[serviceberry]

> If you read a few books on mathematics you think you're easily going to become one of the top mathematicians?

No, but so what? The guy behind 3Blue1Brown probably isn't one of the top mathematicians of his era. But he's having quite an impact. He turned explaining fairly basic math concepts in mathematics into a lucrative job.

And who wrote the textbooks you're referring to? Probably not any of the top 10 living mathematicians. That doesn't make the work less useful.

Is Linus Torvalds one of the top 10 computer scientists? He probably wouldn't describe himself that way, and respected academics mocked his work. The list goes on. I think this is compatible with the premise of the article: it's not about being best, it's about being better than the average bear - and then putting that knowledge to some productive use.

[Earw0rm]

It's about combinations of skills.

0.01%ers in one field tend towards monomaniacal obsession.

Sometimes that's useful. But having mostly depth, and enough breadth to balance it out, is better in most cases than depth only.

People who are all breadth, no depth are worse. Those traits give you MBAs and politicians. That doesn't mean breadth is inherently bad, it's about balance.

The sweet-spot is typically to get inside the top 1% and get 75th or 90th percentile people skills or communication skills. Those can take a lot of different forms, good writers / managers / youtubers / teachers are all in that class but there's not necessarily that much overlap.

[Tainnor]

All those people you mention have studied mathematics for a long time, Grant Sanderson has probably studied it the "least" but that still means a BSc in his case which is not something you accomplish in a weekend. All the textbook authors are usually professors.

[serviceberry]

The parent's quip was that you can't rise to the top of the field. My point is that it's irrelevant.

Textbooks used in college coursework are usually written by academics, for obvious reasons. Plenty of independent learning / pop textbooks are written by "normal people" who aren't tenured professors.

[Tainnor]

It's not about being in the top of the field. Even just getting to the point of being able to halfway competently talk about mathematics takes a grueling amount of work.

> Plenty of independent learning / pop textbooks are written by "normal people" who aren't tenured professors.

Idk, Simon Singh is one very well known example of "pop maths" and he has a PhD in particle physics, that's quite a bit more than just "do the reading for a year". Other examples like Eugenia Cheng and Ian Stewart are similarly credentialed.

It's the same in other fields, really. Yes, you can learn to play simple tunes on the piano relatively quickly, but even just being able to play the full Für Elise just takes so much more than that. Or you can learn Hiragana relatively quickly which I guess means that you understand more about Japanese than 95% of people, but it'll still not be enough for you to engage with Japanese in any meaningful way.

The beginner stage is always the easiest. It's after that that it gets really hard.