A Mathematician's Apology

Content Warning: This section briefly discusses suicide.

The author of the book’s Foreword, C. P. Snow, first met Hardy at Christ’s College, Cambridge University, in 1931. Their first words were about cricket: Hardy grilled Snow on his ideas for playing the game. Snow passed this “exam” and soon was Hardy’s companion in the stands at the cricket pitch. In addition, Snow describes how their friendship became “intellectually the most valuable friendship of my life” (12).

Despite having a mind of great clarity, Hardy didn’t consider himself a genius, though he believed that, for a time, he was the fifth-best pure mathematician in the world. Hardy believed his finest moments were his collaborations with the great mathematicians Ramanujan and Littlewood. Snow considers Hardy’s greatest achievement his ability to turn works of the intellect into works of art.

Hardy had many eccentricities—he hated social introductions, avoided being photographed, and covered mirrors wherever he stayed—that stemmed from his lifelong shyness. Nonetheless, he was competitive, winning top honors at every school he attended, and his “anti-narcissism” took a back seat when he spoke about moral issues. Among them were his atheism, to which he adhered scrupulously, despising religion and refusing to attend services normally required of college members.

Hardy did well on the Mathematical Tripos, a fiendishly tough exam, but hated its emphasis on difficulty over creativity. Although he placed fourth on the first part and, two years later, took top honors on the second part, he later fought to have the exam modified: Its requirements, he claimed, had “effectively ruined serious mathematics in England for a hundred years” (23).

Hardy found great inspiration in the famous French textbook Cours d’Analyse, which teaches calculus in a manner that opened his eyes to the wonders of pure mathematics. He never looked back: Mathematics, and making math analysis more rigorous among its English practitioners, became his lifelong preoccupations.

The collaboration with Littlewood contained ironies: Both men could be obstinate; for a time, they worked at different universities; sometimes they’d ignore letters written by the other. Hardy was secretive about their work methods, yet the nearly 100 papers they produced strongly affected pure mathematics for two decades. Those papers are widely considered the result of the most remarkable collaboration ever undertaken in mathematics.

When an envelope filled with pages of symbols and theorems was delivered to Hardy, he initially believed it was yet another crank paper that scientists sometimes receive, attempting to prove some absurd belief about the pyramids or the Elders of Zion. Hardy set it aside, but the envelope’s theorems nagged at him until he showed them to Littlewood, who concurred that an unknown genius had written the pages.

Hardy arranged to bring their author, Srinivasa Ramanujan, to Cambridge, where he found that the Indian immigrant was poorly educated in math and hardly knew what a proof was. Nonetheless, together they produced five important papers. Ramanujan joined Hardy as a member of the Royal Society, the British science academy. However, he became ill and soon died. His youthful death troubled Hardy, reminding him of the many other mathematical geniuses who had died early. This contributed to his belief that few mathematicians produce anything of value past age 50.

World War I intervened, and Hardy publicly objected to England’s role in the conflict. Nonetheless, he volunteered for service; however, he was rejected on medical grounds. Hardy’s anti-war position put him at odds with Cambridge’s “vociferously bellicose” majority. He agreed with Professor Bertrand Russell’s efforts to halt the war. Russell was kicked out of Cambridge, and Hardy left to teach at Oxford.

Although in his early forties, Hardy did his greatest work during this period, and he acquired a sense of “timeless youth.” Oxford suited him: He was popular there, despite the picture of Lenin on a wall in his apartments. For two years, he presided over a science trade union. In 1930, though, he returned to Cambridge, where he took the senior math chair, and resided there into old age.

Cricket absorbed Hardy despite its encouraged players to be selfish. He poked fun at the game even as he adored it for its “formal beauty.” Another of his hobbies was rating famous people on qualities such as “Stark,” “Old Brandy” (eccentrically tasteful), and “Dim.”

In his early fifties, Hardy had a blood clot to the heart, which stifled his athletic activities, including “real” (indoor) tennis and squash. He felt great dismay as World War II broke out, and he felt helpless as his aging mind ceased to function with its once-youthful sharpness. In these respects, A Mathematician’s Apology is “a book of haunting sadness” (50).

Hardy escaped some of the boredom of his last years by writing, first his lengthy essay on the Russell incident in World War I, and then A Mathematician’s Apology. Working in British government, Snow labored hard on the country’s latest war effort, and—partly because of Hardy’s distaste for war—he and Snow grew apart.

In 1947, his health failing, Hardy became melancholy and tried to die by suicide but survived. Snow visited Hardy at his nursing home regularly thereafter. Each time, they spoke mostly about cricket. Otherwise, Hardy was depressed, resigned to his fate, awaiting the oblivion of death. Shortly before he died, though, Hardy remarked, “If I knew that I was going to die today, I think I should still want to hear the cricket scores” (58).