# GO FIGURE: Proof of Concept

by Susan Sechrist

In David Auburn’s Pulitzer-prize-winning play, Proof, there is a scene between Catherine – the possibly brilliant, probably mad daughter of famous, brilliant, mad, and dead mathematician Robert – and Hal, Robert’s graduate student, in which Hal describes a song his fellow math-buddies play in their band:

Hal: They have this song called “i.” You’d like it. Lowercase I. They just stand there. They don’t play anything for three minutes.”

Catherine: Imaginary number?

Hal: It’s a math joke. You see why they’re way down the bill.

I was already disappointed in Proof as literature about mathematics and mathematicians – I found the fragile-genius characterization of Robert and Catherine simplistic and off-putting – but this exchange made me put the book down. It was a cheap ploy intended to make Hal more of a well-rounded guy and less of a narrow-minded geek, perpetuating the dull myth that math is usually for emotionally stunted, uncreative, and antisocial nerds.

In fairness, I probably expected too much. I only picked up Proof recently after I read Alex Bellos’ fantastic non-fiction book, The Grapes of Math: How Life Reflects Numbers & Numbers Reflect Life, a rollicking, complex but accessible, and fun (yes, fun!) treatise on the beauty, power, and necessity of mathematics. Bellos wrote an inspiring chapter on negative and imaginary numbers and how disruptive they were when they first came on the scene. Around the time Euclid wrote Elements (300 BCE), the Chinese were calling negative numbers “false,” while positive numbers were “true;” centuries later, Indian accountants found a use for negative numbers (it’s called debt). European mathematicians began grappling with negative numbers more seriously when curious equations evolved out of their algebraic experimentation, for example:

We can’t have the square root of a negative number, because the definition of a square root is a number that produces a particular quantity when multiplied by itself – for example, the square root of 4 = 2 because 2 x 2, or 22, = 4. Mathematicians understood that the square root of a negative number was nonsensical, because multiplication automatically makes square roots positive: a negative multiplied by a negative is a positive.

Philosopher Rene Descartes called the square roots of negative numbers imaginary and 100 years later, mathematician Leonhard Euler gave them the symbol i, for imaginary. But imaginary numbers are not just problem children, conveniently labeled and then shunted aside. Imaginary numbers thrived in mathematical research, contributing to beautiful solutions in abstract number theory as well as practical applications in electrical engineering and quantum mechanics. The imaginary number played a role in the development of the Mandelbrot set, a stunning, complex, iterative fractal that helped popularize chaos theory, a branch of mathematics used to analyze unpredictable dynamic systems like weather patterns or water flow; the Mandelbrot set was as ubiquitous in the 1980s as the Rubik’s Cube, leg warmers, and the mullet. (Thankfully, chaos theory persisted while the mullet went quietly into the good night.)

Hal’s easy joke about imaginary numbers – that they are useless, non-existent, empty, silly, or silent – is an illogical conclusion for any mathematician, including a fictional one. Proof had many other problems for me – the stereotypical characters and shallow plot were less than compelling – but my suspension of disbelief was irrevocably ruined by this one snide, smarty-pants gag. I did eventually finish reading the play, but I swore under my breath the rest of the way.

Literature and mathematics are uneasy bed-fellows. C.P. Snow lectured about the gulf between the humanities and the sciences in his famous “two cultures” essay in 1959, lamenting the lack of respect between the disciplines and the absence of a shared language. Snow advocated for an exchange program of sorts between the two – scientists needed to read Shakespeare (to be or not to be) and artists needed to understand the Second Law of Thermodynamics (that entropy, or disorder, increases over time). The pay-off would be a better, broader understanding of how the modern world really works. I would argue that when we are more integrated across these diverse disciplines, we ultimately get better science and better art.

In August of 2014, Maryam Mirzakhani received the Fields Medal, the most prestigious honor awarded in mathematics. She was the first woman to ever win the exclusive prize, awarded every four years by the International Mathematics Union “to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.” Mirzakhani’s research is a fascinating, mind-bogglingly complex study of topology and dynamic systems, something I couldn’t begin to understand with my limited education in engineering calculus; but I could appreciate her work as tremendously important and beautiful. Then I read Mirzakhani’s interview in Quanta magazine:

“As an 8-year-old, Maryam Mirzakhani used to tell herself stories about the exploits of a remarkable girl. Every night at bedtime, her heroine would become mayor, travel the world or fulfill some other grand destiny.

Today, Mirzakhani — a 37-year-old mathematics professor at Stanford University — still writes elaborate stories in her mind. The high ambitions haven’t changed, but the protagonists have: They are hyperbolic surfaces, moduli spaces and dynamical systems. In a way, she said, mathematics research feels like writing a novel. “There are different characters, and you are getting to know them better,” she said. “Things evolve, and then you look back at a character, and it’s completely different from your first impression.”

Mirzakhani’s natural approach to mathematical thinking as narrative exploration is the bridge between Snow’s two cultures. Just like a skilled novelist, she learns about her characters by experimenting with plot and scene and action; just like a novelist, she may go back to a character only to find that it has morphed unexpectedly. Just like a mathematician, a novelist or a playwright can benefit from studying the nature of an asymptotic equation or a divergent series, a sort of mathematical equivalent of metaphor. This was what I learned from Bellos’ Grapes of Math and Maryam Mirzakhani, and what I’d hoped to see in Proof: the two cultures working together to reveal sense from uncertainty, and how even an unanswerable problem provides purpose: the imaginary number on its own is nonsensical, but it does crucial work as part of a larger system.

Proof assumes, maybe rightly so, that many people identify with the idea that mathematics is maddening. There is a quote on the back of my version of the book from John Simon of New York magazine: “Proof is… a play about scientists whose science matters less than their humanity…” Descartes is spinning on his x-axis in his grave – this is the illogical, even inhumane idea that I want to debunk – that science and mathematics are separate from the core of what makes us creative, compassionate, connected humans.

My hope is that this new feature, Go Figure, will explore the portrayal of mathematics and science in fiction and literature to that end – to uncover these deeply emotional and naturally creative connections. Go Figure will include discussions of the successful planned intersections between math and fiction, as well as the unsuccessful or accidental ones. Future Go Figure features will look at Lewis Carroll’s Alice’s Adventures in Wonderland, less as a classic fantasy and more as a caustic critique of advances in 19th century symbolic algebra; Tom Stoppard’s use of mathematics as a foundational metaphor in his play Arcadia; the Oulipo workshop’s literal mathematizing of language to create potential from constraint; authors like Borges, Beckett, and Calvino, who artfully overthrow reality with hyperbolic techniques; and modern masters of speculative fiction like Margaret Atwood, Neal Stephenson, and China Miéville, who create worlds where systems of language – mathematical, computational, and semiotic – coexist to define unique post-Babel civilizations.

Bloom is a particularly meaningful place to explore this subject: mathematics is notoriously mythologized as a field for the young. The Fields Medal is only awarded to mathematicians under the age of 40, giving credence to Proof’s panicked 28-year-old mathematics graduate student who is hearing his topological clock ticking. At Bloom, we celebrate just the opposite: the new gems that are discovered when one veers off the singular path. Exploring authors, including Bloomers, who write about math and science will include an attempt to chip away at the cult of youth that surrounds mathematical and scientific thinking, maybe even putting that inverse proportion of age and prowess on its head – after all, the act of blooming late challenges notions about competence and equilibrium, about what it means to find balance in opposition or what really passes for meaningful and mutual respect between the two cultures.

There’s another Blooming theme that emerges in looking at the synergies between mathematics and literature: the meaningful blurring of hard boundaries that happens with interdisciplinarity and integration. The older we get, with maturity and wisdom, the more adventurous we can become. The segregation of complex ideas into distinct categories ceases to be useful or even necessary – what we once feared or needed some semblance of control over becomes the very source of our later-in-life creativity. Go Figure will celebrate not only the unique parts that contribute to this new whole, but the unexpected, resonant, truthful art that emerges.

Susan Sechrist is a freelance technical writer who is striving to better integrate her creative and mathematical sides. She is the Interviews Editor at Bloom and published her first short story, the mathematically-themed A Desirable Middle, both in Bloom and the Journal for Humanistic Mathematics.

Photo credit: CC BY-SA 3.0, Wikimedia Commons.