Discovery and invention

Yesterday’s Guardian had an interview with crossword setter John Graham, aka Auarcaria, whom I discussed last week. There are several things in this interview that a mathematician is bound to be struck by. His profession is not so different from ours.

First, he switched from classics to theology, because “… he couldn’t understand the maths lecturer”. The profession should hang its collective head in shame.

Second, “he has a checker, a woman in Wiltshire, who keeps an eye on his factual accuracy”. Something like exam checkers, or (stretching things a bit) referees, in our business.

Third, “he resists the argument … that crosswords can be a refuge from the world. ‘For me, it’s a way of life …'”.

The fourth is the most striking.

The most hard-fought question in the philosophy of mathematics is surely whether mathematics is discovered or invented. Now listen to this:

He actively enjoys setting crosswords, as a creative process. “It’s a voyage of discovery. I love the way the word invention both means discovering something and producing something new. That’s how it works. Clues are not something you’ve invented in the sense that they’re completey new – they’re something you discover, about words and about connections. And that’s exciting. The art of the crossword is getting all this stuff into a form that makes sense to people and brings the connection to them.”

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About Peter Cameron

I count all the things that need to be counted.
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8 Responses to Discovery and invention

  1. With the possible exception of a checker/referee, I feel like the above things actually apply to most arts / artists (including rock climbers! – if you’ve never looked at the parallels between rock climbing or bouldering and mathematics, you should really check it out. They even call a new rock to climb a “problem” and finding a way to navigate or climb it a “solution.”)

  2. Jon Awbrey says:

    Between the discovery and the invention,
    Falls the Shadow, who knows, you know,
    By tracking backward, retracing the steps
    Of the tourist, who comes not to conquer,
    But to enjoy the winding stair to the place.

    That all invention is discovery is kin to the Platonic idea that all learning is recollection.

  3. Pingback: Plato’s Puppet Returns | Inquiry Into Inquiry

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  5. volkan says:

    The attempts in answering the question of what is mathematics are often misunderstood by metaphysicists and idealists, such as Platonists, formalists, intuitionists, and logicians. Apart from Platonists the others see mathematics as a product of pure thought. As one of the greatest mathematicians of his time put it: “In reality, mathematics offers not the slightest support for idealism or metaphysics,’’ …

    • Jon Awbrey says:

      A Bit Of Context

      Idealists and metaphysicists not only fall into confusion in their attempts to answer these basic questions but they go so far as to distort mathematics completely, turning it literally inside out. Thus, seeing the extreme abstractness and cogency of mathematical results, the idealist imagines that mathematics issues from pure thought.

      In reality, mathematics offers not the slightest support for idealism or metaphysics. We will convince ourselves of this as we attempt, in general outline, to answer the listed questions about the essence of mathematics. For a preliminary clarification of these questions, it is sufficient to examine the foundations of arithmetic and elementary geometry, to which we now turn.

  6. Jon Awbrey says:

    A Meno Acid

    What answers to the Meno Paradox
    Comes in the moment of realizing —
    Gathering together the building blocks
    Is just the beginning of the building.

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