[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.