Do you have a "male" or "female" brain? Are there really significant brain differences between the sexes and if so, do these differences matter? BBC Horizon investigates.
When it comes to the tricky and explosive question of how much, if at all, male and female behaviour is driven by brain differences, Professor Alice Roberts and I sit on different sides of the fence.
I believe that our brains, like our bodies, are shaped by exposure to hormones in the womb and this may help explain why males tend to do better at some tasks (3D rotation), while women tend to do better at others (empathy skills), although there is, of course, an awful lot of overlap and social pressure involved.
Alice, on the other hand, thinks these differences are largely spurious, the result of how the tests are carried out. She worries that such claims may discourage girls from going into science.
"We live in a country where fewer than three out of ten physics A levels are taken by girls, where just 7% of engineers are women" she points out, before adding "and where men still earn on average nearly 20% more than their female colleagues."
So the BBC's Horizon programme asked us to go and explore the science, put forward research that would support our different views, but also look for common ground.
One of the scientists who has most strongly influenced my beliefs is Professor Simon Baron-Cohen of Cambridge University.
He argues that, broadly speaking, there are two different "brain types". There are empathisers, who are good at identifying how other people are thinking or feeling, and there are systemisers, people who are more interested in trying to take apart and analyse systems i.e. people who are a bit nerdy.
We are all a mix of the two, but most of us are more one than the other. Men tend to sit more along the systemising end of the spectrum, women at the empathising end, though there are plenty of exceptions.
But is this simply the product of social conditioning? Professor Baron-Cohen thinks not, that exposure to different levels of hormones in the womb can influence the brain and subsequent behavour. Some of his most intriguing findings have come from on-going research into a large group of children who have been followed from before they were born.
At around 16 weeks gestation, the children's mothers had an amniocentesis test, which involves collecting samples of the fluid that bathes the womb. The researchers measured levels of testosterone in the fluid and have since discovered intriguing links between those levels and behaviour.
"The higher the child's pre-natal testosterone" Professor Baron-Cohen told me, "the slower they were to develop socially. They showed, for example, less eye contact at their first birthday". They also had a smaller vocabulary when they were toddlers and showed less empathy when they were primary school age.
On the other hand he found that being exposed to higher levels of testosterone in the womb seems to enhance some spatial abilities. "Children with higher levels of pre-natal testosterone were faster to find specific shapes hidden within an overall design."
Further evidence for male and female brain differences comes from research published in the Proceedings of the National Academy of Sciences looking at how different parts of the human brain talk to each other.
Scientists at the University of Pennsylvania scanned the brains of 949 males and females, ranging in age from eight to 22, and found some striking differences.
According to one of the researchers, Professor Ruben Gurr, men showed stronger connections between the front and back of their brain, suggesting that, "they are better able to connect what they see with what they do, which is what you need to be able to do if you are a hunter. You see something, you need to respond right away."
Women, on the other hand, had more wiring between the left and right hemispheres of the brain. According to another of the researchers involved in this study, Dr Ragini Verman, "the fact that you can connect from different regions of the brain means you ought to be good at multi-tasking and you may be better at emotional tasks".
As Alice was quick to point out, this particular study has its critics and even if it is true that our brains are wired differently this doesn't prove it is innate. The human brain is extremely malleable, particularly during adolescence, and any differences you see could simply be the product of stereotyping and social pressure.
The programme contains lots of fascinating studies which can be used to support either camp, but what surprised us both is how little progress there has been in research looking at gender differences in areas like pain.
We know that women experience more chronic pain than men, but are less likely to get treatment. We also know that men respond better to some pain killers (paracetamol), while women respond better to some opioids.
Professor Jeff Mogil of McGill University in Montreal, Canada, thinks this is because men and women process pain differently, something which we should take into account when designing new drugs. Until now much of the basic research has been done with male animals, but he foresees a time when new drugs will be created which are targeted specifically at men or women.
"There's lots of drug development going on and if any of those drugs ever make it to the market and get approved, my expectation will be that they will work in one sex and simply not work in the other sex", he says.
So perhaps we'll be seeing pink pain killers for girls and blue ones for for boys...
HORIZON: Is your brain male or female? is broadcast on BBC Two at 2100 on Monday 29 September.