Do you see why I'm placing the burden of proof on you to show that differences are biologically inherent

Either because you don't understand how bayesian evidence works or because you think the question is social political rather than epistemic.

It might have been marginally more productive to answer "No, I don't see. Would you explain?" But, rather than attempting to other-optimize, I will simply present that request to datadataeverywhere. Why is the placement of "burden" important? With this supplementary question: Do you know of evidence strongly suggesting that different cultural norms might significantly alter the predominant position of the male sex in academic mathematics?

... but also why I believe that this is such a difficult task?

I can certainly see this as a difficult task. For example, we can imagine that fictional rational::Harry Potter and Hermione were both taught as children that it is ok to be smart, but that only Hermione was instructed not to be obnoxiously smart. This dynamic, by itself, would be enough to strongly suppress the numbers of women to rise to the highest levels in math.

But producing convincing evidence in this area is not an impossible task. For example, we can empirically assess the impact of the above mechanism by comparing the number of bright and very bright men and women who come from different cultural backgrounds.

Rather than simply demanding that your interlocutor show his evidence first, why not go ahead and show yours?