Godfrey Harold Hardy
Godfrey Harold Hardy (1877–1947) was a British mathematician who mainly worked in analysis and number theory. A ‘pure mathematician’, he believed the point in mathematics lay in its beauty not its applications. Hardy is also known in Biology circles for the basic principle in population genetics, the Hardy-Weinberg principle!
Early life
G.H. Hardy was born in Cranleigh in the English county of Surrey on 7 February 1877. His parents were very intelligent and skilled in mathematics, but came from poor families and so did not receive a university education. Hardy’s father Isaac was a bursar and Art Master at Cranleigh School, while his mother Sophia had been a senior mistress at Lincoln Teacher’s Training School.
At his Victorian nursery, Hardy argued with his nurse about the efficacy of prayer and the existence of Santa Claus. Despite writing in his most famous essay, A Mathematician’s Apology, that he did “not remember having felt, as a boy, any passion for mathematics”, at only two years old he wrote numbers up to the millions and factorised the numbers of hymns when he was taken to church. He reflects that “I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively”.
Hardy, known as Hardy with the exception of a couple of close friends who called him Harold, was a very shy, awkward and eccentric child. He was said to hate seeing his reflection so much that in later life he covered all of the mirrors in his room with towels when staying at hotels.
Around the age of 20, Hardy decided he did not believe in God. However, he played games of trying to ‘fool’ God throughout his life to amuse himself.
Hardy was the top of his class in most subjects during his school years, however he hated having to collect prizes in front of the school for his achievements. His work paid off, as he won a scholarship to Winchester College in 1889, joining the following year. Unfortunately Hardy disliked everything about the school, the best in England for mathematical training, expect for his academic tutelage.
Work at Cambridge
Entering Trinity College, Cambridge in 1896, Hardy was originally tutored under Robert Rumsey Webb. He was shocked to discover that Webb was not interested in mathematics, only in the tricks of exams. Hardy almost switched to History, however he managed to change his coach to Augustus Love. A.E.H. Love recommended that he read Camille Jordan’s Cours d’analyse, saying he “learnt for the first time as I read it what mathematics really meant.”
G.H. Hardy graduated from Trinity in 1899, became a fellow at Trinity in 1900 and lectured there in mathematics from 1906 to 1919.
Hardy preferred to work in ‘pure mathematics’, due in part to his hatred of war and the military uses mathematics had been applied to, even saying in his Apology that “I have never done anything “useful”. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world”. He further pointed out that mathematicians generally do not “glory in the uselessness of their work” but that, as science can be used for both evil and good, its “remoteness from ordinary human activities should keep it gentle and clean”.
Hardy liked to only work 4 hours every day on mathematics, spending much of the rest of the day on his only other passion: cricket.
Beginning in 1911, Hardy worked with John Edensor Littlewood, in what is one of the most celebrated collaborations in 20th-century mathematics. The next year they published their first in a series of papers with fundamental contributions to a diverse range of mathematical realms, from the theory of Diophantine analysis to divergent series summation, Fourier series, the Riemann zeta function and the distribution of primes. In a lecture in 1947 Danish mathematician Harald Bohr reported that a colleague quipped “Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood.”
Collaboration with Ramanujan
Hardy’s other important collaboration was with Srinivasa Ramanujan, a poor self-taught Indian clerk who Hardy immediately recognised as a genius. On 16 January 1913, Ramanujan wrote a letter to Hardy, who he knew from studying Orders of Infinity. Hardy read the letter in the morning and suspected it was a prank, but he thought in the evening that it was likely genuine as, in his words, “great mathematicians are commoner than thieves or humbugs of such incredible skill”. He invited Ramanujan to Cambridge and began what he called “the one romantic incident in my life”.
Hardy filled in the gaps in Ramanujan’s mathematical education and co-authored several papers with him before Ramanujan returned to India in 1919. Some of their most famous work was around integer partitions, which led to the Hardy-Ramanujan asymptotic formula, a remarkably accurate approximation for the number of ways a positive integer n can be written as a sum of positive integers, regardless of their order. Hardy saw his discovery of Ramanujan as his greatest contribution to mathematics.
On a scale of mathematical ability, Hardy remarked that his ability would be 1, David Hilbert would be 10, and Ramanujan would be 100.
Later years
Following Hardy’s pacifist friend Bertrand Russell’s arrest for publicly lecturing against inviting the United States to enter the war on Britain’s side, and disillusioned by the pro-war sentiment in Trinity College, Hardy left Cambridge to 1919 to take the Savilian Chair of Geometry Oxford.
It is believed Hardy left Oxford to return to Cambridge in 1931 to avoid compulsory retirement at 65. Once again, he was a fellow of Trinity College and held the Saleirian Professorship until 1942.
Hardy suffered a coronary thrombosis, a blood clot in the heart, which prevented him from enjoying sports he loved to play. As well as preventing him playing tennis and squash, he also lost some of his creative powers in mathematics and became constantly bored. In the early summer of 1947 he attempted suicide, but resolved to wait for his death.
G.H. Hardy died suddenly one morning listening to his sister read out from a book about the history of Cambridge University cricket on 1 December 1947.
Legacy
G.H. Hardy was a remarkable mathematician, one the most prominent of the 20th century and a great collaborator, while being a very humble man who was honest about his own strengths and weaknesses. He is credited with bringing “rigour” to British mathematics, improving the nature of proofs in a field where applied mathematics was the main tradition.
He had a wide range of interests, shown by six New Year’s resolutions he set himself in a postcard to a friend:
- Prove the Riemann hypothesis;
- Make 211 not out in the fourth innings of the last Test Match at the Oval;
- Find an argument for the nonexistence of God which shall convince the general public;
- Be the first man at the top of Mount Everest;
- Be proclaimed the first president of the U. S. S. R. of Great Britain and Germany; and
- Murder Mussolini.
Through more than 300 papers and 11 published books, and for helping give Ramanujan’s genius to the world, Hardy’s contribution to the world of mathematics has been immense. And, even though he never wanted to, he has contributed greatly to the world more widely. His work A Mathematician’s Apology remains a brilliant insight into the minds of mathematicians and continues to be read across the world.
A fellow of the Royal Society, awarded its most prestigious Copley Medal for his distinguished part in the development of mathematical analysis in England, twice President of the London Mathematical Society, awarded its most prestigious De Morgan Medal, G.H. Hardy is one of the heartwarming examples of a great mathematician recognised for his work during his lifetime, but throughout it all remaining an honest and down to earth man.