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GODFREY HAROLD HARDY, the celebrated pure mathematician, was born on 1877 February 7, the son of Isaac and Sophia Hardy, of Cranleigh, Surrey. He was educated at Winchester and Trinity College, Cambridge, going up to Cambridge with an Entrance Scholarship in 1896 and reading mathematics. He was placed fourth Wrangler in the Mathematical Tripos of 1898, and obtained a first division in the first class of Part II of the Mathematical Tripos of 1900. He was awarded a Smith's Prize, in company with Jeans, in 1901. In 1900 he was elected to a Prize Fellowship at Trinity; from that time on, he devoted himself to research in pure mathematics. In 1906, when his Prize Fellowship was due to expire, he was put on the Trinity staff as Lecturer in Mathematics, a position he continued to hold until 1919. He was elected a Fellow of the Royal Society in 1910. The University of Cambridge recognized his world-wide reputation as a researcher in the theory of the real and complex variables, and in the theory of numbers, by giving him the honorary title of Cayley Lecturer in 1914. In 1919 he was elected to the Savilian Chair of Geometry in the University of Oxford, with a Fellowship at New College. He respected the title of his Chair to the extent of giving certain lectures in geometry, but in the main he continued his previous interests, though occasionally lecturing on mathematical philosophy for non-mathematicians. For 1928-1929 he was a Visiting Professor at Princeton, N.J., and at the California Institute of Technology, O. Veblen coming to Oxford in his place. In 1931 he returned to Cambridge to succeed E. W. Hobson in the Sadleirian Chair of Pure Mathematics, being re-elected to a Fellowship at Trinity. He was later elected to an Honorary Fellowship at New College, an honour of which he was very proud. He held honorary degrees from Athens, Harvard, Manchester, Sofia, Birmingham, Marburg and Oslo. He was awarded the Royal Medal of the Royal Society in 1920, its Sylvester Medal in 1940 and the de Morgan Medal of the London Mathematical Society in 1929. He was President of Section A of the British Association at its Hull meeting in 1922. He was President of the National Union of Scientific Workers in 1924-26. He was long associated with the London Mathematical Society as member of Council and Secretary, and he had the unusual distinction of being twice President, namely for 1926-28 and for 1939-41. He was an honorary member of many of the leading foreign scientific academies. He retired from the Sadleirian Chair in 1942, and died on 1947 December 1, the day on which the Copley Medal of the Royal Society – its highest award – was due to be presented to him.
Such are the bare formal details of Hardy's life and distinctions. Why are these important for astronomers? Because Hardy was a mathematician who profoundly influenced mathematics in this country, who gave it standards of rigour in which, before him, it had been sadly lacking, and through whose hands passed many of those who were later to become well-known mathematical astronomers. His book, "A Course of Pure Mathematics", first published in 1908, went into edition after edition; generations of undergraduates, in universities the wide world over, were brought up on it; and to those who had the privilege of attendance at his lectures on analysis and the theory of functions, he was the very voice of inspiration, to many indeed a personal friend. But Hardy was much more than a teacher and researcher of international fame. He was a personality – one might truly say the leading personality in the English mathematical world – who radiated an attitude to mathematics which made it
shine as something supremely worth while, something clean and clear and bright and universal (as the Warden of New College has written), something fundamental to the living of the good life, and that the more so the less its utilitarian applications. Some of these feelings about pure mathematics he gave expression to in his "A Mathematician's Apology", but Hardy the man was again something greater even than his fastidious literary style conveyed. His conversation on all subjects was gay, provocative, fascinating; on mathematics inspiring; on cricket encyclopaedic; even on astronomy (of which he affected to be ignorant) knowledgeable and stimulating; on all topics entertaining. Without ever seeking it he was the recipient of much affection and much secret hero-worship. He was through and through intellectually honest; he was youthful in outlook to the day of his death. Though his attitude to religion shocked many people – his Polish pupil Zygmund used to say that Hardy was the only man he had ever known who took God for his personal enemy – yet Hardy's deep reverence for mathematics and for all things of the mind was precisely of the same kind as impels other people to the worship of God; the only enigma about Hardy was that this never seemed to occur to him.
It was at one time said in Trinity that Hardy was a fighter for lost causes. One cause he fought for supremely successfully – the battle for the reform of the old Mathematical Tripos Part I and the abolition of its order of merit. Hardy was an able pamphleteer, and one of his fly-sheets in that controversy claimed that a certain specified number of members of the Cambridge Senate "with mathematical degrees" were in favour of the reform. This number was disputed by the other side, and when Hardy came to verify it, great was his chagrin when he found that he had erroneously reckoned himself as possessing a "mathematical degree", whereas having taken the Tripos at the end of his second year he had proceeded to his B.A. at the end of his third year on the strength of a certificate of diligent study only, thus counting as the possessor of a mere poll degree, which did not rank for subject. But still greater was his joy when he was able to restore the number of his supporters to its original figure, by counting in, as the possessor of a mathematical degree, the venerable classic, H. Montagu Butler, the Master of Trinity, who in remote ages had actually taken the mathematical tripos. This little story, which I had from Hardy himself, well illustrates the attractive whimsicality of his character, and his zest for the odd things of life and learning.
I have indicated that his direct connection with astronomy was slight. He actually became a Fellow of the Royal Astronomical Society in 1918 at the time of the great debates between Eddington and Jeans, doing so in order to be able to attend the debates personally. The writer well remembers one later occasion of a similar character when Hardy took an effective part in a Royal Astronomical Society debate the debate of 1930 December 12, on the subject of stellar structure – when in addition to several other speakers R. H. Fowler was presenting a paper on Emden's and allied differential equations. Hardy seriously discussed Fowler's contribution, but concluded by remarking that of one thing (amidst so much that was the subject of dispute) he was sure, and that was that Fowler's work on Emden's equation, being pure mathematics, would retain its value long after all the various physical theories of the internal constitution of the stars had become obsolete – a prophecy which has in a fair measure been fulfilled.
The writer, though an undergraduate pupil of Hardy's, was never one of his research pupils. But he had the great privilege of knowing Hardy well, both in his Cambridge and Oxford settings. He can bear witness to the fact that after Hardy's social discomforts at the High Table of Trinity, Hardy expanded. and mellowed in a wonderful way, in what was to him the more benign atmosphere of New College. His popularity there was immediate and assured, and he gave back in the intellectual exhilaration of his conversation what he received in. sympathetic friendship. By the time of his return to Trinity his formerly lost.. causes had all been won, and he enjoyed his return. He once remarked that his Prize Fellowship at Trinity was the most important event in his academic career.
For many of the band of mathematicians in Britain, on the Continent and in America – Hardy's death extinguished one of the lights of our lives.
He was elected a Fellow 1918 June 14.
E. A. MILNE.
Such are the bare formal details of Hardy's life and distinctions. Why are these important for astronomers? Because Hardy was a mathematician who profoundly influenced mathematics in this country, who gave it standards of rigour in which, before him, it had been sadly lacking, and through whose hands passed many of those who were later to become well-known mathematical astronomers. His book, "A Course of Pure Mathematics", first published in 1908, went into edition after edition; generations of undergraduates, in universities the wide world over, were brought up on it; and to those who had the privilege of attendance at his lectures on analysis and the theory of functions, he was the very voice of inspiration, to many indeed a personal friend. But Hardy was much more than a teacher and researcher of international fame. He was a personality – one might truly say the leading personality in the English mathematical world – who radiated an attitude to mathematics which made it
shine as something supremely worth while, something clean and clear and bright and universal (as the Warden of New College has written), something fundamental to the living of the good life, and that the more so the less its utilitarian applications. Some of these feelings about pure mathematics he gave expression to in his "A Mathematician's Apology", but Hardy the man was again something greater even than his fastidious literary style conveyed. His conversation on all subjects was gay, provocative, fascinating; on mathematics inspiring; on cricket encyclopaedic; even on astronomy (of which he affected to be ignorant) knowledgeable and stimulating; on all topics entertaining. Without ever seeking it he was the recipient of much affection and much secret hero-worship. He was through and through intellectually honest; he was youthful in outlook to the day of his death. Though his attitude to religion shocked many people – his Polish pupil Zygmund used to say that Hardy was the only man he had ever known who took God for his personal enemy – yet Hardy's deep reverence for mathematics and for all things of the mind was precisely of the same kind as impels other people to the worship of God; the only enigma about Hardy was that this never seemed to occur to him.
It was at one time said in Trinity that Hardy was a fighter for lost causes. One cause he fought for supremely successfully – the battle for the reform of the old Mathematical Tripos Part I and the abolition of its order of merit. Hardy was an able pamphleteer, and one of his fly-sheets in that controversy claimed that a certain specified number of members of the Cambridge Senate "with mathematical degrees" were in favour of the reform. This number was disputed by the other side, and when Hardy came to verify it, great was his chagrin when he found that he had erroneously reckoned himself as possessing a "mathematical degree", whereas having taken the Tripos at the end of his second year he had proceeded to his B.A. at the end of his third year on the strength of a certificate of diligent study only, thus counting as the possessor of a mere poll degree, which did not rank for subject. But still greater was his joy when he was able to restore the number of his supporters to its original figure, by counting in, as the possessor of a mathematical degree, the venerable classic, H. Montagu Butler, the Master of Trinity, who in remote ages had actually taken the mathematical tripos. This little story, which I had from Hardy himself, well illustrates the attractive whimsicality of his character, and his zest for the odd things of life and learning.
I have indicated that his direct connection with astronomy was slight. He actually became a Fellow of the Royal Astronomical Society in 1918 at the time of the great debates between Eddington and Jeans, doing so in order to be able to attend the debates personally. The writer well remembers one later occasion of a similar character when Hardy took an effective part in a Royal Astronomical Society debate the debate of 1930 December 12, on the subject of stellar structure – when in addition to several other speakers R. H. Fowler was presenting a paper on Emden's and allied differential equations. Hardy seriously discussed Fowler's contribution, but concluded by remarking that of one thing (amidst so much that was the subject of dispute) he was sure, and that was that Fowler's work on Emden's equation, being pure mathematics, would retain its value long after all the various physical theories of the internal constitution of the stars had become obsolete – a prophecy which has in a fair measure been fulfilled.
The writer, though an undergraduate pupil of Hardy's, was never one of his research pupils. But he had the great privilege of knowing Hardy well, both in his Cambridge and Oxford settings. He can bear witness to the fact that after Hardy's social discomforts at the High Table of Trinity, Hardy expanded. and mellowed in a wonderful way, in what was to him the more benign atmosphere of New College. His popularity there was immediate and assured, and he gave back in the intellectual exhilaration of his conversation what he received in. sympathetic friendship. By the time of his return to Trinity his formerly lost.. causes had all been won, and he enjoyed his return. He once remarked that his Prize Fellowship at Trinity was the most important event in his academic career.
For many of the band of mathematicians in Britain, on the Continent and in America – Hardy's death extinguished one of the lights of our lives.
He was elected a Fellow 1918 June 14.
E. A. MILNE.
Godfrey Harold Hardy's obituary appeared in Journal of the Royal Astronomical Society 108:1 (1948), 44-46.