The problem is that people are notoriously bad at inductive reasoning. They routinely ignore cases that contradict their hypothesis. If they see a woman who's

The problem is that people are notoriously bad at inductive reasoning. They routinely ignore cases that contradict their hypothesis. If they see a woman who's bad at math, they think "aha! the stereotype is right!". If they see a woman who's good at math, they think, "oh well, there's bound to be exceptions" and promptly forget about her. They only remember the ones that fit the stereotype, so the stereotype is reinforced. You need to repeatedly hammer irrefutable evidence into people's heads before they'll start to forget stereotypes.