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Godfrey Harold Hardy (1877–1947) was the most important British pure mathematician of the first half of the 20th century. Although he is usually thought of as a man, his years from 1920 to 1931 as Savilian Professor of at Oxford University were actually his happiest and most productive. At Oxford he was at the prime of his creative life, and wrote over 100 papers there, including many of his most important investigations with his long-term Cambridge collaborator J E Littlewood. Hardy’s Oxford time-line

1919 Hardy appointed Savilian Professor of Geometry 1920 Comes into office on 19 January 18 May: Gives inaugural lecture on problems in the theory of numbers G H Hardy’s Srinivasa Ramanujan dies Awarded the Royal Medal of the Royal Society 1921 Visits colleagues in Scandinavia Oxford years and Germany 1922 President of the British Association, & Physics section “I was at my best at a little Presidential lecture: past forty, when I was a The theory of numbers professor at Oxford.” 1924 Georg Pólya (first Rockefeller G H Hardy Fellow) visits Oxford A Mathematician’s Apology 1924–26 President of the National Union of Scientific Workers “…the happiest time 1925–26 visits Oxford of his life…” 1925–27 President of the Mathematical Association C P Snow Presidential lectures: What is Introduction to geometry? and The case against A Mathematician’s Apology the Mathematical 1926 Advocates founding the Journal of “He preferred the Oxford the London Mathematical Society atmosphere and said that 1926–28 President of the London they took him seriously, Mathematical Society Presidential lecture: Prolegomena unlike Cambridge.” to a chapter on inequalities J E Littlewood 1927 Co-edits Ramanujan’s Littlewood’s Miscellany Collected Papers 1928 Attends International Congress of Mathematicians in Bologna 1928–29 Spends the academic year in the USA (mainly at Princeton and Caltech) Replaced in Oxford by Oswald Veblen 1929 Awarded the London Mathematical Society’s 1930 Re-launches the Quarterly Journal of Mathematics Lobbies in the Oxford Magazine for a Mathematical Institute 1931 Albert Einstein receives Oxford honorary degree and gives lectures Hardy leaves Oxford and returns to Cambridge G H Hardy’s Oxford years Savilian Professor

The Savilian Professorships of Geometry and Astronomy at Oxford University were founded by Sir Henry Savile, Warden of Merton College, in 1619.

From Cambridge to Oxford Hardy is appointed From 1897 to 1916 the Geometry Although Hardy was not In December 1919 the following notice chair was occupied by William a geometer, a number of appeared in the Oxford University Gazette: Esson, following the tenure of considerations made the Oxford J J Sylvester who was appointed position attractive to him. to it at the age of 69 after returning from the USA. By 1919 he had become SAVILIAN PROFESSORSHIP OF GEOMETRY disillusioned with Cambridge, At a meeting of the Electors held on Friday, where he had resided since entering as a scholar in 1896. He was December 12, GODFREY HAROLD HARDY, MA, sickened by the War and by the Fellow of Trinity College, Cambridge, was elected pro-War attitudes of his colleagues Savilian Professor of Geometry, to enter on office at Trinity College, especially in on January 19, 1920. their behaviour towards , then a young lecturer.

The Electors for the Oxford Chair were: H Blakiston, Vice-Chancellor Revd. W Spooner, Warden of New College (of ‘Spoonerism’ fame) H H Turner, Savilian Professor of Astronomy E B Elliott, Waynflete Professor of Pure Mathematics M J M Hill, Professor of Mathematics at University College, London William Esson Percy MacMahon, former President of the London Mathematical Society C H Sampson, Principal of Brasenose College Esson had been largely responsible for initiating Oxford’s inter- collegiate lecture system, replacing Hardy had initially encouraged W H Young, independent inventor the arrangement in which of the Lebesgue integral, to apply. Later, when Hardy himself decided the colleges mainly operated to apply, he asked Young to withdraw his name, which he did. independently. He was Sylvester’s deputy from 1894 to 1897 when Hardy’s inaugural lecture on failing eyesight prevented Sylvester Bertrand Russell some famous problems of the from lecturing. Esson died in theory of numbers was given in 1916, during World War I, and In 1916 Russell was convicted, and the University Observatory on the election to the vacant Savilian later imprisoned, for his anti-War Tuesday 18 May at 5pm; it was Chair was suspended until the activities. The College removed later published. War was over. Russell’s lectureship, reinstating it in 1919, but as Russell’s most ardent In his inaugural lecture Hardy Eventually, in October 1919, an supporter in the College, Hardy discussed Waring’s problem: advertisement appeared in the found the atmosphere stifling and Every positive integer can be Oxford University Gazette inviting needed to get away. written as the sum of at most applications. The details of the post 4 perfect squares, 9 cubes or 19 included the following: Hardy was also devastated by the fourth powers; does this continue The Professor will be a Fellow of New illness and departure of his co- for nth powers, and how many College, and will receive a stipend of worker Srinivasa Ramanujan, his powers are needed? £900 per year … It will be the duty researches with J E Littlewood of the Professor to lecture and give were not going well, and he was This was Hardy’s first involvement instruction in Pure and Analytical suffering from an increased with Waring’s problem, and Geometry … He is also bound to administrative load. during his Oxford years he give not less than forty-two lectures co-authored six papers with in the course of the academical year. A complete break was called for… J E Littlewood on it.

G H Hardy’s Oxford years Hardy in Oxford

Hardy found himself well suited to life at New College, the college attached to the Savilian chairs.

Hardy at New College Mathematical contemporaries At New College the Wardens “In the informality and friendliness On the mathematical side, The Waynflete Chair of Pure during Hardy’s time were the Revd. of New College Hardy always felt Hardy’s Oxford colleagues Mathematics was created in 1892. William Spooner, who lectured completely at home. He was an initially consisted of the Sedleian Its first occupant was E B Elliott. on ancient history, philosophy entertaining talker on a great variety Professor of Natural Philosophy His interests were in and and divinity, and (from 1925) of subjects, and one sometimes and the Waynflete Professor of his textbook on invariant theory H A L Fisher, who had served noticed everyone in common room Pure Mathematics, the Savilian was highly regarded, but his in government and later wrote waiting to see what he was going to Professor of Astronomy, and mathematics was old-fashioned, a celebrated History of Europe. talk about.” a number of college tutors. mainly involving the exploitation E C Titchmarsh Another mathematics chair was of elementary ideas with skill and New College Fellows in the Hardy’s successor as Savilian Professor added in 1928. insight. He had ‘no sympathy with 1920s included J S Haldane, foreign modern symbolic methods’. H W B Joseph and Hugh Allen. “… the leader of talk in the senior The professor The College then had 300 students, common room, arranging with was Augustus Love, who occupied but at most one student took mock seriousness complicated games the Sedleian Chair for over forty mathematics Finals each year. and intelligence tests, his personality years. He was President of the Among the New College students gave a quality to the atmosphere London Mathematical Society and during Hardy’s time were Hugh quite unlike anything else in my was awarded its De Morgan Medal. Gaitskell, Richard Crossman experience…” His monumental text on the and Lord Longford. Lionel Robbins mathematical theory of elasticity Economist was of great importance, and his lectures to Oxford students were models of clear thinking and style.

E B Elliott

Elliott retired as Waynflete Professor in 1921 and was replaced by A L Dixon, who studied the applications of algebra to geometry and elliptic functions. Both Elliott Twenty years earlier Love had and Dixon were Presidents of the taught Hardy at Cambridge, London Mathematical Society. as Hardy recalled: “My eyes were first opened by In 1928 the Rouse Ball Chair Professor Love, who taught me and was created in Oxford. Unlike its gave me my first serious conception Cambridge counterpart, where it of analysis. But the great debt which is reserved for pure mathematics, I owe to him was his advice to read the Oxford Chair is always held by Jordan’s famous Cours d’Analyse; and applied mathematicians. I shall never forget the astonishment with which I read that remarkable Its first occupant was E A Milne, work, the first inspiration for so many a former student of Hardy’s in mathematicians of my generation, Cambridge. A major figure in and I learnt for the first time what astrophysics, Milne revolutionised mathematics really meant. From applied mathematics at Oxford. that time onwards I was in my way a real mathematician, with sound Later holders of the Oxford Rouse mathematical ambitions and a Ball Chair included C A Coulson Hardy in his room at New College genuine passion for mathematics.” and Sir .

G H Hardy’s Oxford years Teaching and research

While in Oxford Hardy distinguished himself as both a superb lecturer and an inspiring leader of research.

Hardy’s teaching Hardy’s research Hardy was a brilliant and widely The Hilary Term lecture list for Before Hardy there was no The fact that Hardy and admired lecturer. One of his 1920 included a range of other flourishing research tradition in J E Littlewood were now at Oxford students later wrote: lecture courses, including Oxford, although J J Sylvester had different universities made no “Each lecture was carefully prepared, Theory of functions by Elliott, tried to initiate one in the 1880s difference to their productivity; like a work of art, with the Mathematical astronomy by Turner, and particular individuals such as during Hardy’s Oxford years intellectual denouement appearing Electricity and magnetism by Love, Augustus Love were involved in they produced about fifty joint as if spontaneously in the last five and Hydrostatics by Dixon. their own researches. In 1925 papers. Probably the most prolific minutes of the hour. For me these E B Elliott remarked: partnership in mathematical lectures were an intoxicating joy.” Halfway through the term Hardy “I still hold soundly that our history, they co-authored almost commenced a course of lectures business as teachers in a University one hundred papers on a wide In common with most of his introducing the Analytical was to educate, to assist young range of subjects. Oxford colleagues Hardy taught geometry of the plane, given on men to make the best use of their in his own college – there was then Tuesdays and Saturdays powers … ‘But how about research no Mathematical Institute. at 11am in New College. and original work under this famous system of yours? You do not seem Although not a geometer, Hardy Hardy’s lecture courses were always to have promoted it much.’ Perhaps assiduously lectured on geometry models of good organization and not! It had not yet occurred to each term – Analytic geometry, clarity. Fortunately, several of them people that systematic training for Applications of analysis to geometry, have been preserved in notes it was possible.” Solid geometry and Elements of taken by his Oxford research non-Euclidean geometry – as student E H Linfoot. Below is a Hardy determined to change well as branching out into non- page from a number theory course all this. His own research geometrical topics. given by Hardy in 1924–25. interests were mainly in number theory and , and his greatest legacy J E Littlewood to Oxford mathematics was the internationally renowned A joke of the time held that: research school of analysis that he Nowadays, there are only three established there in the 1920s. really great English mathematicians: Hardy, Littlewood and Hardy- Shortly after arriving in Oxford, Littlewood. he introduced Friday evening advanced classes in pure “The mathematician Hardy- mathematics at New College, at Littlewood was the best in which he, his research students, the world, with Littlewood the and any mathematical visitors to more original genius and Hardy Oxford, discussed their current the better journalist.” investigations. Edmund Landau

Hardy’s research students included E C Titchmarsh, (pictured above), E H Linfoot and his later co-author E M Wright. G H Hardy’s Oxford years Oxford preoccupations

In addition to his many research papers, Hardy was involved with a range of other activities.

Hardy’s publishing activities Other Oxford preoccupations Hardy and Ramanujan Other Publications Einstein visits Oxford Hardy’s feud with God In the years prior to Hardy’s In 1926 Hardy persuaded the In May 1931 a major scientific ‘God-free’ Harold Hardy was coming to Oxford he produced London Mathematical Society to event took place in Oxford when an ardent atheist who had a a number of spectacular joint found the Journal of the London Albert Einstein received an permanent feud with God. papers with the brilliant Indian Mathematical Society and in 1930 honorary Doctorate of Science mathematician Srinivasa he was involved in re-launching the and presented three lectures on Below is a bizarre note that he Ramanujan. But Ramanujan Quarterly Journal of Mathematics. the theory of relativity at Rhodes wrote in the form of an imaginary became ill and returned to Madras The first issue (shown below) House; a blackboard from one cricket match between himself in March 1919. He died a year featured many prominent Oxford lecture is still preserved in Oxford. and God, in which Hardy, of later, shortly after Hardy’s arrival mathematicians of the time. Merton College arranged a special course, won. in Oxford. Hardy was devastated: dinner for Einstein, which Hardy, “For my part, it is difficult for me Love, Dixon and Milne attended. to say what I owe to Ramanujan – his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.”

Hardy also found time for the occasional general article. In the In 1921 Hardy wrote a beautifully Oxford Magazine of June 1930, he crafted obituary notice, described bemoaned the University’s lack by the Manchester Guardian as of attention to mathematics and ‘among the most remarkable in the encouraged it to build up a fine literature about mathematics’ mathematical school, observing: For the next three years Hardy ‘mathematicians are reasonably wrote a number of papers based cheap, but they cannot be had for on, and extending, Ramanujan’s nothing’. He urged an increase work. Meanwhile, he was working in the number of mathematical through his colleague’s extensive lecturers, proposed more research notebooks and papers, and in activity as essential for the future, 1927, with two others, he published and lobbied for the creation of a Ramanujan’s Collected Papers. Mathematical Institute.

Hardy’s main relaxation was cricket. Here, during a British Association meeting in Oxford in August 1926, he leads a team of MATHEMATICIANS versus THE REST OF THE WORLD. His team included Titchmarsh, Bosanquet, Linfoot and Ferrar. G H Hardy’s Oxford years From Oxford to Cambridge

After eleven fruitful years in Oxford, Hardy decided to return to Cambridge for the rest of his days.

Hardy leaves Oxford Sayings of G H Hardy Although he was very happy at Hardy’s successor as Oxford’s In the 1920s Hardy had many Oxford, Hardy chose to resign Savilian professor was his first preoccupations besides his teaching his Oxford Chair and return to research student, E C Titchmarsh, and research. He was heavily Cambridge, following the death who explicitly asserted that he involved with several national in 1931 of E W Hobson, would not lecture in geometry. societies, becoming President Cambridge’s Sadleirian Professor Since then, the specification for of the Mathematical of Mathematics. the Chair has been relaxed and its Association: occupant can now be selected from In spite of all Hardy’s efforts to any area of pure mathematics. In his first presidential establish an analytical school in address, What is geometry?, Oxford, Cambridge remained the After his departure to Cambridge, Hardy asserted that: mathematical hub of England and Hardy returned to Oxford for “I do not claim to know any Hardy wished to be considered for several weeks every summer geometry, but I do claim its most prestigious mathematical to enjoy the atmosphere, see to understand quite clearly chair. Moreover, he was now aged his college and mathematical what geometry is.” 54, and if he remained at New colleagues, and captain the New College he would have to yield College Senior Common Room He also joked that the only up his rooms upon retirement; if cricket team in their annual match geometrical result that he he returned to Trinity College he against the college servants and had ever proved was: could live there for life, as indeed the choir school. “If a rectangular hyperbola did Littlewood. is a parabola, then it is also He also returned to give the first an equiangular spiral.” Hardy was successful in securing lecture to the Invariant Society, the Sadleirian chair, and the Oxford University’s undergraduate following notice duly appeared in mathematics society (still the Oxford University Gazette: flourishing); this was in Hilary Term 1936 on the subject of Round numbers (those with few different SAVILIAN PROFESSORSHIP prime factors). OF GEOMETRY The Electors to this Professorship propose shortly to proceed to an election of a professor in the place of Godfrey Harold Hardy, MA, Fellow of New College, who has resigned as from the beginning of Michaelmas Term, 1931.

By this time the stipend had As President of the National Union On visiting America: increased to £1200 per year, of Scientific Workers, Hardy’s During his year in America Hardy and the Statutes now recognised left-wing leanings emerge clearly wrote to a New College colleague: the importance of research: from the following remarks to an “This country is in many ways the The duties of every Professor audience of scientists: only one in the world – it has its shall include original work by the “…although our jobs are very deficiencies (tea γ, paper β–, … , Professor himself and the general different from a coalminer’s we are dinner rather an uninteresting supervision of research and much closer to coalminers than meal, and at 6.30). But American advanced work in his subject capitalists. At least we and the football knocks all other spectacles and department. miners are both skilled workers, absolutely flat: the sun shines not exploiters of other people’s more or less continuously: and for work, and if there’s going to be a quietness and the opportunity to be line-up, I’m with the miners.” your own master I’ve never come across anything like it.”

These posters were conceived by Robin Wilson, with the assistance of Raymond Flood and Dyrol Lumbard.