This Thanksgiving I am thankful for all the vertical reflective surfaces in the Boston area.

Good Will Hunting

The Social Network

Thanks to these windows and mirrors, our genius janitors (Good Will Hunting) and entrepreneurial college students (The Social Network) can work out their formulas in an aesthetically pleasing manner with an inherent visual metaphor for self-reflection, intellectual clarity, and access — just through a window — into the analytic mind.

Bret Schneider of Chicago Art Criticism writes:

A Beautiful Mind

For some reason it is common among films portraying genius to aestheticize their intellectual process by showing the protagonist writing on glass, mirror, or other reflective surfaces. In Good Will Hunting the film opens with the solitary genius writing abstract mathematical formulae on mirror, with few other objects in sight. A man and his mind, alone in a room. Oh wait, but also an obscure writing utensil that one would need to go far out of their way to procure. A Beautiful Mind has a similar scene, where the main character, a sociopathic math genius, writes his ideas on transparent glass. A plethora of pi glyphs and some mundane squares, punctuated by some other recognizable shapes like triangles and greater-than or less-than symbols writ in white mar the view of his dormitory window. Apparently geniuses are too pure for paper.

The following deleted scene from Good Will Hunting finds him math-ing away in his grungy Southie studio apartment. We see library books, and then a rare moment of him writing on notebook paper (actual paper!), which transitions to a scene in which he walks to the room’s periphery and starts writing on the wall.

Furthermore, a close look at the following still from the film also shows that Will has at one point resorted to doing math (homeomorphically irreducible trees, perhaps?) on the window shade. (Also check out Will’s beer of choice — a box for locally brewed Sam Adams sits in the lower left corner.)

Mathematician Keith Devlin (who discussed the math of Good Will Hunting on NPR’s Morning Edition in 1998; their conversation is considered here on Blog Will Hunting) defends this trope.

One of the most derided scenes in Good Will Hunting is where the hero starts to write equations on a bathroom mirror. Conveniently forgetting that the great Irish mathematician Alexander Rowan Hamilton scratched the key identities for the quaternions on a stone bridge — the only writing surface available to him at the time inspiration struck him — the critics scoffed that no mathematician would ever do such a thing. … Depicting a mathematician scribbling formulas on a sheet of paper might be more accurate (and you’ll see Crowe doing that in A Beautiful Mind, just as we saw Damon doing it in Good Will Hunting) but it certainly doesn’t convey the image of a person passionately involved in mathematics, as does seeing someone write those formulas in steam on a mirror or in wax on a window, nor is it as cinematographically dramatic.

That sums it all up rather nicely, I think. Both a visually-striking metaphor and a shorthand for the urgent intellectual passions of a genius, this cinematic cliché, like any other, gets its storytelling work done efficiently… even if the readiness of the appropriate writing utensil for such a purpose is rather unlikely.

When Ben Affleck’s character enters the Harvard bar in Good Will Hunting he announces, “So this is a Hah-vahd bar. I thought there’d be… equations and shit on the wall.”

Sorry, Ben — “equations on the wall”? That’s only in the movies.

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