It seems that the best economists, like Levitt(economics w/o math), Lucas(history), Fama(Romance languages), Duflo(history), Greenspan(music), maybe, haven't taken much math before doing an economics PhD. Yet the standard advice for admissions is that unless you do a full math minor or at least a physics major, you have no shot whatsoever at top 20 programs. Why is there such a discrepancy between the training that some of the top leaders of the field received versus the requirement?

And for the life of me, I can't see how a math minor can help in coursework -- it seems that coursework, including the math camp, can almost be learned from scratch, from my experience. Someone with no math in undergrad can do linear algebra, statistics, constrained optimization, and differential equations, as long as he/she can take first order conditions and then do algebra; you literally don't need to know anything else. Real analysis can help I can see that since you need mathematics to express your ideas, but from looking at the Rudin book i can't see how this is made out to be so difficult as long as you know what the symbols are saying. For me, calculating integrals ad nauseum seems much more tedious and a lot more work; proofs are just straightforward if you have can read them.

Also, why should any undergrad strive to be superstars in math unless he/she is aiming for a math/physics or related degree? In terms of understanding the world, I cannot see how pure math can help. In the end, you're proving hypotheses, not mathematical formulas, for which I think philosophical logic is the most useful in terms of training. Mathematical logic is already a branch of philosophy anyway, and if you look at higher level philosophical logic they are way harder than real analysis and only dealt with in 4th year math courses or mathematics grad school.