[clarry]

I don't think it's a decent assumption for "almost everyone" in the west. I'd say it often is the case that you won't have enough free time for such studies unless you trade cash (income) for the free time. At which point you may not have much after paying the bills. Or you're unemployed and, well, don't have the cash. You suggest trading some of that free time for cash, as if unemployment were something people solve by snapping their fingers and choosing to make a trade. That sounds a bit insulting towards all the people (who are many) that struggle with unemployment in western countries.

[throwaway729]

> You suggest trading some of that free time for cash, as if unemployment were something people solve by snapping their fingers and choosing to make a trade

Not at all; I meant in the form of a loan, where free time is time you would otherwise spend retired.

And I was also assuming that you already have a decent job that allows you to work 40 hours or so and make a comfortable enough living to consider spending your free time learning math.

Frankly, I can't possibly imagine trying to do something like learn advanced mathematics while also struggling with un- or under-employment. I grant that there are probably people far more motivated and resilient than I assume :-)

[bpchaps]

Such as Ramanujan. ;)

[throwaway729]

Sure, there are outliers. My post explicitly deals with the common case only.

[bpchaps]

Yes, but think about those in between the outliers. Troubled situations and many cases where loans aren't feasible or possible.

I'll pass on a world where policy and education only deals with the common case.

[throwaway729]

Of course. I hate the higher ed situation in the US as much as the next guy and wish we could move closer to the systems available in much of Europe, especially Germany (perhaps without the pre-high school bifurcation).

I interpreted this thread as being about advice to a typical person interested in learning math who exists in the society we (specifically, Americans) live in today. For the exceptional, the appropriate advice is of course different.