What do little girls like? As a child, I preferred Lego to dolls and, if asked what I wanted to be when I grew up, was apt to reply: a detective, or a reporter. My parents were scientists, so our household was in some ways less obviously gendered than most (though I went on to do an arts degree, two of my sisters read biochemistry and maths at university). Nevertheless, it was always in the air: the way girls should be, and therefore are. By the time I was a teenager, I’d learned to feel quite odd about certain of my tastes and aptitudes. I’d also internalised various stereotypes. I took great pride, for instance, in my map-reading – not because map-reading is intrinsically difficult, but because some small part of me accepted that women are not supposed to be any good at it.

No wonder, then, that reading Gina Rippon’s careful and prolonged demolition of the myth of the “female brain” left me with a powerful sense of relief. Here, at last, are things I’ve long felt instinctively to be true, presented as demonstrable facts. Professor Rippon is a researcher in the field of cognitive neuroscience at the Aston Brain Centre at Aston University, Birmingham, and an advocate for initiatives to mitigate the under-representation of women in Stem subjects. In The Gendered Brain, she shows how we first arrived at the conviction that the female brain is “different” (and thus inferior), how this misperception persists into the 21st century, and how the latest breakthroughs in neuroscience can, and should, dispel such fallacies for ever. It is a highly accessible book. It’s also an important one. Quite apart from how interesting the science contained within it is, it has the power – if only people would read it – to do vastly more for gender equality than any number of feminist “manifestos”.

She is supremely clear-eyed when she comes to unpick the reasons why there are still relatively few women in science

Our determination to look for differences between male and female brains may be traced to the 18th century: another way of proving that female biology was essentially deficient and fragile. In the 19th century, doctors and scientists developed a mania for measuring and weighing brains, tasks they performed by various means, including the pouring of bird seed into empty skulls (the amount required to fill it was then weighed). When this approach proved inconclusive, declarations of inferiority gave way to an insistence that the differences between men and women were “complementary”; that women, though they might not be suited to education or politics, had “compensating gifts” in the form of intuition.

What is fascinating is that even after the development of new brain‑imaging technologies at the end of the 20th century – technologies that, in essence, reveal how similar the brains of men and women are – the idea of the “male” and “female” brain has persisted both in science and the media. Simon Baron-Cohen, whose work in the field of autism has made him into something of a science superstar, has noted that you don’t have to be male to be in possession of what he calls a male brain (ie, to be a systemiser rather than an empathiser). But it’s no good. This line falls on deaf ears. The stereotypes persist.

Brick by brick, Rippon razes this history and, for the (non-scientist) reader, what she says is revolutionary to a glorious degree. To sum up: the notion that there is such a thing as a female brain is bunkum, more or less. Furthermore, now that we know our brains are highly plastic, and for so much longer than we once thought, our aptitudes and behaviour must be linked not only to nurture rather than sex, but to life itself: to all that we do and experience down the years.

The science in Rippon’s book is complex and multilayered. But she looks, too, at the pernicious influence of psychobabble. Evolutionary psychology comes in for something of a kicking, as do adherents of Freudian doctrines. She is brilliant on baby brains: on the reasons why, say, children may appear to prefer gendered toys, baby girls recognise faces more easily, and baby boys walk earlier. (Mostly, such things can be laid at the door of their carers’ expectations.) She is supremely clear-eyed when she comes to unpick the reasons why there are still relatively few women in science. Above all, she has the research that proves – back to my Lego – that women are as good (or as bad) at visuospatial processing as men.

For me, though, perhaps the most thought-provoking part of her book has to do with hormones. According to Rippon, recent work has shown that, far from a woman’s period having an effect on her ability to concentrate, there may be a link between the ovulatory and post-ovulatory phases in her menstrual cycle and positive behavioural changes such as improved cognitive processing. It’s not much of an exaggeration to say that I felt like cheering when I read this, and perhaps such information will provide food for thought for those campaigning for women to be given so-called menstrual leave.

Menstruation still carries a stigma; I wish that it didn’t. But received opinion and science are often miles apart, and once women are in possession of the full facts – once they stop internalising what others (women, as well as men) are inclined to tell them about their bodies – they may experience a new freedom. As Rippon shows repeatedly, there is nothing in our biology to justify the ongoing gender gap. Those who insist otherwise are standing in the way of progress.

• The Gendered Brain: The New Neuroscience That Shatters the Myth of the Female Brain by Gina Rippon is published by Bodley Head (£20). To order a copy, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £15, online orders only. Phone orders min p&p of £1.99