"Genius" is like "rich": as actually used, it's implicitly a comparative term. When someone talks about geniuses they usually mean "people much smarter than me"

"Genius" is like "rich": as actually used, it's implicitly a comparative term. When someone talks about geniuses they usually mean "people much smarter than me" (either in general intelligence, in so far as that's meaningful, or in a particular area like mathematics or music or languages). I think this sort of usage is so deeply ingrained that there's not much point in trying to counter it by adopting a fixed formal definition (e.g., someone elsewhere in the thread said something like "genius means IQ >= 140, get over it"). Instead, either pick a definition and say what definition you're using or use it informally and live with the fact that sometimes you'll be misunderstood. In this particular case, it seems reasonably clear that what she means by "geniuses" is "people with the sort of ability the big names in mathematics generally have": her point is that mathematical progress depends not only on the Gausses and Thurstons and Ramanujans but also, just as much, on the ordinary mathematicians who, yes, are generally also extremely bright but are very conscious of the gulf between them and the famously-brilliant ones. (Is it absurd to say "just as much"? No, because there are a lot more ordinary mathematicians than once-in-a-generation ones.)