But not by the reckoning of whoever coined that phrase.
Most work in pure mathematics -- even outstandingly brilliant work done by outstandingly brilliant people -- is never useful outside pure mathematics. If you regard pure mathematics as very valuable in its own right, that's no problem. But if you care mostly about practical benefits, you might think that someone with the mental characteristics needed to win a Fields Medal would have done better to use that wonderful brain for something that benefits the world more.
(For my part, I'm glad that some people with wonderful brains use them to enrich pure mathematics, because I happen to love pure mathematics. But I think those more practically minded people have a point.)
>Most work in pure mathematics -- even outstandingly brilliant work done by outstandingly brilliant people -- is never useful outside pure mathematics.
Perhaps this is untrue on a timescale of decades or centuries.
Applications mine from pure math all the time. See this SO answer for a wide range of other fields' problems that were solved with pure math. I see things from cryptography, graphics, distributed computing, chemistry, ...
http://math.stackexchange.com/questions/280530/can-you-provi...
It's hard for me to understand the ratio of the relative body of work that turns out to be useful versus the relative body of work that hasn't seen application yet. Across all institutions, pure mathematics is an extremely small field; yet their papers have an (almost) infinite amount of time available to find an application.
Most work in pure mathematics -- even outstandingly brilliant work done by outstandingly brilliant people -- is never useful outside pure mathematics. If you regard pure mathematics as very valuable in its own right, that's no problem. But if you care mostly about practical benefits, you might think that someone with the mental characteristics needed to win a Fields Medal would have done better to use that wonderful brain for something that benefits the world more.
(For my part, I'm glad that some people with wonderful brains use them to enrich pure mathematics, because I happen to love pure mathematics. But I think those more practically minded people have a point.)