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Mathematics & Reality

April 18, 2010

Most writers on the subject seem to agree that the typical working mathematician is a Platonist [views mathematics as discovery] on weekdays and a formalist [views mathematics as invention] on Sundays. That is, when he is doing mathematics he is convinced that he is dealing with an objective reality whose properties he is attempting to determine. But then, when challenged to give a philosophical account of this reality, he finds it easiest to pretend that he does not believe in it after all.

– Philip Davis & Reuben Hersch, The Mathematical Experience

3 Comments leave one →
  1. agent229 permalink
    February 14, 2011 8:00 am

    I love Hersh’s work. I studied math and now teach it, and I find that the view espoused in the quote is pretty uncommon among math people and teachers alike. I find that Hersh’s philosophy not only makes the most sense, but also can help students succeed in math by demystifying it. Instead of making them feel like they’re trying to access some universally true, mystical, and confusing concept that just won’t come to them (making them feel like it never will), I can tell them frankly: this is just something someone made up at some point. It’s beautiful and possibly useful and worth studying, but there’s no rhyme or reason to why the notation is just how it is or why the words we use are the way they are… it was just a decision made by a human. It seems to help them relax đŸ™‚

  2. dmonk permalink*
    February 14, 2011 12:02 pm

    Thanks for your comment, agent 229!

    Personally I find the relationship between math and reality to be very intriguing. Sometime math seems arbitrary (and maybe this approach makes it easier to learn it), but there are other times when it seems as if mathematics has the power to reveal deeper parts of the world we live in. For me — a non-mathematician — it is fun to contemplate what these realities might be (without ever actually doing the math)!

    Thanks again.

    + D-Monk

  3. March 11, 2011 3:44 pm

    This is a nice topic. We had debated this in class when I was still in high college. I am not a mathematician, but I think, it’s a mixed of both.

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