I saw the above quote on Jeremy Kun's and it really hit a note with me. This was in the context of the Fourier transform, in that physicists were using it to discover elegant identities before there was a rigorous mathematical foundation for it.
I am curious to learn of instances in which this occured in reverse; that is, a purely mathemtical discovery has found successful applications in the applied or social sciences. By purely mathematical, I mean the only incentive for discovering it was the spirit of better understanding - as opposed to, solving a technical problem from physics or engineering. For example, Ito's stochastic integration along with martingale theory allowed for a revolutionary method of pricing financial derivatives, from which an entire new profession (financial engineering) followed. In particular, it was financial economists (Black, Scholes and Merton) who used the new mathematical results to solve a previously unsolved problem. On the other hand the development of Monte Carlo integration was motivated by the technical need of the atomic bomb development.
I am soliciting other examples for when people ask, "what is this stuff you're doing good for, anyways?"
