"[String theory] has led us in strange directions that we couldn't conceive of; it's revealed depths of mathematical structure that we couldn't have anticipated". Watch a video interview with Professor Michael Green, winner of the 2014 Fundamental Physics Prize.
Are there more irrational numbers than rational numbers, or more rational numbers than irrational numbers? Well, there are infinitely many of both, so the question doesn't make sense. It turns out, however, that the set of rational numbers is infinite in a very different way from the set of irrational numbers.