There is a ton of evidence, but you need to watch out for certain data:
When looking at IQ and mental differences between sexes you need to take a look at some studies as the marxists love to cite those studies done at ages 2-3 or 12 to prove superiority for women. Women go through a faster growth period around age 12-14, but that is equalized at age 15-16 and then men go even further.
I do think that average mental capacities are identical in aggregate which makes sense, but the distribution is very different.
That means that there are more morons and geniuses among men. At the upper-level of geniuses the distribution is 5000 to 1! Even MENSA level has roughly 66% men vs 34% of women.
So all top-level professions are automatically more likely to be filled by men by sheer reality of IQ distribution.
But it gets worse - in addition to that unequal distribution you have the following mental/emotional differences:
+ men have far more interest in abstract thought, things vs people
+ men are far greater risk takers
+ men have a far more single-minded mental pattern being able to spend years and years over some inane subject like the leg-muscles of some Amazonian frog species or calculating inane formulas for decades
+ men are far more competitive and do love to compete with other men - evolution made us that way
+ men are more aggressive, single-minded, opportunistic, single-minded, hierarchical
Women can never ever compete with men, because evolution has not designed them that way. So even in the future most society will be shaped by men with a few female exceptions.