The Mind of a Genius — Too Pure for Paper?

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

Good Will Hunting mirror
Good Will Hunting
The Social Network window
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 window
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.)

Will Hunting at the window

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.

Homeomorphically Irreducible Trees of Degree Ten have nothing to do with Function Analysis

Good Will Hunting scene

I once watched Good Will Hunting with a math student, and she scoffed at the so-called impossibility of the problems on the hallway blackboard.

Her skepticism is validated by Professor Robin Wilson of Gresham College:

[youtube 811LbompjPg 425 344]

That’s right, homeomorphically irreducible trees of degree ten have nothing to do with function analysis.  And this particular problem isn’t that hard.

However, when the film was released, some were simply impressed that they actually used real math.

On NPR’s Weekend Edition back on April 4, 1998, host Scott Simon spoke with mathematician Keith Devlin about the plausibility of the math in the film.  Devlin’s opinion is that “they got the math right,” and describes the blackboard problem:

What they did that was very smart was… they had to make sure that it was a problem that someone like Will Hunting, who was innately a genius but had no mathematical training, someone like him had to have been able to solve the problem… and graph theory is one of the few areas of mathematics where that can happen. Someone could literally come out of the streets — or come along the corridor at night with a mop and a bucket, which is what the Will Hunting character does — and if they’ve got the ability, they don’t need the training, and they can just solve it. They have just got to be smart.

The Weekend Edition clip is definitely worth a listen in its entirety; they go on to discuss the real life story of self-taught mathematician Srinivasa Ramanujan, part of the inspiration for the Will Hunting character, as well as what the filmmakers get not-so-right.

Good Will Hunting scene
"It looks right," says Tom.

Fame, fortune, and their name printed in the auspicious MIT Tech!

The problem Professor Lambeau puts on the hallway chalkboard sets off such excitement as to the identity of the mystery mathematician that his next class is overfilled with students eager to learn who the “silent rogue” could be. When I first saw the film, I thought that the joke — “Is it just my imagination or has my class grown considerably?” — was that everyone enrolled in the massive lecture course actually showed up, which never happens in large lectures. Instead, I think the implication is simply that nearly everyone who heard about the Hard Math Problem being solved was eagerly attending in awe; in short, this is a really big deal.

So big a deal in fact, that people are running as fast as they can to get to the lecture hall.

Someone solved the theorem on the hallway chalkboard!!
Someone solved the theorem on the hallway chalkboard!!

Only in repeated viewings did I realize, this quick scene is not of running students late for class, but instead, it depicts the electric excitement on campus that disrupts the normal pedestrian flow, pulling academics into a sprint toward the lecture hall, books and briefcases in hand, to behold who solved the theorem.

Addendum: In this curious eagerness they find companionship.  Could this be the result of “goodwill hunting”?  They look for math but find companionship, but maybe it was companionship they were looking for all along?  Because nerds don’t have friends?