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.”
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.”)
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.
Pingback: Plato’s Puppet Returns | Inquiry Into Inquiry
Pingback: I Wonder, Wonder Who | Inquiry Into Inquiry
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,’’ …
A Bit Of Context
Thanks. I nicked this for the Quotes page.
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.