[xyzzyz]

This is exactly right. I could also get a PhD degree in math myself (I dropped out after obtaining Master during which I obtained novel results in algebraic geometry), but after meeting and interacting with actually smart people, it became clear to me that I’m just not nearly on the same level. Research level mathematics requires completely another level of sheer brainpower that most people don’t even imagine exists.

[laingc]

Adding my voice to this too. I have a PhD in Differential Geometry and would consider myself to have been a decent student and researcher. The "good" people in my field were more than a head and shoulders above me, and the "great" people were somewhere off in the stratosphere.

The nature of Mathematics is that the potential depth of understanding and progress is essentially infinite, which frees truly spectacular minds from the constraints they would experience in other fields.

[octopoc]

Is that because the "good" people in your field were just way more obsessive about the topic?

I feel like there are some topics that I'm obsessed with that I'm so much more informed on than most people in my field that I can run circles around them. They would call me super smart if the things I'm obsessive about mattered. Sometimes they have mattered. But I know better than to talk about them at length because people get bored.

[throwaway81523]

I don't think you need that super fast brain to be good at math. I'm sure it helps, and I know some people who have it and I felt I could never be like them. But I've also known some really top mathematicians (one Fields medalist in geometry and one of the biggest cheeses in mathematical logic) who weren't like that, and I felt like I could keep up with them, at least on a conversational basis (I don't claim that I would have been much of a researcher if I had stayed with it, much less at their level). Pure brainpower goes a long way, but personality and commitment count for a lot all by themselves.