The Conjecture

A short story

Author’s note: Sometimes it isn’t possible to trace the origins of a story. It comes from a dream, or from some vague yearning, or from nowhere you can identify. But sometimes you know precisely where it comes from. Such is the case for today's offering. It is a short story of 6000 words, once considered average. Sadly, 6000 is a lot of words in the digital age. I urge you to set aside a little time and a little concentration for this one. It is a character study and a story of transformation, and could not be told any more concisely.

‘The Conjecture’ is a story of despair and redemption (not mine). When I was an undergraduate at SUNY-Albany, I got to know a couple of the mathematicians on the faculty. My major was physics, so I had to take a lot of math, which I found fascinating. In time, the culture of mathematics came to fascinate me more than the mathematics itself. I took a course with a young professor who was appropriate in the classroom but inappropriately crude/blunt during office hours. He described his profession as a house of horrors, full of vain, insecure, cruel men (they were all men back then). Imagine that. Yet to the unworldly kid I was, the news came as a shock. In the story, you will meet such a wide-eyed undergrad (also not quite me).

Then there was another man, an avuncular, circumspect, kindly mathematician who shared a tragic story. A colleague of his woke in the middle of the night with the proof of an important theorem fully formed in his mind, a career making discovery. The next morning he had forgotten it. Soon afterward he committed suicide.

These are the disparate elements I used in ‘The Conjecture.’

For the mathematically uninitiated: Theorems—the ‘proofs’ of high school geometry—are the gold that mathematicians lust after. Conjectures are unproved theorems; that is, someone's guess about where to dig for the gold.

The Conjecture

For ten years Jeffery Griffen had worked on a single mathematical problem. At the heart of the problem was a conjecture first posed in the 1970s by the German mathematician Neumann. There had been a time when Griffen was optimistic that a solution—a  proof—was just a few pages of calculations away. But it had been a long winter, both outside his office window and in his private meditations, and the famous problem lately seemed insoluble; worse, it seemed insoluble by him.

The problem was in fact a series of problems, connected to each other and to the original conjecture by logical threads that after a decade he could claim to understand only imperfectly. He had admitted as much in his last paper, one of a series he hoped would mark his trail through the labyrinth. More than marking the trail, Griffen well knew, he was laying claim to it. There were other workers in the field. It was said that Wu at Princeton was working on nothing else. But Wu hadn’t published, and on his good days Jeffery Griffen didn’t give a thought to his Princeton rival. On those days the problem became so beautiful that nothing outside it mattered, least of all the small concerns of a reputation. His humility was a kind of joy, and in it he understood that the private work of a mathematician more than compensated for the public insults which were everywhere a part of the professional culture.

Lately when he thought of the professional culture he thought of his department chairman. A man with a powerful memory, the chairman had been slighted by a remark Griffen made at a colloquium; he hadn’t intended it as a slight, but the chairman took it that way and responded with a long calculated hostility that included poor teaching assignments, stingy funding, and public snubs. The hallways had become an uncomfortable place. The men’s room was another. There were two urinals, and he sometimes found himself beside the chairman, wordlessly pissing. Both men spent a good deal of time drinking coffee, and almost as much time discharging it, and the unpleasant silence was long. The fixtures they stood at were the low, exposed sort, and Griffen got to know well, perhaps because there was no conversation to distract them, the chairman’s penis. It was an ugly and formidable instrument, rather like its owner’s intellect. Griffen felt qualified to judge. Professionally their work was related, and there had even been a time when they discussed it. When the ritual at the urinals was complete and they were again side by side washing, the chairman would say “Jeffery,” no more. He was a large jowly man, gracelessly aging, with a stentorian voice that rang in the head long after speech had stopped. Griffen would reply “David,” imitating the man’s curtness exactly. And to think that they had once been friends!

In a sense Griffen escaped the life of a mathematician by doing mathematics. The epiphanies kept him going, just as they had lured him into the field when he was young. He considered whether he would have become a mathematician if he’d been told what a community of wretches it really was. And then he remembered that he had been told, by example if not in words. His undergraduate adviser at Stanford, a gentle and gifted young man, had become despondent over his work. Then he had become delusional. Griffen visited him in the hospital, to have his thesis reviewed. He expected a place of some drama but found the ward slow and quiet, patients staring out a window or at a television or at nothing at all. One man sat in a trance, expressionless except for an involuntary trembling of his lips, with an open book on his lap. It was a mathematics book. His advisor had insisted by letter that that no one else could evaluate Griffen’s thesis—and then was unable to make any sense of it. In a voice lifeless and unfamiliar he told his student that clear thinking was impossible here. Griffen understood it was the drugs that did this, but then so did the illness itself, so what choice was there? The impression was powerful, heartrending, even tragic. But it was in no way discouraging. In fact the episode had the opposite effect when he brought his thesis brilliantly to conclusion on his own.

*

Griffen decided it would be as good an afternoon as any for an epiphany. They came, these instants of illumination, always after a long period of frustration. He was accustomed to this. But the frustration had gone on too long this time; it was as if he’d reached a wall that was too high to go over and too wide to go around. The symbols on the paper in front of him, which seemed to have somehow leaked in a chalky mess onto the blackboard, were an attempt to try an entirely new path. But after most of a day of work this path too had led to the wall. Every path for the past year had led to the wall. He was working on the manifold problem. He had been working on the manifold problem since the previous winter. It seemed appropriate that the window was frosted along the bottom in the same geometry it had assumed the year before. The manifold problem itself was at root geometrical, and he wondered if the shape of the frost on the window was a clue or an omen. And then he wondered if wondering that was a sign of how hopeless things really were. There was in this business not the slightest room for the irrational. Or was the irrational the one essential ingredient? He meditated for a moment on the fractal-like geometry of the frost. It was like one of the hills he could see darkening in the distance, turned upside down. The fractal approach he’d never thought to try. He picked up his pen. Then he put it down. In the shabby office chair he leaned back with a loud creak and rubbed his eyes.

Suppose he solved the manifold problem. There remained the supermanifold problem. If he solved the supermanifold problem he might be able to demonstrate the weak symmetry. The weak symmetry, as far as anyone had been able to foresee, would lead to the strong symmetry. The Conjecture itself, the prize, was somewhere at the end of a tortuous, uncertain chain. Of course whoever proved the Conjecture would be on the short list for the Fields Medal. Yet this possibility—the highest award in mathematics—felt not only impossibly remote but an insufficient compensation. Years ago Griffen allowed himself to imagine winning the Fields Medal, which at the time didn’t seem such a grandiose goal, or even a goal at all, but a likely consequence of the joyful preoccupations he was prone to. So much had flowed naturally from these preoccupations: his job, tenure, his work on the most important unproved theorem in set theory, even his decision not to marry.

There was a knock. His office door was closed for a reason, the hours posted. In years past he had left the door open, and students respected the hours. Now—since his ill-fated remark to the chairman and the onerous teaching load that had come of it—he kept the door closed, and students seldom respected the hours. He had three hundred seventy-nine freshmen in two morning lectures. For some reason most of them found calculus incomprehensible. They expected him to make it comprehensible, at times that were convenient to them. Office hours, a closed door, these things meant nothing. He waited; usually the student would go away. This one knocked again. Griffen had been a teacher once; that is, he had understood that what to him was a simple conceptual question was to the students an existential threat. He used to respond to the fear in their eyes, and enjoy making the fear go away. On the wall were a couple of tarnished plaques, university awards for teaching. He had been as proud of this part of the job as of the other, more scholarly part. When exactly had this changed? He glanced at the papers on his desk. It was not a difficult question.

The knock came again and he opened the door. A young man came in.

“Why don’t you come in?” said Griffen.

The young man sat down in Griffen’s chair.

“Why don’t you sit down?” said Griffen.

“I got everything but the last step,” said the young man, in a state of evident excitement.

“Put it on the board.”

“I don’t want to erase anything important.”

“Put it on the board.”

“That looks pretty important.”

“It’s nothing.”

“Are you sure, Professor Griffen?”

“Put it on the board.”

He wasn’t entirely sorry he’d answered the knock. It was a student not from one of the big lectures but from a tiny seminar he taught on number theory. An opportunity to talk, perhaps agreeably, about real mathematics. The seminar was technically for seniors but this kid looked much younger.

“Remind me,” Griffen said wearily.

“Randy Lawson. I was in here last week.”

“I have a lot of students.”

“There’s only six of us in class, Dr Griffen, so I thought . . .”

“Nevertheless.” He squinted at him. “Math major?”

The student, lanky and blonde, with dark eyes that betrayed emotion, nodded quickly. In these eyes Griffen read love, not fear.

“What do you plan to do with it, Randy?” The kid looked at him as if the question was absurd, and Griffen realized it was. “Never mind. Keep writing.”

The small confusion in the class proof was quickly cleared up. The discussion led to other avenues, other theorems. The student’s mind was nimble and able to make leaps. This was gratifying, but also troubling: the price of admission to the field, which few could actually meet, was such a mind. Of course the boy was insensible of any professional hazard. In fact he grew more reverential as the conversation deepened. At one point he opened the slim textbook and pointed to a particular passage. His finger trembled as he spoke.

“This is so . . . did you . . .?”

Helpfully Griffen said, “You’re wondering how much of the mathematics in the book is mine.”

“Sort of.”

Griffen had seen students starstruck before, and understandably. Their world was still small. Usually he let it go, but something made him want to disabuse this skinny kid.

“Virtually none of it, Randy. Maybe a couple of alternative proofs in the appendix. When you write a textbook it’s usually just a new presentation of old information. It’s really about money, or prestige. I wrote this one when I was just out of grad school, thinking it would help me get a job. The other ones—”

“You wrote more?”

“Yeah. Those I wrote to make a buck.”

“Did you?”

“Of course not. Nobody buys math books.”

This information quieted the boy, and Griffen attempted to look out the window. Already this was impossible. It was four o’clock in the afternoon and completely dark. A southern California native, he was still waiting, after fifteen years, to get used to the winters up here. The inverted mountain etched on the glass seemed to be changing as he watched.

“Do you mind if I ask you something?” the boy asked.

“Yes.”

“Really, Dr Griffen.”

“I really do mind. But I have the feeling you’re going to ask anyway.”

“Are you always this cynical?”

“Yes.”

“Sorry. That’s not what I was going to ask. Okay, you say the books don’t have anything new in them. So what exactly do you work on?”

“I was afraid you’d ask that.” It was actually Griffen’s standard response, and most students didn’t dare push the matter. This one was different.

“That stuff I erased—did it have anything to do with multiple manifolds?”

“How the hell do you know that?”

“From the Annals of Mathematics.”

“Christ. Already he’s reading the journals.”

“Trying. A lot of it goes over my head.”

And some of it evidently did not. This one really was different—smarter, more persistent, more vulnerable. Griffen felt an urge to protect, long dormant, possibly a reflex left over from the days when he gave a damn. He remembered being told by someone once—it might have been the chairman, before he was the chairman—that protecting these kids was the vital part of the job no one prepared you for.

Discussing the Conjecture with even the most advanced student wasn’t realistic; it was simply too abstruse. The perfectly reasonable question about what exactly he did work on took away what was left of his equanimity, perhaps because he’d been asking himself the same thing lately. The lesser question about manifolds might have spurred an interesting talk. Much of it was settled mathematics, and it was particularly elegant. He imagined an explanation that went to the heart of the topic—he was capable of one on a moment’s notice—and the rapture it would cause in a student like this one. He could use a little of the old rapture himself.

Suddenly a squall of snow swept across the glass. They both turned to look. Griffen saw that the etched pattern, whatever its significance, was gone. The cold seeped through the old window, and when Griffen looked back at the boy he knew what sort of lesson was required.

“How old are you, Randy?”

“Nineteen.”

“This is a senior seminar.”

“I am a senior.”

“You’re too young.”

“But I thought I was doing okay.”

“You’re doing fine. What I mean is you’re too young for this—” He held out his hand to take in the sagging shelves of monographs, the papers lying like sediment on the desk, the conference announcements from years gone by. He picked up a copy of the Annals. “You should be over twenty-one to read it. Probably you think this is mathematics.”

“What is it?”

“At your age, child abuse. Look at this paper. It claims to prove an important corollary in set theory, a career maker. It wasn’t out a week when a fallacy was discovered. It was all over the internet. The guy was up for tenure and now he’s looking for a job. Have you heard of Mancuso? That’s who punched a hole in the poor bastard’s argument. They call Mancuso the Invalidator. He hasn’t published anything himself in years, just looks for other people’s problems. And he’s started a thing, there’s a lot of Mancusos out there. Everyone says it’s best for the field, an international truth squad. And logically you can’t disagree. But everyone’s scared. The profession’s turning into a haunted house.”

The boy’s dark eyes had narrowed. Was he getting the message? Griffen, feeling protective, doing his job, moved vigorously for the first time in hours. Spittle flew as he talked.

“I was nineteen too when I graduated. Already doing original work. Couldn’t wait to get to my desk in the morning. There was something so pure and fresh it was exciting to breathe. I took the ideas from the air and wrote them down. The satisfaction . . . ” The wall above the boys head, which he happened to be addressing, had blurred. He could see the distorted shape of one of the old teaching plaques. Usually terse with a student, he found himself talkative now in a way that was reckless and cathartic. “I’m telling you this,” he said to the wall, hearing his own voice cracking, “because I wish to god someone had told me. I’m telling you because you have the rare thing that lets you do this incredible human activity. And you’re probably sitting there wondering how the highest form of human thought turns into such shit? Right? Am I right Randy?”

It was evident from the boy’s eyes that he found this fascinating and not the least bit unsettling, like an especially challenging math problem.

“A couple of years ago I was at a conference. Mancuso gave the featured talk. There was plenty of new mathematics being presented, but Mancuso, with the same old shtick, was the big draw. He called it A New Paradigm for Validity or some such nonsense. Of course the hall was full. People sat in the aisles. You’d think the guy would be a little remorseful with so much blood on his hands, but he had everyone cracking up. The implication, the real thesis of the talk, was that destroying careers is entertaining. Everyone’s laughing but inside they’re scared. Scared that if they don’t show Mancuso how wonderful his sick paradigm is he’ll come after them.”

Griffen stopped and blinked, trying to clear his vision. He had more to say, much more, but there was a clot in his throat.

After a respectful silence Randy Lawson asked, “Is it all so, you know, dark?”

How could he tell a boy with every blessing, including the blessing of innocence, that it is all darkness—and that somewhere inside is a tantalizing light? You could get lost in the darkness looking around for that light. Beyond the porous window the wind made a sound as if there were something unwholesome outside you couldn’t see and wouldn’t want to.

“If you don’t mind, Dr Griffen,” the student said, “I’ll still read the journals. Please don’t report me. I think the stuff in there is neat.”

*

Griffen lived in a condominium a few miles from campus. It was part of a large development built in a grove of Douglas firs, cheap modern buildings interspersed among the giant trees. Carpets of pungent needles took the place of lawns. Needles found their way into gutters, shirt pockets, drinks. It seemed mathematically significant to Griffen that the trees never ran out of needles, but filled the sky like one of his theoretical infinities. On this night the trees were agitated, blacker masses moving against the black sky, humbling the condo units and their feeble human light. He stood for a while outside his car in spite of the cold, seeking some comfort in all this outsized nature.

The condo was small; he used half of it. The living room contained a couch and an elaborate rack of stereo equipment; a wall was lined with shelves holding hundreds of old vinyl records. Another room was empty entirely. Every wall was bare. In the tiny kitchen dishes filled the sink and fruit rotted in a bowl. Griffen took a box from the freezer and a tray from inside the box. The tray he put in the microwave, and in four minutes he was eating, still in his overcoat and boots. He pushed the food away after a few bites and rummaged on the cluttered table for something to read. Nothing interested him. He readied for bed and decided to pass the evening the way he passed many evenings. He went to the wall with the oldest part of his collection and bent to squint at the narrow spines. After a lengthy search he pulled out a well-worn jacket with the long face of John Coltrane on it: a beautiful face, he had always thought, and haunted. When he bought this album, in a San Francisco shop thirty years ago, he knew from the look of the great saxophonist’s eyes that he was troubled, and this had been incomprehensible: how could a creativity so inexhaustible leave room for unhappiness? Back then his own creativity simply excluded it. He cleaned the vinyl disk inside and operated the delicate mechanism—all of which took longer than preparing and eating his supper—and he heard in the music what he couldn’t hear years before: the union of imagination and despair.

Much later Jeffery Griffen would consider the irony of something so momentous happening on such a bleak night. Now, as he lay on the couch listening to Coltrane improvise as no one had before or since, he thought only that this was as unlikely a night for an epiphany as any. And then, suddenly, all that mattered was the mathematics.

It came to him the way so many solutions had, in sleep. He was dreaming of a distinctive geometry, rather like the frost on his office window. This led to a simple, almost childlike way to bridge two previously separate issues in the mysterious proof, and just like that the weak and the strong symmetries were one. Which dissolved the manifold problem. Which opened, in the wide wall that had been his miserable destination for so long, a door no one had ever noticed. In his dream he went through the door and there, on the other side, was the Conjecture. He didn’t so much prove it as stumble across the fact of its inevitability. Then he willed himself awake. The room glowed unnaturally, a light he thought at first had something to do with human, if not divine, creation. But it was the display of the Sony amplifier. The proof seemed to be written across the blue ceiling. He tried to memorize it before it faded back into the inaccessible place it came from, always a danger with the nocturnal idea.

In his pajamas Griffen made his way to the table, pushed aside the half-eaten tray, and sat down to write a few things down on a scrap of paper. Only a few things were required. The approach was that direct and elegant. There was confirmation too in this, since all great mathematics is at heart simple. He set down with surprising ease an equation, a single, subtle, beautiful equation, and decided the occasion was worth marking. He considered a drink, or another side of Coltrane, or both. But these would only interfere with the thing he wanted to celebrate, which was the transparency of his thoughts. So he put on his slippers and stepped outside, where the wind had died down and the moon, nearly full, appeared behind fractal-like clouds. It was a few hours before dawn. The light drew his gaze upward to the tree canopies, and he realized that here was no infinity after all but something countable. In the still air he could see every needle but decided not to count them now. The cold was tolerable, even in pajamas. In fact he was barely aware of it. If he didn’t have to go back inside and sleep a little before his eight o’clock lecture he would happily stand here for the rest of the night. A thermometer hung on the post beside him, and in the moonlight he read the temperature: fifteen degrees below zero.

*

Griffen overslept badly. When he woke he knew the lecture hall was already filling. His exertions had taken more out of him than he’d realized. In his haste, and in the chaos of the house, he couldn’t find the essential scrap of paper. This did not matter. After class he would again follow the line of reasoning, expand on it, put in the final details. And soon he sat down to do just that. A notebook was readied to receive the important—did he dare say historic?—equation. But the equation would not come. He tried writing some things down—he tried writing many things down—but the logic of the night refused to come out in the day. He was unconcerned. On the kitchen table was, if not the full solution, then its essence. He resisted the temptation to cancel the rest of his classes and go home. The day passed with regal slowness. He saw the chairman and spoke his name and nothing more with a new satisfaction, the thrilling pressure of his discovery behind the single word. He was enjoying the anticipation so much that he prolonged the drive with stops at the bank and the grocery store. Once home he put away his few things and even tidied up the kitchen a little before glancing at the paper on the table. The difficulty came when the paper wasn’t on the table. It wasn’t under the things on the table or mixed with the other papers on the table or beneath the table. It wasn’t anywhere, as he discovered during the long night he systematically tore his home apart.

*

The name of Griffen’s advisor was Dorian Meyer. Griffen had tried to keep in touch after graduate school but his letters went unanswered. He knew that the ill man had made some sort of recovery and gone back to teaching, but it must not have worked out because soon Griffen heard of his retirement. Of course Meyer was only a few years older than Griffen, so retirement was just a polite way of saying he was unable to work. As it turned out he was unable to live: the mathematician jumped from the Bay Bridge when he was just thirty-six. Even in a profession littered with human wreckage a suicide caused people to talk, and Griffen wept when he heard the news. But he did not attend the funeral—he was working on the Conjecture.

In recent years he had been thinking of his old mentor a good deal. He thought of Dorian when a promising young mathematician named Lundgren became too depressed to teach his classes. He thought of Dorian when one of the few women on the staff, a good-natured statistician who was everyone’s friend, required a sudden leave of absence for undisclosed reasons. He thought of Dorian when the department topologist told him in the locker room after a squash game that he wasn’t playing with his usual energy because of a new medication. And then there was Hornbaker. Hornbaker had been the previous chairman, a star in his field and a man who exuded confidence and charm. One morning Hornbaker’s secretary said something that upset him and he beat her unconscious with a golf club. The police came and took the man away in handcuffs while his students watched, and in the trial that followed the lawyers argued that the defendant was himself a victim—of the unusual stresses of his job. The attacker went to jail anyway; the secretary recovered to work for the present chairman; and Griffen was left to wonder if Dorian Meyer, who had been in the vanguard of all this misery, was still trying to teach him something about the profession thirty years later.

Griffen, a teacher of some distinction once, knew that in mathematics the mind had to be prepared for the most difficult ideas. Surely this was true for other sorts of learning. He wondered if these unhappy years could be a kind of preparation for Professor Meyer’s lesson. Even more so the recent blow, the lost proof. Or was it too late for him? He had been witness to his old advisor’s cautionary story and ignored it, just as young Randy Lawson ignored him. Was the siren song simply too powerful?

Still he worked on, industriously and sometimes frantically, trying to reconstruct the fundamental equation. But there was a constant distraction that had never been there before. It was despair. He scribbled at his desk late at night, looking up only to take the measure of his pain. He worked in his mind while he drove, but the deep woods along his route captured his attention; he imagined walking into them thinly dressed, never to emerge. He drifted off during lectures, wondering what these kids would think if he did in fact disappear. Does it begin this way? Does it begin in professional disappointment and end in the woods,  or on the Bay Bridge?

But his unhappiness seemed to have a limit, unlike that of Meyers, Hornbaker, et. al. The self-destructive fantasies simply lost their appeal. He found himself conventionally unhappy and willing to endure it—almost glad to endure it. Some people got pneumonia and recovered, and some did not. Some people had a setback and got on with things, and some did not. Griffen had a habit of work that went back thirty years, and surely the readers of his previous papers expected something of him. So he listened again to the Coltrane record, to try and reproduce the conditions of the revelation. He was inspired, but not in the way he expected. He found not the elusive equation but the music, the troubled, transcendent music that was the only thing outside of mathematics that had ever mattered ultimately to him. The door he had discovered in the wall that night had closed, and he knew it would not open for him again. He accepted this. Already something new was trying to find its way in around the edges of his desolation, and when Griffen took the trouble to examine it he found that it was not new at all but the oldest feeling he could remember. He did not resist it.

*

One day Griffen was listening to the sputter of the radiator working futilely against the cold when he heard the now-familiar voice call his name. He ignored it.

“Dr Griffen.”

“I’m a little busy.”

“Did you hear the news? There’s been an announcement. This guy at Princeton put up a paper this morning—”

He opened the door. “Hello Randy.”

“Everyone’s getting together in the colloquium room to talk about it. The chairman said you and this Princeton guy work on the same problem. He told me to come down and get you.”

“Wu actually published something?”

“I thought maybe you didn’t see it so I downloaded it for you. I think it’s a proof.”

The boy held out the pages and Griffen glanced at them. Comprehension was immediate. How could it not be? Right there in the abstract, easy to recognize now that it was in front of him, was the equation, essentially as he had written it down at his kitchen table.

“Are you coming? Everyone is saying this is kind of historic and you should give a little talk. You’re the department expert.”

“Is that what they say?”

The boy looked at him with a sympathy Griffen had expected from no one. “Maybe this isn’t such good news for you.”

“It’s terrific news.”

“I could tell them you aren’t in. That I looked everywhere and—”

“I appreciate that, Randy. Tell them I’ll be down in a few minutes.”

*

The series of lectures Jeffery Griffen gave on the new proof by Wu of the Neumann Conjecture were well attended. There was some astonishment at how quickly he was able to prepare the material—especially for the impromptu talk the morning the proof was made public. The esoteric ideas seemed to be on the tip of Griffen’s tongue right from the beginning. Like all breakthrough work, Wu’s proof launched new lines of research. A cottage industry of Neumann spin-offs quickly emerged, and Griffen contributed a paper himself on certain details of the manifold problem that Wu had overlooked. But the glory went to Wu when the Fields Medal that year was awarded, with a citation that mentioned “a signal contribution to set theory through a demonstration of one of the great unsolved problems of twenty-first century mathematics.” Griffen sent him a congratulatory note and invited him to speak on campus; Wu declined curtly, replying that a number of other institutions, which of course meant more prestigious institutions, had already made the same request.

The chairman attended Griffen’s lectures. In fact he organized them. He addressed respectful questions to his former friend inside the colloquium room but not outside. Even so Griffen took this as a sign of a thaw, and perhaps commiseration. The chairman knew of Griffen’s long history with the Conjecture, and as an old mathematician he had had his share of reversals. A few years ago he’d been a victim of Mancuso. But the Invalidator did not even take a shot at the hottest new theorem, as big a target as it was. The argument, as Griffen knew well, was airtight.

Griffen didn’t mind working in the wake of Wu’s famous paper. The pickings were easy and the mathematics was enjoyable. Now that the pressure of making history was gone the work was a kind of leisure, and he did it in moderation.

Leaving the building early one day he saw from behind a large man with an impressive head of white hair and a tattered leather bag. He was walking quickly, lost in thought, and Griffen almost let him go, as he had for the last year. But the day was fine—spring had come, finally—and he was in an expansive mood. He called out to his old friend..

“David!”

The chairman looked up, stopped—and smiled.

“Jeffery.”

“I’m going your way,” said Griffen.

“And it looks like I’m going yours.”

They left the path and walked where the ground was soft and uncertain. There were still shadowy places where snow lingered, as it would through late May.

“I’ve been hearing nothing but good things about your teaching,” said the chairman.

“I’m rediscovering an old pleasure.”

“Excellent. For years you were the most popular guy in the department.”

“Thanks. I like to think we take our teaching seriously at the college.”

“Damn right.”

“Which I suppose implies that you’re going to give me less of it?”

The chairman’s heavy jowls moved with amusement. From somewhere in the high branches of the elms just coming into bud came the song of a bird, a masterful improvisation Griffen remembered from previous springs. He had never seen the bird and couldn’t see it now.

“I think you’ll be happy with the new teaching assignments, Jeffery. Now I want to ask you something.”

“Nothing technical, I hope. I’m off duty.”

“Were you one of the reviewers for the Wu paper?”

“No.”

“So you didn’t get an early look at it?”

“I saw it when you saw it. A bit later, actually. A student brought it to me.”

“Yes. Young Lawson. He has something, you know.”

“Yes he does. He wants to go into the field.”

“I wrote him a strong recommendation this morning,” said the chairman. “To Harvard, no less. Whether I’m doing him a favor or not I have no idea.”

“You have to wonder,” Griffen said, “if he knows what he’s getting himself into.”

The chairman smiled sagely. “Of course he doesn’t. Did you?”

A mound of snow appeared in their path and the two mathematicians leaped over it with the agility of younger men. Soon they reached the point of parting.

“You know I proved it, David. The Conjecture.”

“I thought so. How did Wu beat you to the punch?”

“Bad luck.”

“I feel for you, Jeffery. I’ve been there myself. We all have.”

Griffen thought to differ, but he said only, “Thanks, David, but I wouldn’t shed any tears.”

*   *   *

It was in the pocket of his pajamas, where it had been through several washes. He must have put it there unconsciously that night. With some sadness he noted that he would have looked in the pocket if he’d known pajamas had pockets. It was one of an infinity of things he didn’t know. The scrap was folded and brittle. He spread it out with care and saw that the elegant equation, now known as Wu’s Theorem, was still legible. This did not surprise him. All this devilish human ingenuity—he was thinking of modern detergents but also of clever and petty mathematicians—could never wash away a truth so eternal.

The author would like to thank the Editors of The Notre Dame Review for permission to reprint this work.