Professors P and Q sat across from me in the mathematics common room at the University of Cambridge. They were American professors, visiting the UK from a large midwestern university. I was an American student, visiting Cambridge on a fellowship for the 1979-1980 academic year. I was reading a mathematics text, trying to mind my own business.
P and Q were deep in discussion, trying to answer the question "Why are there so few female mathematicians?" Since they were Americans, I could hear every word.
They examined the premise that it was due to prejudice and discrimination. They rapidly dismissed that, on the grounds that the people in power in mathematics were just like them, and they were obviously good people who couldn't possibly unfairly discriminate or succumb to prejudice. Much as I tried not to eavesdrop, from that point on I felt as if I were listening to two bumbling detectives trying to solve a murder mystery. They had ruled out the obvious suspect. Who were they going to declare to be the culprit, and how were they going to get there? I had heard such debates many times before, so I had my suspicions about where they were heading. Nonetheless, I ardently hoped for better.
They eliminated one premise after another. Could it be lack of opportunities? Surely not. Lack of interest? Well, maybe, but that wouldn't fully account for it. They considered everything they could think of, until they were left with only one option.
At that point, I just couldn't restrain myself. It was clear what they were about to say, and I didn't want them to say it. Too many times had I heard (always male) professors conclude that women weren't as good at mathematics because they were genetically inferior.
I introduced myself to P and Q, apologized for listening to their conversation, and told them that the answers to their question were prejudice and discrimination. (Actually, it's likely I told them there were three reasons: "discrimination, discrimination, and discrimination", alluding to the adage about real estate and location.) I pointed out that Ivy League universities had only recently begun to admit women, and were, even then, doing so in small numbers. I told them some recent stories about Harvard, from personal experience. And I pointed out some facts about the recent history of (and discrimination against) women at Cambridge.
I don't know whether any opinions changed. Their minds were probably made up before they started. But they listened politely, even though I disagreed with them. (I wish that happened more often nowadays!)