I suspect that someone who likes hard fact and in-depth analysis, is comfortable with math, and is generally intelligent is going to have a skill set that's transferrable into a wide variety of fields.

• I believe that it's partially a selection effect – things other than intellectual ability seem to matter more in other fields than they do in math. For example, in the experimental sciences, research often takes place in the context of a large lab, and I would guess that the principal investigator's administrative skills probably make a big difference.

• I believe that doing math does increase general intellectual caliber. But I believe that there are other activities that have the same effect. My experience has been that as long as the material is intellectually substantive and there are feedback loops to learn from (whether in the form of feedback from others, or data to test your beliefs against, or the test of being able to construct a valid proof), spending time thinking about it is conducive to intellectual growth. Math could be the best such thing that you have access to, but in principle there are other things that can fill the same role.