Re:The Oracle of Arithmetic
by vladsotirov on Wednesday June 29, 2016 @12:53AM
(#11999567)
It's not enough to like the work for it to be easy: it's also important that your work be appreciated and encouraged. Scholze happens to be interested in a popular/prestigious subfield of mathematics, but my experience suggests there's a substantial number of talented mathematicians who leave academia and mathematics itself for some kind of industry job because their interests are in more obscure/less glamorous subfields of mathematics, meaning that they receive little to no support (or even respect) from their colleagues.
For example, consider William Stein's recent exit from academia that was discussed at https://news.ycombinator.com/item?id=11883987 motivated by essentially the same lack of support; now imagine how many don't even make it to tenure before they have to struggle with their interests and values being misaligned from those of the academic mathematical community.
Stein left academia because he builds tools, and academia is only interested in mathematical results from academics. His work is seen (by the mathematicians) on par with Intel, Dell, and the notebook paper manufacturers, not a part of the pure math department.
To be #1 like Tao requires being a born genius -- recognized as a prodigy by the age of 5, extremely well supported by ambitious parents, and having a lifelong insatiable curiosity and work ethic.
It takes a bit less to be an average mathematician, though.
Part of me wonders what would have happened if I'd gone that way, because my uninformed 18 year old self thought that studying a mix of engineering and management would be the best way to make sure I didn't end up running a restaurant. I'd grown up in one, and I wasn't keen on my kids doing so. So even though I quite liked math (I did contests) I chose something that seemed a bit more practical.
Now I realise it's not exactly bad for your career prospects to have a math degree. There's a family of sciences (and math) that tend to produce employable graduates in tech related areas. People who can code, people who can use math (without delving too deep), people who've visited the evidence in a range of natural sciences.
Anyway, there's an atmosphere of awe about guys like this and Terence Tao, like you have to be born a certain way to reach those heights. I wonder a bit about the environment required as well. I suspect it's a lot less gift, and a lot more hard work than it seems (well, hard work is easy if you like it). Along with being fortunate enough to have the environment that takes you along at the right pace. That math teacher who sees you've reached the edge, and spends the time to show you what lies beyond. I had that, I still keep in touch with him. Maybe what I needed was a peer who was interested, too.
Then again, there is something about the pure math people that's quite special. With a physicist or chemist, the person needs to be shown a bunch of stuff, and digest it. Naturally there's a limit to how much resource can be directed at such a person, they need lab time, and they need simply sheer time to digest the mass of existing evidence.
Maybe a mathematician can comment on this: With pure math, everything is obvious, yet hiding in plain sight. Theorems that will be proven in the future will rely on things that are already known, we just haven't come across a connection yet. Everything is a forehead-slap, why didn't I think of that? For the moment as a non-mathematician, I've only had that feeling with things that are known. Things like the proof there's an infinite number of primes just seem obvious once you know them. The moment when you understand it, you do the forehead-slap. It seems the only thing preventing us from learning the next thing is that nobody has come across it yet.