[inglor_cz]

I was good enough in maths to get a PhD from Commutative Algebra, but the really good ones were on another level, where you could barely follow their thoughts (especially real-time; anything can be attacked with enough patience, but it was precisely the speed of their train of thought that humiliated you the worst).

People like Erdös were gods in the mathematical universe.

[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.

[sapsucker]

I 100% agree that some people are innately superior at math, the mental arithmetic abilities (at a very young age) of human calculators like Von Neumann are proof enough of that.

But I also agree with the other poster that it's kind of dangerous/distasteful to imply that mathematical ability is something that is not necessary to cultivate, or at least not worthwhile unless you're the next Galois.

A lot of students are already lacking in grit and give up on difficult subjects, not realizing that areas like math require a lot of discipline, struggle, and engagement to cultivate. This hierarchical nonsense about it only being worthwhile for the "chosen few" NBA superstars is not productive, especially with Ameria trailing most developed nations in mathematical and scientific literacy (which has real societal consequences, IMO).

[wolverine876]

I saw a study from long ago, maybe the 1980s, which researched US and Chinese high school education. As I recall, people in the US high schools mostly thought that success in education was due to natural talent, while people in the high schools in China thought it was overwhelmingly due to hard work. The kids in the Chinese schools did much better on the tests.

> This hierarchical nonsense about it only being worthwhile for the "chosen few" NBA superstars is not productive

Agreed. It also takes away the dreams of and opportunities from a lot of people.

[xyzzyz]

The point here is that while it is perfectly reasonable and probably desirable to encourage people to become proficient in mathematics, there is an enormous chasm from there to most modern research mathematics. The sports analogy is that while it is good idea to encourage people to be physically active, for example by playing recreational basketball, it would be completely ridiculous to expect even a strong amateur basketball player to be able to hold his own in the actual NBA.

[wolverine876]

I understand. I think math research is much more in reach than the NBA, and thus is a bad analogy that discourages people, etc.