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>You ever hear this line: "Winning the Fields medal tells you two things about a person, that they were capable of achieving great things and that they didn't."

>You ever hear this line: "Winning the Fields medal tells you two things about a person, that they were capable of achieving great things and that they didn't." Would you mind explaining this a little bit more, please? I would imagine that significant or groundbreaking mathematical discoveries qualify as "great things" by someone's reckoning.

gjm11 12y ago
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.)
- pervycreeper 12y ago
  >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.
  - gcr 12y ago
    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-provide-me-historical-examples-of-pure-mathematics-becoming-useful http://math.stackexchange.com/questions/280530/can-you-provi... The list is expansive if you care to look for it.
    - gjm11 12y ago
      It's definitely true that there's a large quantity of pure mathematics that later turns out to be useful outside pure mathematics. The question that's relevant here, though, is what fraction of pure mathematics is ever useful outside pure mathematics. I think this would be difficult to measure. My guess: only a small fraction, but some of that turns out to be incredibly useful.
      - gcr 12y ago
        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.

gjm11 12y ago

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.)

pervycreeper 12y ago
>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.
- gcr 12y ago
  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-provide-me-historical-examples-of-pure-mathematics-becoming-useful http://math.stackexchange.com/questions/280530/can-you-provi... The list is expansive if you care to look for it.
  - gjm11 12y ago
    It's definitely true that there's a large quantity of pure mathematics that later turns out to be useful outside pure mathematics. The question that's relevant here, though, is what fraction of pure mathematics is ever useful outside pure mathematics. I think this would be difficult to measure. My guess: only a small fraction, but some of that turns out to be incredibly useful.
    - gcr 12y ago
      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.