DailyDirt: Computers Are Really Good At Math, So When Will Shalosh B. Ekhad Get Tenure?

from the urls-we-dig-up dept

There are a lot of math problems that can be more easily solved with a computer because humans are prone to errors and get tired... and have lives outside of math. There are already several examples of computer programs that have helped to prove some important mathematical conjectures, but sometimes the resulting proof is too hard for humans to double-check. So we just have to write more programs to check our programs. (And hope that the computers don't conspire against us.) If you'd like to read more awesome and interesting stuff, check out this unrelated (but not entirely random!) Techdirt post via StumbleUpon.
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Filed Under: ai, algorithms, artificial intelligence, doron zeilberger, kepler conjecture, logic errors, mathematics, proof, shalosh b. ekhad, thomas hales


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  • identicon
    Lawrence D’Oliveiro, 14 Aug 2014 @ 5:31pm

    Is Mathematics Becoming A Science?

    Maths has traditionally been considered different from “science”, because science involves both theory and experiment, whereas maths can be considered to be entirely theory.

    Except that now you have to run computer programs to test out proofs, those programs can be considered to be actual practical experiments in mathematics.

    So now that maths has both a theoretical and a practical side, doesn’t that make it very much just another “science”?

    reply to this | link to this | view in chronology ]

    • identicon
      Andrew D. Todd, 14 Aug 2014 @ 8:52pm

      Re: Is Mathematics Becoming A Science?

      Mathematics is defined at the foundational level by axioms. Computer Science, notwithstanding its name, is a branch of mathematics. Where it matters, Physics is defined by experiments in the real world, and problems of perception. In Physics, theory is only valid insofar as it can be used as a basis for manipulating a system in such a way as to produce sizable effects, well beyond the scope of measurement error. Theology reasons from faith.

      Of course, in the upper reaches of Modern Physics, there is an increasing quantity of material for which empirical testing is pragmatically impossible, and this material is no longer Science, but has become Mathematics or Theology.

      reply to this | link to this | view in chronology ]

  • identicon
    Neil, 14 Aug 2014 @ 5:51pm

    Pi

    How many digits can they get to in Pi now? 3.14159......

    reply to this | link to this | view in chronology ]

    • identicon
      Lawrence D’Oliveiro, 14 Aug 2014 @ 8:31pm

      Re: π

      You’re sitting in front of a computer, why not ask it:

      ldo@theon:~> python3
      Python 3.4.1 (default, Jul 26 2014, 13:46:45)
      [GCC 4.9.1] on linux
      Type "help", "copyright", "credits" or "license" for more information.
      >>> import math
      >>> math.pi
      3.141592653589793

      reply to this | link to this | view in chronology ]

  • identicon
    william e emba, 15 Aug 2014 @ 7:32am

    While Doron Zeilberger is certainly a distinguished mathematician, he is notoriously cranky and insultingly overstates his hostile Johnny One-Note opinion regarding the 99% of mathematics that is still computer-free ad nauseum.

    The first item above is stupidly just a rehash of the second item. Both are just vintage Zeilberger. Quoting him about the future of mathematics is kind of like quoting Alexander Abian in all seriousness about NASA's forthcoming missions.

    reply to this | link to this | view in chronology ]

    • icon
      John Fenderson (profile), 15 Aug 2014 @ 8:51am

      Re:

      A computer is a brain-extension tool, much like a hammer is a hand-extension tool. Taking pride in doing advanced mathematics without a computer is like taking pride in building a house without a hammer: impressive, yes, but of no practical importance unless you're stranded on a desert island.

      reply to this | link to this | view in chronology ]

      • identicon
        william e emba, 15 Aug 2014 @ 9:10am

        Re: Re:

        Your statement is ignorant gibberish. The percentage of mathematics that computers are able to help us with is extremely tiny, perhaps only 1%.

        reply to this | link to this | view in chronology ]

        • icon
          John Fenderson (profile), 15 Aug 2014 @ 9:21am

          Re: Re: Re:

          My statement was perfectly coherent English. You understood it, after all, so it couldn't be gibberish. Further, what is ignorant about it? Are you saying that the computer is not a brain-extension tool? If so, then the only ignorance is yours.

          "The percentage of mathematics that computers are able to help us with is extremely tiny, perhaps only 1%."

          Citation, please. I've worked with a large number of mathematicians and physicists (who are, at heart, applied mathematicians). You know what they all used to help with their math work? Computers. Admittedly a tiny sample, but remarkably consistent.

          reply to this | link to this | view in chronology ]

          • identicon
            william e emba, 15 Aug 2014 @ 10:21am

            Re: Re: Re: Re:

            Gibberish has more than one meaning, that you bother to show how my statement is nonsense according to one such meaning is pointless flailing. Although now that you mention it, I would not consider the computer a brain-extension tool. A rather simplistic metaphor, at best.

            I am a mathematician, and have done decades of both pure and applied work. And I am also an experienced programmer, going back to the end of the punched card era.

            The estimate I made is pretty obvious: just look through the journals. Unlike you, I do not count millions of cash registers in action and millions of taxpayers running an app as distinct mathematical activity.

            reply to this | link to this | view in chronology ]

            • icon
              John Fenderson (profile), 15 Aug 2014 @ 12:10pm

              Re: Re: Re: Re: Re:

              "is pointless flailing"

              What you call pointless flailin, I call highlighting a pointless and uncalled-for personal attack.

              "I am also an experienced programmer, going back to the end of the punched card era."

              Welcome to the club! Not sure how either of our bona fides is relevant to this discussion, though.

              "Unlike you, I do not count millions of cash registers in action and millions of taxpayers running an app as distinct mathematical activity."

              I don't understand what you're saying here. I specifically said I was talking about advanced mathematics.

              Why are you so hostile? I find it baffling unless you're just trolling. I don't think I said anything that could reasonably be considered offensive to anybody.

              reply to this | link to this | view in chronology ]

              • identicon
                william e emba, 17 Aug 2014 @ 9:38am

                Re: Re: Re: Re: Re: Re:

                The word "gibberish" did originally mean something imitative of language without being language, but its meaning has generalized to include "nonsense, whether or not grammatical". To try and explain how I said something that made no sense, when actually I made sense, just not in a way you were aware of, is just a waste of time. Very popular on-line approach enjoyed by numerous on-line idiots.

                Unlike you, I don't count thousands of physicists running the same suite of numerical PDE solvers as distinct mathematical activity. For the same reason I don't count millions of cash registers, etc.

                Look through the journals. Seriously. I've been doing so my whole life. You'll see about 1% computer-based mathematics. In some fields the proportion gets higher. For example, theoretical computer science seems to be about 10-20% computer-based. Numerical analysis is about 80-90% computer-based. In some fields, the proportion has jumped significantly in recent years, for example, the rise of Grobner base computations in commutative algebra and algebraic geometry.

                But overall, the proportion is remarkably low.

                As for hostility, well, 2 out of the 3 "news" items were quoting Doron Zeilberger engaged in his typical rant. And it's pretty obvious you have no real experience with "real" mathematics, just some low end computational stuff. There's a tiny number of stereotyped problems that the computers do amazing stuff with (including many kinds brilliantly discovered by Zeilberger), there's a larger number where computers are able to make doable an otherwise impossible proof (four-color theorem, new Fields Medalist Bhargava's proof of the 290 theorem), there's a goodly number where computers, especially graphics, have proved indispensable to discovery and understanding (Birch-Swinnerton-Dyer conjecture, minimal surfaces, fractals), yet these are still a tiny proportion of all the mathematics people do.

                And all you've got is a childish sci-fi claim about "brain-enhanced".

                reply to this | link to this | view in chronology ]

            • icon
              John Fenderson (profile), 15 Aug 2014 @ 12:13pm

              Re: Re: Re: Re: Re:

              Forgot this bit:

              "just look through the journals"

              That's nonresponsive. Looking through the journals wouldn't answer this question.

              reply to this | link to this | view in chronology ]


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