Of Proof and other things.

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Over the last couple of days, I’ve seen a couple of days that made me think hard about all sorts of things. The first, at least, is tangentially related to the subject of this blog, and so I feel justified in writing about it. I’d been waiting to see Proof for a long time; the play comes with a heavy reputation having won the Pulizer prize and a Tony Award for its author, David Auburn. It’s even had the ultimate accolade of being made into a movie, starring Anthony Hopkins of all people.

It deals with the story of young mathematician, struggling with the death of her father – another mathematician, who had done brilliant work in his early 20s and then gone steadily, slowly crazy, looking for messages encoded into the Dewy Decimal system of cataloguing library books. The eponymous proof – of a theorem mathematicians have been wrestling with ‘for as long as there have been mathematicians’, although we never learn its identity – lies in one of the many notebooks that lie scattered around the house.

The production was good, gripping at times, and we, the audience, were drawn into the world of the characters. Yet I came away disappointed and even a little angry. I’d expected a play that was to mathematics what Michael Frayn’s magisterial Copernhagen was to physics; a serious attempt to engage with the ideas and mental landscape of a subject. The language of Copernhagen is filled with physics; we see Bohr and Heisenberg on stage discussing their work and – miracle of miracles – can follow along. When friends and I produced the show in Cambridge (cast : entirely arts students, crew : entirely scientists…) I would stand by the doors during the interval, and listen to our audience talk about the ideas in the play.

Proof, on the other hand, might as well have been about flower arranging. Or molecular genetics. Or stock-car racing, or anything at all for all the presence maths had. A few technical terms are dropped in – a reference to Hilbert spaces and elliptical forms suggests that the playwright had been reading press coverage of the solution to Fermat’s last theorem – but no explanation offered. Characters talked often of prime numbers – but never allowed the audience to glimpse why anyone might care.

For the play to be as good as I’d wanted it to be, I needed to believe in the character’s motivations and thoughts, yet not one of the mathematicians on stage ever gave us a glimpse of that. It was as if the show was about struggling painters, who had forgone any suggestion of belief in their art. Without that, the play felt unfinished.

Actually, it’s funny I mention painters as an analogy. The one theme that did get underlined was that mathematics is an art form, not a science. It’s something that’s been uppermost in my mind since I read a document known on the net as Lockhart’s Lament (warning – 25 page PDF).

It was written a few years ago by Paul Lockhart, a mathematician who left academic life to become a teacher. The first paragraphs capture the gist :

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where
music education has been made mandatory. “We are helping our students become more
competitive in an increasingly sound-filled world.” Educators, school systems, and the state are
put in charge of this vital project. Studies are commissioned, committees are formed, and
decisions are made— all without the advice or participation of a single working musician or
composer.
Since musicians are known to set down their ideas in the form of sheet music, these curious
black dots and lines must constitute the “language of music.” It is imperative that students
become fluent in this language if they are to attain any degree of musical competence; indeed, it
would be ludicrous to expect a child to sing a song or play an instrument without having a
thorough grounding in music notation and theory. Playing and listening to music, let alone
composing an original piece, are considered college, and more often graduate school. .

Is maths in the same situation? Read the rest, and let me know if you agree or disagree.