Naturally it depends on the other alternatives on the table, and how far one wants to go. But I do know several people who report that learning the subject changed how they think in general, not only in the context of math.
I would have to add another point on the anecdotal side for this. I made it through Real Analysis (barely!) when I was a math major—and it made a significant difference on the thought process I go through when I consider things. If nothing else, it was very instrumental in breaking the “good rhetoric = good argument” connection I’d been operating under up until that point. And this was long before I’d any notion that places like CFAR or LW even existed.
(I will disclaimer that it also made certain kinds of communication more difficult—because most folks don’t like it when you try to make their opinions rigorous—but that could as easily be from how I implemented those ideas as from the change in thinking itself. )
I am not sure the cost-benefit analysis is favorable, in particular for people who do not intend to become professional mathematicians.
Naturally it depends on the other alternatives on the table, and how far one wants to go. But I do know several people who report that learning the subject changed how they think in general, not only in the context of math.
I would have to add another point on the anecdotal side for this. I made it through Real Analysis (barely!) when I was a math major—and it made a significant difference on the thought process I go through when I consider things. If nothing else, it was very instrumental in breaking the “good rhetoric = good argument” connection I’d been operating under up until that point. And this was long before I’d any notion that places like CFAR or LW even existed.
(I will disclaimer that it also made certain kinds of communication more difficult—because most folks don’t like it when you try to make their opinions rigorous—but that could as easily be from how I implemented those ideas as from the change in thinking itself. )