Why Are Men Smarter than Women?

I was listening to a Guardian podcast on genius when it occurred to me why more men get credited with advancing society, leading most men and lots of women, incidentally, to believe that men are smarter than women. A lot of it has to do with the differences between male brains and female brains, and what society expects of each sex.
(Men also have been doing a very good job of holding back society - through wars, various kinds of harmful dogma, self-serving beliefs and practices - but that's another post perhaps. This "paradox" supports a recent observation that men tend to occupy the extremes of good and bad, while women occupy more of the middle ground.)

Genius is a complex phenomenon, and often identified only in hindsight. A quirky little boy or girl with strange ideas and perspectives will probably be noticed for being different, but not valued for his or her individual outlook unless it yields a discovery, invention, remarkable work of art, or the like. In other words, if you're going to stand out, you have to earn acceptance more than the average person!
Not every genius with the potential for that breakthrough ticket to public acceptance and even adoration finds the right opportunities to shine. We'll never know how many Marie Curies, Isadora Duncans and Virginia Woolfs died in childbirth or toiling in a field - not to mention the Mozarts, Newtons, and Picassos coughing away in attics unable to find the money for basic materials.
To get to that invention or symphony, a person needs talent and opportunity, no doubt about that. But personality - mainly, determination and belief in oneself and one's work - probably separates the sheep from the goats most of all.
That's where male-female brain differences - and how society boldfaces them - come in. Men in general have a greater ability to take a project and focus on it to the exclusion of everything else. The modern cliché of the unkempt computer nerd has historical precedents in the mad scientist or long-haired crazy composer. Men are also more likely to be collectors (another form of monomania). Women are better multitaskers and generalists. While shallow thinking and attention combined with a talent for forming connections can have brilliant results, they do not tend to translate into works of genius. Gregor Mendel grew hundred of pea plants before he was able to discern the patterns of trait inheritance later called genetics. Not only was he incredibly patient and focussed and smart, he was a monk with no other job, no bills to pay, no kids to run after! If a woman did something similar, she'd be called an oddball for opting out of her "true role" as a wife and mother.
If men discover more, change more, it may be because they use their intelligence for deep focus - and tend to find support in family and community for doing so. They also may be more singleminded when it comes to pursuing a socially peripheral project that they alone find worthy; women tend to listen to criticism more.
Things are changing a little. Women with the ability to devote long hours in the lab or at the writing desk are scorned far less than they used to be, and the opportunities needed to advance (money, education, support) are more abundant in many parts of the world. But the female need to form interpersonal connections (and be praised for the ones she does form) may preclude the creation of those really big breakthroughs - the ones that make it into the history books, even if most tend to be written by men.