a cover of Philip Ording’s 99 Variations on a Proof
which is a mathematical cover of Raymond Queneau’s Exercises in Style
If you give an essayist a math problem, for instance:
x3 – 6x2 + 11x – 6 = 2x – 2
Fuck math, I’m an essayist.
Or else she might say,
I love math, but I haven’t done it in years, I’m an essayist.
If she is a certain kind of essayist, she might respond to your equation with an abstract but ultimately unhelpful and likely pretentious allusion:
“To know x = to know (everything – x).” [i]
Or else she might offer an equally ill-fitting, only vaguely math-adjacent, but more fun pop culture reference:
“The limit does not exist!” [ii]
If neither one of these quotes feels sufficiently satisfying, she might begin again by retracing a tangential anecdote:
There was a math teacher at my high school, I forget his name, who was married to the history teacher—I forget hers, too. They always held hands in the hallways. He was rumored to teach in hyper-speed so he’d have two whole weeks free at the end of the schoolyear to tell his students the story of how they’d met; apparently, it was The Greatest Love Story Of All Time. But his students were sworn to secrecy, and I never took his class…
If the essayist is sometimes a little uncomfortable with the personal nature of her chosen genre, she will choose to reply with an alter ego to help relieve the burden of the first-person, to speak with a stand-in sometimes called the speaker (where speaker ≠ writer), sometimes the essayist, or sometimes even just a single, simple letter, an ‘I’; which, in its vacancy, can become universal, a functional placeholder for multiple possible truths.
Let ‘x’ be a real number.
If she loves a good braid, which what essayist doesn’t, she may opt to weave in another thread, which will, of course, feel random at first:
The first game of ‘ultimate,’ also called ultimate frisbee, took place in a parking lot at Columbia High School in New Jersey, in 1968. The sport was the casual after-school creation of a group of friends, but its appeal proved contagious; an alumnus of CHS got his hands on a copy of the rules and founded an ultimate team at Staples High School in Connecticut in 1970, and before long, there was a CT league, and from there the trend went national.
The essayist might consider numbering her paragraphs, to make her essay response into a fragmented work, as in this classic of the genre:
“100. It often happens that we count our days as if the act of measurement made us some kind of promise. But really this is like hoisting a harness onto an invisible horse…” [iii]
If she chooses to do so, she will then consider the way a numbered fragment is formatted. She’ll look back at the page full of fragments and think:
This looks just like math homework—like a sheet of word problems.
If you try, then, to redirect this essayist to your chosen problem by restating it, this time more directly:
100. Let ‘x’ be a real number. If x3 – 6x2 + 11x – 6 = 2x – 2, solve for x.
The essayist is likely—at first—to once again skirt the question. This isn’t because the essayist doesn’t love a good math problem, but rather because she thinks a good essay, and a good essayist, always resists the finite or definitive answer. A good essay, she thinks, thrives in irresolution, indecision, uncertainty. As she’ll be all too happy to inform you:
An essay, from the French essai, is an attempt. It isn’t an answering, but a mind at work.
If the essayist is a writing teacher of some kind, perhaps the instructor of a college composition course, she might include this etymology lesson in her class materials one day; and if one of her students is playing games on their phone during that class, the essayist will recall Mr. Wetzel—who, of course, taught the essayist’s high school precalculus class and wrote her college recommendation letter, who didn’t give the essayist too much flack when she got bored of math and began solving the NYT crossword in class; who, in fact, after she’d gotten into college, would regularly stop by her desk to say:
You got 24-Down wrong. The first letter is ‘S’.
When some of the essayist’s students (the engineers) ask her then for some more concrete rules, what they should or shouldn’t use as a title, whether their essays should be five paragraphs or six or seven, and if there’s a good formula or template for an A+ conclusion, she’ll take solace again in writing’s lack of solutions:
There’s no wrong answer when it comes to writing something new, something original, an essay that is yours.
She’ll even give them a second, more math-inspired response:
There can be multiple correct answers (in writing). Multiple factors go into it (writing beautiful essays).
And if those students ever roll their eyes at the essayist’s exuberance for essay writing (which, let’s be honest, would not be unwarranted), she will find herself recalling her old AP Calc teacher, Mr. Wilkes, who bounced around the front of their classroom at Staples High with a puppy’s energy, puppy-eyed, exclaiming:
I’m teaching you guys the highest level of math I know! Think about that—you’re only what, seventeen, and one day soon you’ll know more advanced maths than I do now! By the time you’re my age—and I’m not that old—think how much more advanced you’ll all be!
He was assuming they would continue studying math in college. His students, including the essayist, used to make fun of his overenthusiasm a little. Thinking of this now, the essayist will feel sorry and a little embarrassed that she never took another math class after that.
Instead, she studied how to become an essayist.
Maybe she stopped taking math then, when she started writing, because she assumed she no longer had a use for that kind of thinking—that, as a creative writer, now, she was done forever with all that hard logic. Or maybe she’d just fallen into the bad trap of demanding real-world applications from her academic pursuits—that common failure of imagination, learning not for learning’s sake, which her high school teachers had always been so frustrated by, and accustomed to:
“In my Pre-Calculus class last year, when Mr. Wetzel was asked, “When are we ever going to use logs (logarithms)?” He wisely replied, ‘In a fire.’” [iv]
By now, the essayist will be feeling the need to perform some essayistic research. She’ll start out by googling how to factor cubic equations but will get sidetracked clicking through links, chasing stray inquiries, seeking endless revelation ‘til she’s thick in the archives of her high school’s newspaper and then knees-deep in the axiomatic philosophies of David Hilbert, a mathematician who argued that geometry’s central concern was simply the relations of otherwise arbitrary terms:
“One must be able to say at all times—instead of points, straight lines, and planes—tables, chairs, and beer mugs.”
The essayist may then take a different tack completely, and decide to deliver an aside to the reader stating her essay’s intentions directly:
I want to show you, show myself, how math is essayistic—how essays are math, or mathematical. I’m trying to examine how that overlap works.
Shift again, to the indirect, back to research. Another math teacher at the essayist’s high school, Mr. Jolley, was niche-famous for being a ‘Johnny Appleseed’ of Ultimate Frisbee, meaning he’d been one of the first to help the sport spread. Legend had it he’d founded the second ever Ultimate team at her high school in the ‘70s, out of a group of some math students he’d had who loved frisbee.
“Last Wednesday, Al Jolley, Staples math teacher and frisbee coach, was seriously injured when he attempted to make the famed “oral grab” (trying to catch a frisbee in his mouth). Suffering a broken jaw and loss of three teeth, Jolley commented, “shirpvgmn….’” [v]
If you are left wondering how you got here and try, one last time, to rephrase your original question in a different way:
Suppose that among four consecutive numbers, the product of the first three equals twice the third. What’s the fourth number? [vi]
The essayist will hem and haw. She’ll change the subject again, not because she’s resisting, but because she’s just discovered she doesn’t actually know how to solve this one. She’s forgotten all her math moves, so, as essayists are wont to do when their chosen tools fall short, she’ll look elsewhere for a functional answer of sorts:
“All players are responsible for administering and adhering to the rules. Ultimate relies upon a Spirit of the Game which places the responsibility for fair play on every player. Highly competitive play is encouraged, but should never sacrifice the mutual respect between players, adherence to the agreed-upon rules of the game, or the basic joy of play.” [vii]
An essay, too, has no referee. Thus the essayist may better be able to understand its basic relations if she is able to abstract some of the above terms, and say—instead of respect between players, agreed-upon rules of the game, and basic joy of play—the essayist’s fidelity to a reader, the expectations or qualities inherent in language, the basic joy of play (this one stays the same).
Group like terms on one side: x3 – 6x2 + 9x – 4 = 0.
Math, as play which, too, operates under agreed-upon rules (let ‘x’ be a real number), might reasonably make for a natural gateway to a sport like Ultimate; or, at the very least, Ultimate’s proliferation by a math teacher and his students makes some sense. Both are concerned with the spirit of the game. Math isn’t just about answers or practical use, but also about fire, pursuit:
Rewrite to seek out commonality: x3 – x2 – 5x2 + 5x + 4x – 4 = 0.
At this point, the essayist will pause solving to consider how her high school math teachers instilled in her the same stylistic values which she still strives for in writing today, how they had waxed rhapsodic not over correct answers, really, but rather over their explanations, mathematical proofs:
Take a look at this solver’s organization, the elegance of expression, their creativity in seeking out the solution this way….
The essayist’s obsession with tracking the mind at work closely echoes math’s insistence on showing one’s work. The word proof originates from Latin probare:
To show; put to the test; inspect.
In a weird way, these math dudes, whose classes she remembers much better than most of her English ones, were the very first essayists she ever knew. No wonder, now, when the essayist is locked into the central heat of writing an essay, she always feels herself becoming more analytical, calculating; not formulaic, but determined to inspect the problem from all sides, willing to experiment with a range of tools…
Factor: x2(x – 1) –5x(x – 1) + 4(x – 1) = 0.
The essayist had not given up math at all, she’d just started solving with language rather than numbers.
Factor: (x2–5x + 4) (x – 1) = 0.
If the essayist has gotten this far in her proof, she will be startled to make what, once made, is an obviously accurate realization, a turning point with proven veracity, shown out in her work: the essayist’s Ultimate game, her Greatest Love Story of All Time, is and has always been, since high school, math.
Factor: (x – 4) (x – 1) (x – 1) = 0.
The correct answer, or a mathematician’s desire to seek it, isn’t irrelevant, exactly, but merely one of the necessary conditions for the game, a prerequisite for attempting to solve, much the way the essayist is guided to the page in pursuit of elucidating truth, or Truth. That truth is, in many ways, an arbitrary term; the meat or measure of any proof or essay is not the solution but how it is solved, how the game is played out, which makes any answer somewhat beside the point. But the win, admittedly, still feels rewarding:
x = 1, or x = 4.
[i] Pataphysical Essays by René Daumal.
[ii] Cady Heron, in Mean Girls.
[iii] Bluets by Maggie Nelson.
[iv] “Counting On Math in the Real World,” Inklings (Staples High School Newspaper).
[v] Ultimate History, Staples Grads; https://www.ultimatehistory.com/founders/Pg/staples.html/.
[vi] 5 Puzzle, in Philip Ording’s 99 Variations on a Proof.
[vii] Spirit of the Game, World Flying Disc Federation.
Julie Lunde has an MFA in nonfiction from the University of Arizona. Her work has been published or is forthcoming in Western Humanities Review, Pigeon Pages, and the anthology Letter to A Stranger: Essays to the Ones Who Haunt Us (Algonquin, 2022) among other places. She serves as an assistant nonfiction editor at DIAGRAM and is the writer in residence at her dog's house. See more at julielunde.com.