If only men were from Mars and women from Venus. Then, presumably, it would be easy to tell their brains apart. Men's would be green, and women's lovable. The stereotypes of the male and female brain dealt with in books such as Men are from Mars, and Why men don't listen and women can't read maps are just that. Their over-simplifications get in the way of understanding what is really happening.
Just looking for differences between male and female brains has been problematic. Fighting the equality war seemed to make it a taboo area for research. Now that neuroscientists, using techniques such as magnetic resonance imaging, are venturing in, the truth is turning out to be complex and subtle.
Take the standard left-brain, right-brain argument. For verbal skills and logical thought, consult the left hemisphere of your cerebral cortex. It's the side that warms to rote learning and a sequential drip-feed of data.
The right deals with the bigger picture. It's the visual, spatial and creative hemisphere - able to see patterns where the left only sees details.
And we know that girls are more "left-brained" and boys more "right-brained" - which is why girls are good at languages and boys find it hard to show how they worked out an answer. Agreed?
Not really. In fact the idea that boys use one side and girls the other of the brain doesn't wash. Set a brain of either gender a task and you'll find few that do not show activity in both hemispheres, says John Geake, professor of education at Oxford Brookes university and chair of the Oxford cognitive neuroscience and education forum.
When it comes to language, for example, the left side tackles the mechanics of grammar and speech production, but the right has a role in inferring meaning and deciding whether the speaker is happy, sad, or about to hit you.
Professor Geake is impatient with attempts to compartmentalise the brain.
The theory of "multiple intelligences" which is influencing some schools'
teaching methods gets short shrift.
"Clearly you use the same sorts of brain processes in all subjects and areas at school. It doesn't make sense from a brain point of view to try to be that compartmentalised." So, alas, women don't have shoe-buying or chocolate "centres", any more than men have joystick control and a clothes ironing "particle".
"I call it a mapping problem," he says. "There is no centre in the brain for maths, no centre for music, no centre for any of these things. And while the brain is clearly modular, what those modules actually do is still a matter for debate."
Girls are more "bilateral" than left-brained, he says. They are more likely to use both hemispheres, and boys are more likely to use specific areas on either side. "Girls seem to have many of their modular functions more distributed around the brain and boys tend to have them more extremely lateralised - either on one side or the other."
This dovetails, maybe too neatly, with the perception that girls are better at multi-tasking and boys at developing areas of expertise. "You can tell evolutionary stories about girls having babies on hips and looking for food, whereas boys go out and concentrate on one thing for hours. They may be hunting a wild animal - or watching football."
Areas of expertise easily become obsessions, generally a male thing.
Simon Baron-Cohen, professor of developmental psychopathology at Cambridge university, has suggested that autism, often characterised by narrow interests and affecting far more boys than girls, is an extreme manifestation of the male brain.
This, he says, is a "systemising" organ, whereas women's tend to be "empathising" - a skill also lacking in autistic people.
The tendency for boys to systemise, he says, can be traced back to our hunter-gatherer past.
"You can make evolutionary arguments why it was more important for males to focus on systems - they needed navigation to get home, they needed to make tools, for example. But it is hard to test these theories. It is easier to focus on what you can measure currently."
Such measurements include his research on testosterone and the foetal brain, due to be published later this year.
The two sex hormones - oestrogen is the female equivalent - are the most important chemicals in brain development. During pregnancy a male foetus experiences a testosterone surge that shapes his body - and mind. The hormone acts more on the right hemisphere, inhibiting the left's development.
It also strengthens, for example, the areas that deal with spatial awareness and, crucially, is thought to affect the corpus callosum. This large bundle of nerve fibres connects the two cerebral hemispheres and is thicker and broader in girls. Their better connection may explain their tendency to use both sides of the brain more than boys.
Professor Baron-Cohen, who is also co-director of the Autism Research Centre in Cambridge, studied 58 baby boys and girls. Infants with higher levels of pre-natal testosterone were less willing to make eye contact when they were one-year-old, and had a smaller vocabulary at 18 months. Now aged four they find it harder to fit into new social groups and have narrower interests.
"Generally," he says, "girls seem to be talking earlier and developing vocabularly faster."
Another systemising-empathising difference has been found at birth.
One-day-old baby girls look longer at a human face than boys, who look longer at mechanical mobiles.
And work carried out at the University of East Carolina in 2001 found that when children studied facial expressions the boys processed the data using more of their holistic right hemispheres and the girls more of their detail-processing left. While both could identify expressions, girls were better at detecting fine changes, giving them an empathetic edge.
Girls, of course, have the edge in other ways. As this year's GCSE and A-level results have just reminded us, boys are behind in almost every exam league table. They are also ahead on special needs such as autism, dyslexia, and even stuttering.
"Boys are having a tough time," says John Geake. "There are those who can do extremely well who are not being challenged, they either mind their own business or go nuts. And at the other end you have boys who are pretty well learning disabled and school doesn't add anything to them. In the old days they could have gone and ploughed furrows, getting a job that required muscle. Now they can't."
So has the testosterone that shapes the male brain put boys at odds with an education system with its emphasis on rules, on story-telling, and on sequential learning?
Professor Michael O'Boyle, a psychologist at Melbourne university, says that the enhanced development of the right hemisphere in boys can be a curse and a blessing. Earlier this year he and American colleagues studied 60 male adolescents, 18 of whom were very gifted mathematicians. The boys viewed letter pairs flashed to either the right or left side of the brain via the left or right eye, or one letter flashed to both sides simultaneously. They were then asked if the letters were the same or different.
For average students, identification was easier when both letters went to the same side of the brain - no transfer of data across the corpus callosum was needed. But the gifted students were faster when the letters went to both sides.
This indicates, says Professor O'Boyle, that their right hemispheres were on top form. "Its contributions were integrated into the sort of grand network required to perform things like high-level maths." In these gifted boys the "right hemisphere and its specialised contributions are co-ordinated and orchestrated into a kind of whole-brain response".
Crudely, they combined the connectivity of girls' brains with the expertise of boys - and triumphed.
John Geake says the next decade of brain research will concentrate on this connectivity, how the parts of the brain communicate. Girls tend to be more distributed, more bilateral. Boys tend to be more lateralised. But they are still connected up.
"The key is connectivity. If you have a superhighway you can outperform the girls. If you have a country lane, you can't."