The conversation is usually about the higher end. Higher variance would also lead to a greater number of math underachievers. I'm pretty sure the numbers play this out, but I think lower bounds on achievement tend to be heavily skewed by 'nurture'. Also, this assumes a symmetric curve. This highlights the gross over simplifications even a more advanced model suffers from. We're modeling brains here, after all, with one or two numbers.

But you are technically incorrect. You can see more of a certain group in the high end if there is higher variance with equal mean.

Everything you said here is true but I'm not sure what it has to do with what I said.

You are focusing on the highest end of the curve, presumably because that's where things like advancements in math (and the status it brings) lie.

I'm saying that even if you leave aside the entire discussion about a possible gender gap at the ends of the spectrum, there were other people who were suggesting that the gender gap in mathematical ability might be just like the gender gap in physical strength. This study seems to indicate that this isn't the case, therefore it's a valuable part of the discussion.

If you want ammunition against those claims, you should go back to math, not these studies: all claims show the gap to be small and the mean to be very close.

Most importantly he variance between groups is smaller than between individuals. This means that you have no way of knowing when you meet someone whether they are good at math because of their sex. That's the most important lesson for most people: don't be biased, because you're probably wrong.

The same argument applies to the race/IQ discussion. Variance between groups is smaller than between individuals.

So even if the claims of innate superiority are correct, you should treat individuals with respect.