I’m struggling to keep up.

We are told that gender is terrifically important and that people must be free to define themselves as they please in the eyes of the law. Yet we’re simultaneously told that gender doesn’t exist and that, beyond the obvious physical differences, men and women are identical. So which is it?

The second assertion meets George Orwell’s definition of an idea so stupid that only intellectuals could believe it. It is maintained in defiance of both scientific consensus and common sense. Yet, probably for that very reason, it is enforced with remarkable nastiness.

A high school principal in North London is in terrible trouble for saying that girls often prefer not to study physics. “There’s a lot of hard maths in there that I think that they would rather not do,” Katharine Birbalsingh told a parliamentary committee. “I think cultural issues do play a part, but it’s wrong to have this idea that we ought to have 50% girls in all subjects and 50% boys.”

You can imagine the howls of protest, the demands that she be removed from her post — just as Lawrence Summers was out as president of Harvard University for making the same point in 2005.

Both educators were saying things that are uncontroversial among neuroscientists, psychologists, and, come to that, parents. But politicians and columnists will not allow them to be voiced. Our public discourse insists on the pretense that all the differences between the sexes are caused by conditioning. If we didn’t give boys trucks and girls dolls to play with, we’re supposed to say, they’d turn out exactly the same.

Thirty years ago, the feminist neurophysiologist Ruth Bleier put it this way: “A person’s gender is an arbitrary, ever-changing, socially constructed set of attributes that are culture-specific and culturally generated.”

I can see why her argument might have a certain intuitive appeal, if only because most of us can call to mind examples of children being treated differently. But a mass of empirical evidence suggests that aggregate personality differences between the sexes are innate and constant across different cultures. The genetic sequences that cause them are being identified, and their effects are visible even in early infancy. Baby girls are more distressed by the cry of another child, for example, and smile more at their mother’s presence. This is not always true, but it is true on aggregate, often enough to form a visible pattern.

The chief difference is the obvious one. It was stated as long ago as 1911 by Edward Thorndike, one of the founders of educational psychology, who summarized it as lying “in the relative strength of the interest in things and their mechanisms (stronger in men) and the interest in persons and their feelings (stronger in women).”

Well, duh. Men, in general, are more interested in systems, and women, in general, are more interested in people. Simon Baron-Cohen of the University of Cambridge, the world’s leading authority on autism, believes that that condition is a kind of extreme male brain — an exaggeration of the masculine interest in algorithms, rules, and mechanisms. A similar argument was made by Hans Asperger, after whom the syndrome was named, in 1944.

This is not to say that women can’t be autistic. They can, just as men can be anorexic. But there is a difference in aggregate.

Much of the anger at Birbalsingh stems from an inability, or, more likely, a willful refusal, to understand statistical distributions. If you say that men tend to be taller than women, you are not claiming that every man is taller than every woman. Almost everyone can see that. But make the same point about relative interest in physics, and a lot of people will deliberately misunderstand you. “So you’re saying girls can’t do math?”

For what it’s worth, Birbalsingh is one of the most successful teachers in the world. She has founded a school in a deprived area of North London and, by an extraordinary combination of discipline and high expectations, achieved some of Britain’s best grades. The children at her school, of both sexes, are routinely pushed into trying difficult things.

But ability and interest are two different things. I have a 16-year-old daughter who wants to study math — you specialize earlier in Britain than in the United States. It would be outrageous to tell her that math is not for girls. But it would be no less outrageous to push her into it so as to fill some quota.

Put it another way: The sin of prejudice lies in assigning to people the real or imagined average traits of their group, not in acknowledging that overall group differences exist. Again, that is so obvious that you surely have to be an intellectual not to understand it.