Questions 1-10 refer to the following information.
Prose Fiction—Higher Numbers
"Why do I always feel like I'm on my way to a duel?"
Anton grumbles—I wonder if he means it. My brother
begins sliding the mess of papers that veil his desktop
and spill to the floor on either side of him into crisp, tidy
5 stacks. Lifting one that has floated near my foot, I glance
to the characters—Ψ, i, γ, e. Greek and Roman; I know
these alphabets, but their arrangement on the page
belongs to neither language.
"Higher numbers," he once said to me, grimacing. I
10 suppose he hasn't used real numbers much at all in his
graduate work, and I'm not sure I have the right
vocabulary to even muse on what he does—all fields and
modules, I imagine; the outer limits of abstract algebra
are more mysterious to me than those cuneiform
15 crosshatchings on the stele of Hammurabi. Anton
finishes assembling his notes and stands to snatch his
last page from my hand. Marking my place in the book
on my lap, I raise my eyes to see him adjust the collar of
his jacket and toss a scarf around his neck.
20 "évariste Galois," I say to him, grinning.
He stares, "What do you know about Galois theory?"
"Not a thing," I reply, "You're like Galois on the way
to his duel."
He rolls his eyes, "Funny. Don't wait up for me at
25 dinner tonight."
"Big day?" I ask, watching him take a stale muffin
from the plate our Mother shipped us for our birthday last
week.
"Exam, class, grading, class, exam—more grading
30 maybe," he bites into the muffin, "Don't wait up."
He turns and starts down the narrow corridor to our
door.
"Let me know if you need a second," I call, returning
to my book.
35 I hear his footsteps stop in the hall, "—For the duel.
Funny."
The door snaps shut and he's gone. Duels. I suppose it
was something done by people who were either very
poetic or very violent. The poets usually lost, I imagine.
40 Pushkin died in a duel with a French officer. I think
Manet fought a duel with swords in the forest of Saint-
Germain-en-Laye. Zola was his second. Andrew Jackson
shot a man down with more than three hundred dueling
kills to his name. I suppose with a count that high the
45 statistics must catch up with you eventually. One in fifty
thousand Americans will die drowning, one in five are
conversational in two languages, and one in two have
fired a gun.
I wonder if two twins ever fought a duel. I hope not.
50 Like most twins, Anton and I were very close when we
were younger. We still are, I guess, but the older we get,
the less our lives seem to overlap. Remembering the
fastidious and elaborate figures of his notes, I wonder if
the poem I'm studying—Cummings' "r-p-o-p-h-e-s-s-a-
55 g-r"—would seem as strange, glyphic, and vaguely
beautiful to Anton as his higher numbers do to me.
Probably not. Letters are my passion; numbers are his.
And while there's no geometry to my poem, I suspect
that there's a poetry to his equations.
60 There is an elegant answer to why polynomial
expressions of higher degrees cannot be solved in the
simple algebra of coefficients, radicals and arithmetic.
Galois theory—I do know a little about it. But not
because the math interests me; the man does—or boy,
65 really, I suppose. His life was…poetic—polynomials,
permutations, premonitions. I have my own work to see
to today, but I'll wait up for Anton tonight. It's true our
ages are increasing, and the simple solutions that once
sufficed can't resolve the trouble of these higher
70 numbers—the interactions are inconsistent, disconnected
and chaotic. I'll wait up anyway. I can imagine him
vividly, cloistered in a carrel with his papers late into the
night, until the librarian taps him on the shoulder.
"Time to go. We're closing up."
75 When he shuffles into our apartment, trailing clods of
snow and slush, perhaps we'll talk a while, or perhaps
we'll just go to bed. After the duel, Galois lay dying; shot
down by an opponent whose name history has not
remembered. The night before he'd spent in a jail cell,
80 scrawling out his last, cryptic theorem in a letter to
Auguste Chevalier. But his last words were for his
brother—"Don't cry, Alfred. I need all my courage to die
at twenty."