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’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.