I've discussed this issue here: http://lesswrong.com/lw/h3f/drowning_in_an_information_ocean/

most relevant part:

Then there are the nagging exact sciences people. They come to you at night, haunt you in your dreams, telling you how much you should study math, how math is important for this, for that, and for that. Most disagree which branches of math are important, stats being the most universal like. If I were to learn to all the math I was told to learn, that would be at least 3 years more. Scott Young can do an entire university course (CS) in one year, Nick Bostrom kept that pace for 6 or 7 years. Most people don't get the mix of time, luck, capacity, resources and most importantly, motivation, to pursue such Homeric tasks.

I've never doubted Math is awesome. What I did doubt, and to this day I have seen few who doubt with me, but good examples being Peter Thiel, more strongly, and Jared Diamond and Dan Dennett, less strongly, is that so many young talents should be drawn into physics and math (and chess). Why should we make people who are really smart do the things in which it is easier to detect being smart? Companies don't ask their best employees to devise ever better and more complicated IQ tests just because IQ tests are good predictors of how good a worker will be. The goal is not to costly signal being near the upper bound in intelligence. The goal is using your intelligence to pursue your goals. Sure, lots of it will be signalling instrumentally, but once the dust settles, don't get fixed in proving the constructibility of enormously large polygons, or beating Kasparov.

So far I've tried to make two cases: Even with prima facie narrow interests, anyone is bound to be drowning in an ocean of information, and the interconnectedness and requirements to understand narrow interests may be much larger than one's initial expectancy. Secondly the main modulator of what to do with intelligence (your own, or someone else's) should be to tune it with goals and interests, not with easy detectability.