 he earned his M.A., then the highest degree at English universities. When his Prize Fellowship ended in 1906, he became a lecturer in mathematics at Trinity, teaching six hours a week and leaving time for research. On 16 January 1913, Ramanujan wrote to Hardy after reading Hardy’s book *Orders of Infinity* (1910). Hardy read the letter in the morning, initially suspecting a crank or prank, but by evening he decided it was genuine, reasoning that “great mathematicians are commoner than thieves or humbugs of such incredible skill.” He invited Ramanujan to Cambridge, beginning what he called “the one romantic incident in my life.”

After the Bertrand Russell affair during World War I, Hardy left Cambridge in 1919 to take the Savilian Chair of Geometry at Oxford, becoming a Fellow of New College. He spent the 1928–1929 academic year at Princeton University in an exchange with Oswald Veblen, who went to Oxford. Hardy gave the Josiah Willard Gibbs lecture in 1928. He returned to Cambridge in 1931, becoming a fellow of Trinity College again and holding the Sadleirian Professorship until 1942. It is thought he left Oxford to avoid mandatory retirement at age 65. He served on the governing body of Abingdon School from 1922 to 1935. In 1939, a coronary thrombosis ended his ability to play tennis and squash, and also sapped his mathematical creativity. Bored and distracted, he wrote a privately circulated memoir about the Bertrand Russell affair. In early summer 1947, he attempted suicide with a barbiturate overdose. After that, he resolved simply to wait for death. He died suddenly one early morning while his sister read aloud from a history of Cambridge University cricket. Hardy is credited with reforming British mathematics by introducing the rigor that had long been characteristic of French, Swiss, and German work. British mathematicians had largely stayed in the applied tradition, revering Isaac Newton (as seen in the Cambridge Mathematical Tripos). Hardy preferred the methods of the *cours d’analyse* dominant in France and actively promoted pure mathematics, especially against the hydrodynamics that was a major part of Cambridge mathematics. He worked only four hours a day on mathematics, spending the rest of his time talking, playing cricket, and engaging in other gentlemanly pursuits.