She also discusses “The Luminaries,” by Eleanor Catton, winner of the 2013 Booker Prize. Every year, Dr. Hart and a friend speed-read the shortlist. That year, once she got three-quarters of the way through “The Luminaries,” she realized there was something mathematical going on: The chapters displayed a geometric progression, halving in length one to the next. She also noticed “a twelveness happening” — there are 12 chapters, and 12 signs of the zodiac each instantiated in one of the main characters.
The structure, by Dr. Hart’s reading, had a compelling effect. “It’s refining and refining and refining, gradually waning down, until it’s quite poignant by the end,” she said; the two main characters, the luminaries, seem trapped in their destinies. “It’s a feeling of inevitability, closing in the kernel of the love story at the center of the entire novel.”
Such constraints and structures are most successful when not imposed frivolously, she added: “That’s not what it’s about. And that’s not what mathematicians do. We don’t invent a structure for no reason, like some silly intellectual game. We find structures lying around, and we explore them.”
Last term at Birkbeck, Dr. Hart taught the first module of a course called Explorations in Mathematics, giving students a taste of real mathematical research, which entails becoming comfortable with uncertainty.
“Real mathematics involves not knowing what is going on, not having any idea what to do, and then playing around and hopefully finding your way through,” she said.
Finding the way often involves imposing structures and constraints on a problem. The tension, Dr. Hart said, is between wanting the most general result possible and actually being able to prove something. “You could prove hundreds of rubbish theorems about your very precise special case, but nobody would care because it has no wider implications or applications,” she said. “You want just enough structure to hang your ideas on, but not so much that you are boxed in.”