On 7 June, 1890, a Cambridge examiner added a bizarre twist to the annual ritual of reading out the examination results from the balcony of the Senate House: Philippa Fawcett, of Newnham College, he said, had been ranked ‘above the Senior Wrangler’ in the Mathematics Tripos. The Senior Wrangler was the idiosyncratic local name given to the student who came top in the examination. The reason why Philippa was ranked ‘above the Senior Wrangler’ was that women weren’t formally allowed to take Cambridge degrees but they were allowed to take part in the examination. Philippa had beaten all her male rivals.

The announcement produced a sensation in the university: when Fawcett’s name was read out a large crowd erupted in pandemonium and the slight young heroine was carried in triumph back to her college, where she was feted with bell-ringing and gong-banging, bonfires, dancing, feasting and a victory ode.

Hail the triumph of the corset.

Hail the fair Philippa Fawcett,

Victress in the fray,

Crown her queen of hydrostatics,

And the other Mathematics,

Wreathe her brow in bay.

The news went global. The New York Times ran a piece on ‘the kind of girl this Senior Wrangler is.’ The Daily Telegraph proclaimed, in somewhat over-wrought prose, that ‘once again has woman demonstrated her superiority in the face of an incredulous and somewhat sympathetic world … And now the last trench has been carried by Amazonian assault, and the whole citadel of learning lies open and defenceless before the victorious students of Newnham and Girton. There is no longer any field of learning in which the lady student does not excel.’

The reason for the furore was that, since its introduction in 1748, the Mathematics Tripos had gained a reputation as the ultimate test of both raw intellectual ability and mental stamina. History and classics could be dismissed as tests of memory and cramming. English literature was resisted precisely because it was a ‘woman’s subject.’ But mathematics was the real deal – and the Cambridge Mathematics Tripos was the world’s most demanding examination. Becoming a senior wrangler was the equivalent of winning Wimbledon. Those who missed the top slot include some of the great names in British intellectual history such as Lord Kelvin and J.J. Thompson (Second Wranglers), G.H. Hardy and Alfred North Whitehead (Fourth Wranglers), Bertrand Russell (ninth) and John Maynard Keynes (twelfth). People who wore the garland were feted for life.

Philippa was the only daughter of two leading members of Britain’s liberal intelligentsia. Her father, Henry, had also been a Cambridge mathematics star – he was ranked Seventh Wrangler in 1856 and quickly elected to a fellowship of Trinity Hall. Two years later a tragic accident threatened to blight a brilliant career: Henry’s father shot him in the face during a hunting accident, blinding him in both eyes. But Henry was not the sort to let mere blindness slow him down: he became professor of political economy at Cambridge in 1863, a member of parliament in 1865, and postmaster general in 1880. He was also one of the most vigorous advocates of open competition: in 1869, he moved a resolution demanding that all civil service posts should be open to competition, and in 1880 he opened clerkships in the post office to women as well as men.

Her mother, Millicent, was a member of one of the first families of British feminism, the Garrets. Millicent was not the first Garret Henry had wooed: her elder sister, Elizabeth, a pioneering doctor, turned him down. But the union in 1867 proved to be a marriage of true minds despite the fact that Henry was fourteen years her senior. Millicent worked as enthusiastically on female-focused reform projects as her husband did running the Post Office, the centrepiece of Britain’s information revolution: she was chairwoman of the National Union of Women’s Suffrage Societies and a co-founder of Newnham College (an infant Philippa toddled around her parents’ drawing room as senior academics and their wives planned the introduction of female education to Cambridge). Today’s Fawcett Society, a charity devoted to women’s rights, is named after Millicent.

It would be unkind to suggest the Fawcetts treated Philippa as a ‘project’ in the same way that James Mill treated poor John Stuart: there are wonderful stories of the young Philippa taking her blind father skating on the River Cam from Cambridge to Ely, a journey of fifteen miles, guiding him by whistling. But they certainly threw themselves into her education and delighted in her triumphs. Before she went up to Cambridge they arranged for her to have special coaching with a top professor at University College London, Karl Pearson, who had himself been ranked Third Wrangler at Cambridge before becoming a first-rate statistician and leading proponent of eugenics. When Philippa arrived she was already fairly famous: her mother had co-founded her college and her father was professor of political economy. Newnham treated her as a prize racehorse, handing her over to Mary Ellen Rickett, the college’s most successful performer in the mathematics Tripos to date, to prepare her for the Tripos, as well as bringing in the university’s top male coaches.

Philippa went on to have a successful but not stellar career: she certainly doesn’t have a place in the pantheon of great senior wranglers. She spent a decade teaching and researching at Cambridge, holding a lectureship at Newnham (which didn’t yet have any fellows) and publishing papers on fluid dynamics. In 1902, she left Cambridge for South Africa, taking up a job training future mathematics teachers at the Normal School in Johannesburg (later the University of Pretoria) and spending her spare time establishing schools. In 1905, she returned to England to work in the education department of the London County Council (LCC). She died at the age of 80 in 1948, two months before the law was changed to allow women to receive Cambridge BAs.

Her decision to abandon Cambridge may have had something to do with her gender. The Senior Wrangler Philippa was bracketed above, Geoffrey Thomas Bennett, went on to enjoy a comfortable academic career, winning a prize fellowship of St John’s and, shortly afterwards, a teaching fellowship of Emmanuel, where he remained, with breaks for war service, until 1943. Philippa had to content herself with a temporary lectureship at a poor college that couldn’t formally award degrees. Virginia Woolf drew a striking sketch of the way men continued to occupy the best positions in ‘the citadel of learning’ in A Room of One’s Own (1929). A men’s college she visits is the product of ‘an unending stream of gold and silver’ that has poured forth over the centuries. The fellows enjoy the finest food and an ancient library.

But Philippa may also have left because she knew she would never be in the very top flight of mathematicians. Spending your life as an undergraduate tutor might be acceptable if you had the luxury of St John’s or Emmanuel at your disposal, as her undergraduate rival did, but not if you were stuck in the equivalent of a boarding house, training girls for a qualification they weren’t formally allowed to take.

The story of the rise of women has often been written in terms of collective struggle and heroic political gestures. Women agitated for the vote in their millions. Suffragettes chained themselves to railings, starved themselves almost to death and threw themselves in front of the king’s horses. But there is another story behind the public one: one that is meritocratic rather than egalitarian and individualistic rather than collectivist. Bureaucrats and lawyers extended the principle of open competition to the other half of humanity. Educational reformers such as Miss Beal and Miss Buss created women’s schools and women’s colleges. Lonely scholars burned the midnight oil to prove that they were just as good as men, if not better.

Examinations were ideal engines of the feminist revolution because they weren’t tainted with the suspicion of subjectivity or favouritism. The idea that women were not up to serious intellectual work was deeply entrenched at the time: in Sex in Education; or a Fair Chance for Girls (1873), based on a study of seven female students at Vassar College in the United States, Dr Edward Clarke argued that women who were subjected to the same demanding course of advanced education as men developed ‘neuralgia, uterine disease, hysteria and other derangements of the nervous system.’ Champions of women’s rights seized on examinations as a way of exploding such prejudices. Women’s schools such as the North London Collegiate and Cheltenham Ladies’ College emphasised examinations in rigorous subjects rather than training in needlework and comportment. Women’s colleges did their best to prepare their most promising students for these intellectual trials of strength, feeding them delicacies, making sure that they got the right mixture of sleep and exercise, boosting their morale and making heroines of their most successful pupils. Several other examination prodigies paved the way for Philippa: Girton’s Charlotte Scott was informally bracketed as Eighth Wrangler in mathematics in 1880, and the same college’s Agnata Ramsay was the only candidate of either sex who was deemed fit to occupy the first division of the first class in Part Two of the Classical Tripos in 1887, soliciting an offer of marriage from the 55-year-old Master of Trinity, H.M. Butler, which Agnata accepted.

Though the number of female university students was small – and the number of female Wranglers vanishingly small – the achievements of intellectual pioneers nevertheless changed popular perceptions of women’s abilities. Gilbert and Sullivan satirised the fashion for rigorous female education in their 1884 operetta, Aida, whose eponymous heroine founds a female-only university in which women are taught they are superior to men. Cartoonists made hay with images of educated women riding bicycles in bloomers, or sitting in their studies, pince-nez perched on their noses, surrounded by piles of books and papers. Punch magazine derided women for living on ‘nothing but foolscap and ink.’ Novelists turned ‘graduate girls’, many of them educated at Newnham or Girton, into stock characters: Grant Allen’s The Woman Who Did was a ‘Girton Girl’; McDonnell Bodkin’s lady detective, Dora Myrl, was, improbably, both a ‘Cambridge Wrangler and Doctor of Medicine’.

Philippa’s triumph was an important moment in the rise of the meritocracy as well as the rise of women. The meritocratic idea had started to revolutionise Britain in the mid-nineteenth century. Patronage was abolished in favour of open competition in both Oxbridge colleges and the higher civil service. Examinations replaced wire-pulling as the main method of selection. Intellectual families began to dominate the higher reaches of the British state: Fawcett is just one surname that keeps recurring along with Keynes, Darwin, Sidgwick and Runciman.

The revolution may have been a bit slow: when this author first went to Balliol (in 1977) and All Souls (in 1980) they were both all-male institutions. But the logic has nevertheless proved irresistible: the last few decades have seen a succession of firsts in British society, from the first female Home Secretary to the first female commissioner of the Metropolitan Police Force (two years below me at Balliol, as it happens) from the first female prime minister to the first female fellow of All Souls, to the first female editor of The Economist. Women now make up the majority of students in American and British universities. And society is increasingly divided, not between women and men, but between the exam-acing classes and the exam-failing classes. The corset is long gone. The triumph of Philippa Fawcett is here to stay.