Attractors which lead to people being unable or afraid to attempt other activities are much less credible as values than those which leave one with many options.
I think I see what you’re saying here. Attractors that are irreversible dead ends are more likely to represent miscalculations. But still, that doesn’t rule out the possibility that some people really like working on abstract math, really value academic status, and/or have a large comparative advantage in doing math, and therefore for them going into math is a rational choice. Furthermore, it seems likely that such people would be more concentrated among the top mathematicians.
I think your other argument is that according to your model of human psychology, most people would find it more fun to be a polymath than to specialize in one area. That makes some sense to me, but obviously it’s hard to put a lot of credence in it without seeing some strong empirical evidence.
Based on these two arguments, it seems to me there’s a reasonable chance that Terrance Tao went into math by mistake, but your level of confidence still seems unjustified. Did I miss anything else?
I’m sure that there are many people who really like abstract math. Your right about my claim about polymaths. My best guess is that Tao was right to go into math but would be best served by staying in math but broadening his focus somewhat now. The fact that he doesn’t seem to be driven by any particular problem strengthens it, but I’m still not all that confident of it. I’m a lot more confident that he should put a bit of effort into becoming a multimillionaire in a small part of his spare time, simply by selling very expensive consulting services, and less effort into housekeeping, driving his own car, and whatever else he spends his time on other than math, but it’s possible to me that he has done so and possible that he has relatives and/or friends who would envy him and make it a net loss.
One can simply see if people produce less or different stuff after tenure as one measure.
I think I see what you’re saying here. Attractors that are irreversible dead ends are more likely to represent miscalculations. But still, that doesn’t rule out the possibility that some people really like working on abstract math, really value academic status, and/or have a large comparative advantage in doing math, and therefore for them going into math is a rational choice. Furthermore, it seems likely that such people would be more concentrated among the top mathematicians.
I think your other argument is that according to your model of human psychology, most people would find it more fun to be a polymath than to specialize in one area. That makes some sense to me, but obviously it’s hard to put a lot of credence in it without seeing some strong empirical evidence.
Based on these two arguments, it seems to me there’s a reasonable chance that Terrance Tao went into math by mistake, but your level of confidence still seems unjustified. Did I miss anything else?
I’m sure that there are many people who really like abstract math. Your right about my claim about polymaths. My best guess is that Tao was right to go into math but would be best served by staying in math but broadening his focus somewhat now. The fact that he doesn’t seem to be driven by any particular problem strengthens it, but I’m still not all that confident of it. I’m a lot more confident that he should put a bit of effort into becoming a multimillionaire in a small part of his spare time, simply by selling very expensive consulting services, and less effort into housekeeping, driving his own car, and whatever else he spends his time on other than math, but it’s possible to me that he has done so and possible that he has relatives and/or friends who would envy him and make it a net loss.
One can simply see if people produce less or different stuff after tenure as one measure.