It feels strange to see adults that opine on every subject, from nuclear fusion energy, to virology and financial markets, like they know it all, to suddenly "I was never good at math", like a clichee party conversation.
I mean, I get it: It first feels strange and magical, since even the explanations of some of the vocabulary take more time than we are willing to devote to a single thought. But instead of digging in and looking up what "Borel measurable" might mean, the HN crowd rather watches the x-th numberphile video/emotionalized Quanta blurb.
/rant
More to your points:
> Your kid has a greater chance of being a multi-millionaire NBA player than being smart enough to understand this stuff
There are >5000 math phds each year, so no, getting into the NBA is harder.
> Even 18th century math would be a challenge for many math grad students. Just crazy
Not sure, what this is supposed to mean. Certainly as a math grad you should be able to _understand_ 18th century math. Now, to _come up_ with the stuff is something else entirely. But I'm not sure how many engineers would claim they had discovered the telegraph, were they be born instead of Gauss.
People like Erdös were gods in the mathematical universe.
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.
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.
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).
> 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.
On the other hand, I think this is a great way for us science-y types to get a good handle on how hard being an NBA player is: NBA players are the moral equivalent of near-Fields-medallists; that's how good they are compared to the rest of us.
I'm no mathematical slouch — I've done grad work in Math, taught myself differential geometry, etc.; but it'd be fruitless to compare me to Terry Tao. There's really no reference for how good he is at math compared to me. I think, analogously, you wouldn't be able to compare a college-level basketball player to, say, Michael Jordan.