We've come a very long way. According to a recent Higher Education Policy Institute report, British female students are now ahead of men by almost every measure of university achievement. They have been entering higher education in greater numbers and are more likely to get places, even in such high-status subjects as law and medicine, where they also gain better degrees.
But let's not get too carried away. Only recently, Times Higher Education reminded us that women in universities earn less than men and are less likely to be promoted to senior positions. There are still pitifully few female vice-chancellors and plenty of obstacles discouraging girls from studying engineering and science.
But still, we've come a long way. Such a long way that it's easy to forget that only just over a century ago, women weren't admitted to universities at all. In a stirring new book, Bluestockings: The Remarkable Story of the First Women to Fight for an Education, Jane Robinson traces the fight for women to be accepted in higher education through interviews with 120 pioneers, many of whom speak movingly about their university experience. "Oxford gave me a vision, opportunities, a life I had never dreamed of, and my gratitude is enormous," recalls one, while another describes her three years at the University of Cambridge as "a walled garden separated from the rest - a garden full of voices, freedom and some intimations of immortality".
The turning point came, according to Robinson, when Emily Davies founded a small residential community where young women were able to study for degrees. Three years later it became Girton College, Cambridge, the first women's college in the country.
It was this achievement that paved the way for thousands more women to follow, even though they were not allowed to graduate until much later and encountered bitter prejudice, not least from male undergraduates who campaigned viciously against any encroachment of women into their hallowed sanctuary.
In 1897, there were riots at Cambridge when it was suggested that women should be granted official membership. Men brandished banners proclaiming "No Women" and "Down with Women". In 1899, the Durham University Journal published a piece titled "The Intellectual Inferiority of Women", which argued the folly of allowing the fairer sex to assume any parity with men. Such views were echoed by the clergy - most notoriously by Dean Burgon of Chichester, whose 1884 sermon declared women eternally inferior to men.
Then there were the medical objections to women's education, rooted in the belief that cleverness in women was suspect because their brains were "naturally incapacitated". In the 1870s, Henry Maudsley, the pioneering English psychiatrist, argued that if a woman's limited energies were directed towards the mind rather than the body, we would end up "a puny, enfeebled, and sickly race". A doctor lecturing at Harvard University at the same time argued that female graduates' brains had been worked so hard that their wombs had atrophied.
Later in the century, a Cambridge professor refused to lecture to an all-women gathering since "there is nobody here". Meanwhile, at the University of Oxford, John Ruskin was concerned that any "bonnets" turning up to his lectures would "occupy the seats in mere disappointed puzzlement".
Such questions about women's capabilities haven't really gone away. Only a couple of years ago, Lawrence Summers, who was then the president of Harvard, suggested that women may not have the same innate abilities in maths and science as men. He said that while no one knew why, "research in behavioural genetics is showing that things people attributed to socialisation" might actually have a biological basis - and that the issue needed to be studied further.
Summers' remarks, unsurprisingly, provoked fury among senior female academics, but they were condoned by a number of male commentators, who saw him as the victim of a feminist witch-hunt. So beware of too much euphoria over the current triumphs of female students. Advances for women are practically always countered by a backlash.
Early female academics were ever conscious of this danger, fearing that any lapse would offer detractors evidence for a case against them. It's an anxiety brilliantly evoked in Dorothy L. Sayers' novel Gaudy Night, set in a women's college in Oxford in the 1930s. The heroine, Harriet Vane, is invited there to investigate an unpleasant mystery, since involving the police might incur adverse publicity. "Nothing is more prejudicial to the college in particular and to university women in general," explains the dean, "than spiteful and ill-informed gossip in the press."
These days the backlash can take on subtle forms. I've been surprised, for example, when external examiners comment, as they regularly do, on the predominance of women students on our media courses. Asked what I'm going to do about it, I reply that I'm not going to do anything. As someone who has spent most of her career working to improve the representation of women in both education and the media, I'm hardly likely to object to the fruits of either enterprise.
I would, of course, be concerned about any evidence that male candidates were suffering discrimination. But since this is clearly not the case, I can't see why we should be concerned by the imbalance. We are, after all, educators, not social engineers.
But, protested one examiner, if this goes on then the media will be completely dominated by women and men won't get a look-in. And how would I feel then?
That, I replied dreamily, would be absolutely marvellous. Then we really would have come a very long way indeed.