This is really key in these discussions and it can never be overemphasized, because it always seems to be forgotten immediately.
The signal that population averages tell you about any one person is so little as to be almost meaningless, that it should be immediately overwhelmed by the signal you get from actually knowing and interacting with that person. And yet people still act as though they can learn something meaningful from population averages about their own friends, colleagues, and even spouses.
Yes, absolutely. Another issue I forgot to mention is the converse problem: the use of this stuff to hand-wave away the impact of past social injustices and biases.
"There are fewer women in advanced math... could that be related to gender differences in brain structure and cognition?"
The answer is: yes it theoretically could, but it could also be due to the fact that until very recently (like 1-2 generations or less depending on where you are) women were strongly discouraged from pursuing such professions and in some cases were actually not allowed to study at the same institutions or in the same circles as men.
That seems to me to be a more likely explanation. Most institutions have since liberalized their rules and have even engaged in recruitment efforts to bring more women into the field, but even with such changes and efforts it takes a long time for human societies to change. Large-scale human group behaviors, customs, and preferences are really sticky and changing them usually takes generations in the best case... unless there's some extreme forcing function like a war, pandemic, powerful state edict, depression, etc. There hasn't been an extreme forcing function pushing more women into advanced math.
If women continued to be vastly under-represented at the top of mathematics after 100 more years of relative openness and cultural liberalism, I'd start to entertain the possibility that it's a result of gender differences in brain function.
The signal that population averages tell you about any one person is so little as to be almost meaningless, that it should be immediately overwhelmed by the signal you get from actually knowing and interacting with that person. And yet people still act as though they can learn something meaningful from population averages about their own friends, colleagues, and even spouses.