[SamReidHughes]

Your theories would be plausible if the number of girls competing at a close-to-top level wasn't outnumbered by the number of boys who by any life-background metric would have no business being there. I'm talking about trailer park kids, poor immigrants, schizophrenics, and absolute slackers here. It will take some training and practice to get on an IMO team -- because your competition is doing so -- but at levels below that, girls are outnumbered by boys making no special effort in math that just show up and get high scores on contests.

Realize that anybody that would be at, say, top-500-high-school-students-in-USA math level will be the sort of student that coasts through all their math classes from K-12, with the typical schedule taking pre-calc in 10th grade, with no studying and no stress at all, easily the best in their class, assuming the school system just ignores their talents. There would have to be 250 girls in this situation, of which those that finish over the top 500 threshold on things like the AMC or AIME or earlier contests are outnumbered by boys with less "support" that just show up and get high scores on math contests.

Also, in my experience in middle school there were many girls that were quite competitive in 24 game, that just disappeared in more mathy contests like MathCOUNTS.