Sitting at his desk, within his small office on the third floor of Foggity Hall, Professor Paul Lundmire worked arduously on the problem before him: how to get these rascally elliptic equations to behave. He poured all his energy into his task, for it was one key to the most profound problem he had ever tackled. Yet the difficulty of the work did not discourage him, for while working, he occupied a realm somewhat offset from our third dimension, offset by a well defined, yet spiritual amount, connecting him to the world of rational ideas. Within this strange dimension, he wallowed in bliss.
Suddenly, he was aware of a rapping at his office door. Professor Lundmire decided not to respond to the knocking. He knew he was being rude, and that whoever stood outside and patiently tapped on the frosted glass window should be let in, but he had important work to do. After all, it probably wasn’t another staff member, or even an administrator (he shuddered), but only some lowly student, come to beg for a better math grade. Well, he was busy, and doing important work, and simply would not open the door.
“Paul,” came an all too familiar voice, “are you in there? Open up, we’ve got to talk.”
‘Jesus,’ thought Lundmire, ‘it’s Stanley Shelldig.’ The division head for the Science and Mathematics Department could not be ignored. He quickly rose and hurried to the door. Opening it a crack, he peeked out. “Sorry, Stan,” he muttered, as he stepped back and let the large blond man into his office. “I was working and didn’t hear you.”
Shelldig walked around the office, looking at the great clutter of books and papers collecting dust on bookshelves and two desks crammed into the small space. “Don’t you ever clean this place?” asked Shelldig.
Abruptly Paul realized that his Department Head was looking for a place to sit. He hurried to an old oak captain’s chair and brushed a stack of ungraded term papers onto the floor. “Here, sit down, Stan, let’s talk. We never have time to talk. We’re getting some good work done on the Riemann problem. We are still…”
Shelldig held up his hand as he interrupted. “Yes, yes, I know. You’ve told me, and your crazy graduate student, Vinh, has told me. That’s why I’m here. Don’t you ever answer your voice mail? I’ve been trying to get in touch with you all week. Now the committee meets tomorrow. They’re going to review your progress to see if you can justify continued funding…”
Alarm buzzed through Paul like a skill saw. He jumped up and raised his hands over his head, as if, in his hurry to speak, they had no place to go and would dangle at the end of his arms until needed. “Stan, we must have more time! We’re close, but not that close. The Riemann hypothesis, well, you know how tough it is. It’s the last great unsolved problem…”
“Yes, yes, I know all that,” said Shelldig. “But you must realize that you’ve been using a lot of computer time. I thought mathematicians didn’t need computers, that they solved everything with pencil and paper.”
Paul shook his head. “That was in the old days. Of course we’re not using the computer to prove anything, but we need some better estimates of T.” He quickly walked to his chalkboard, and not wanting to erase anything already there, he found a small blank space on the far right. Scribbling symbols he slipped into his magic realm. “You see, Stan, we have to project the critical strip onto a sphere. That way, all the non-trivial zeros will be projected into a finite space. If one is off the line…”
Shelldig stood. “Yes, yes, you’ve told me. But Paul, you have to realize that the committee likes results. If you could just discover a new element, or maybe design a new motor that used less gas, something useful. I know this Riemann thing is important, but important to whom? Riemann has been dead for over a hundred years and no one has proved his crazy hypothesis yet. How important can it be?” He walked to the door and opened it. “Now you show up tomorrow to tell the committee what’s going on. It would also help if you told them you were almost done with the computer. Computer time is damned expensive, and Vinh is always over at the center, bugging them for more access.”
As Paul stared at Stan Shelldig’s face, he realized that the administrator had light blue eyes. Why hadn’t he noticed that before? “I’ll try, Stan, but we need a little more time.”
Shelldig shook his head as he left Paul’s office. “You had better get it together, Paul. They want results. They’re ready to pull the plug and fund someone else.” And suddenly Shelldig was gone and the door was closed.
Paul sank back into his chair. ‘God,’ he thought, ‘we need more time, more computer time, lots more.’ He would have to talk to Vinh; Vinh would have to write some more efficient computer programs. Vinh could do it; he was the best graduate student that Paul had ever taught. Paul picked up the phone and dialed Vinh’s number, for he knew were Vinh had to be: either his office or the computer center.
“Yes,” came the student’s high voice.
“Vinh, it’s me. Do you have a better T yet? We need a better handle on T.”
“Yes, yes,” said Vinh in his heavy accent. “More T, better T. I get better T.”
“I need it tomorrow. The committee meeting, remember? It’s the 15th already.”
“Oh, no, not tomorrow, I need more time, more computer time. You give me more time, a week, no, a month. I get T then.”
“Vinh, you don’t understand, we have to show more progress.”
“This is hard problem, Professor Rundmire. It very very hard, very important problem, you know.”
“Yes, Vinh, but I have to show the committee that we’re making progress. I promised them we would. You do want to finish your degree, don’t you? Now we have to get a better T or alpha will just be all over the place.”
“You make it too hard, Professor. I need more constraints on T. You get better constraints, and I get T fast. You see.”
Damn, it was always the same: better this, and better that. “Okay, Vinh, I’ll try.”
“Yes, Professor, you get good constraints, and I do it in one run.”
“Can you do it tonight? Can you get the results tonight?”
“Yes, yes, tonight. You get constraints and computer runs fast. You see.”
“Yes, I will Vinh. I’ll call back.” He hung up the phone and stared at the chalkboard. It wasn’t the precise part of the problem he was working on, but that didn’t matter. This was a do-or-die situation: he had to find better constraints on the value of T so that Vinh could get a good estimate. Then the solution to the problem could go forward.
He walked to the board and, taking hold of the eraser, wiped two dozen formulas into oblivion. Could he do it? Could he do this job in one afternoon? Was he a world-class mathematician, in the league of Gauss and Cantor, or was he just a bubbled-brained dander-head, full of false dreams of glory? Well, the next few hours would tell the story. He selected a fresh piece of chalk and began in the upper left corner. By magic, Professor Paul Lundmire was transformed to his special fairyland, a land of odd charm and delight, a world where he felt neither pain nor fear, but only pure, unadulterated pleasure. From the fingers of his right hand flowed the symbols, arranging themselves in formulas upon the chalkboard.
He worked surely, confidently, moving along, going down some blind alleys, only to back up and begin again. Finally he came to a critical point, a mountaintop with no place to go. He needed some special insight to continue. Suddenly, and for no apparent reason, the vision of a three-legged dog came to him. This was certainly a special clue. One leg was missing, and he had to find it. It would be on some other mountaintop, off in the fog, but connected through sorcery to his current mountain. Was it a special generating function? Yes, of course. He began to scribble furiously, stretching himself. A generating function to produce all the alphas to constrain T, it was perfect. Slowly, with precision, the generating function displayed itself on the board. Paul’s delight was boundless; he’d never seen such a function before.
As he worked, as he drew ever closer to the final equation, he noticed something was different, he was slightly off balance. He stopped writing and looked at his left arm. It was gone! He looked at the chalk he held in his right hand. Yes, he’d started with two arms, but now had only one. How had he lost his arm? Was it the generating function? He looked at the chalkboard. Yes, that must be it! In his hast, he’d stepped too close to the board, and the generating function had somehow gobbled it up.
It all made sense as he remembered the different lives of the great mathematicians. Had so many not given of themselves in their quest within the magic realm? Did not Euler lose his sight for the corporeal world after seeing so much of the rational world? Had not Descartes and Riemann died relatively young? How about Ramanujan, the most brilliant mind of the twentieth century, hadn’t he died at just thirty-two? They all gave of themselves for their discoveries. Now he, Paul Lundmire, would join their ranks and be in the history books. He had given his left arm for the new function. It would be the Lundmire function, such a lovely name.
He glanced at his watch, but it was gone of course, gone with his arm. He looked at the wall clock; it was late, and Vinh would need the Lundmire function. He carefully scrutinized the board and decided that he had enough, enough for Vinh to make his computer run.
Paul dropped the chalk and picked up the phone. Without his left arm, he had to cradle the phone receiver against his shoulder and dial with his right hand. This now situation would require some slight adjustments. Vinh’s phone rang, but the answering machine came on. “This Mr. Vinh. Not here. Call back,” followed by a tone.
“Listen, Vinh, this is Lundmire. I have it, the constraints. It’s so easy, a generating function. Now, get a pencil and write this down.” Paul proceeded to read his new formula into the answering machine. “And remember, Vinh,” he concluded, “I need the results by morning; I need it for the meeting.”
There was nothing more to do. He had done the impossible and would gain an incredible victory the next day. Word would spread from Oldenbroken University: Lundmire had cracked the code; he’d solved the riddle and the Riemann hypothesis. Time to go home and get some much needed rest.
As he entered the foyer to his house he encountered his wife coming in the opposite direction. She stopped when see saw him. “Oh, hello dear, I was just leaving. Your dinner is in the kitchen.”
He was shaking with anticipation. “I did it, Louise, I solved the Riemann hypothesis. That is, I’m going to solve it. I’m so close. I found…”
But she wasn’t listening. She was sorting through advertising circulars she had picked up from a small desk. “Yes, dear, I’m sure you have. Now I have to run down to headquarters. We’re having a sit-in or something tonight. It’s all very important.”
He would try one more time. “Louise, I’ve achieved a monumental breakthrough, and I’ve lost my left arm.”
She looked at him and smiled. “I’m sure you have, dear. Now don’t forget to feed the cat, I may be late. Those rotten S.O.B.s at Grudenbloggen Meats refuse to stop killing those poor cows with those horrible electric rods. Why can’t they put them to sleep with some little humanity? The fight must go on, Paul.” She walked past him and to the front door.
“Louise, I’ve lost my left arm!”
She smiled, and he suddenly noticed that her eyes were hazel. “That’s nice dear,” and she was gone.
That night Paul was frantic with concern for he couldn’t reach Vinh to make sure he’d received the Lundmire function. Yet, Vinh’s answering machine was turned off, so his student must have received his message. That night he dreamt of the three-legged dog and a huge computer that Vinh was building. The computer was so large that it required the atoms from every star within the Milky Way Galaxy. Still the computer was too small!
Shaving and dressing for the meeting the next morning presented a set of small, but not trivial problems considering he had the use of only one arm and hand. But he persevered. Every few minutes he called Vinh’s office, without luck. He tried Vinh’s home number. Vinh’s wife answered. “He no here, Professor Rundmire, he no come home, he no at office. Where is he? What you do with him?”
Paul was confused. Why wasn’t Vinh at his office, or even the computer center? Jumping into his car, and driving with one arm, he visited both locations, and still Vinh was gone! At the computer center he heard a strange story from Fat Popper, the night supervisor. “Oh, yes, your man, Vinh, was here alright. He was most excited. He was jabbering and sweating like a cold potato. Said he was going to be famous. He submitted a big run, and then just vanished. Don’t know where he went.”
An icy fear began to circulate within Paul’s stomach. The Lundmire function had already claimed his arm. Had it gobbled up Vinh, accent and all? Was Vinh now drifting about within the ethereal dimension of rationality, living with and bumping into all the great ideas of the cosmos?
He would have to fake it at the committee meeting, for surely, Vinh had taken his secret with him. He hurried to the meeting room, stopping at the men’s lounge to tidy up his hair. Once inside, there was no hesitation as the committee asked for his progress. He sat before them, seven ever-serious souls dedicated to the task of rewards and punishments; punishments for those who fail to divine the truth, but great rewards for those who succeed.
A frontal attack would do the trick. “Ladies and gentlemen,” Paul began, “I have discovered a function so fundamental to all of mathematics that Oldenbroken University will be a star on every map, and a revered word spoken from every tongue.” He was, admittedly, pouring it on a little thick, but he knew they loved theatrics. “I have discovered the Lundmire function, a function that will lead to the solution of the Riemann hypothesis, the most important problem of all mathematics.”
Mrs. Smythe, the committee’s chairwoman, would have none of it. “But Lundmire, it was the Riemann hypothesis you claimed you could prove. Now, have you done it? And why do you have just one arm? Didn’t you once have two?”
“Precisely,” continued Paul. He extracted a piece of chalk from his suit pocket. “I will just demonstrate this on the board so you may all see.” He began writing the Lundmire function on the chalkboard. He could hear mumbled whispering behind him and realized the committee was impatient. Reaching the far right of the board, and the end of the Lundmire function, a veil opened in the center of his brain, as a new, yet unsuspected connection popped into his consciousness. “My God!” he exclaimed as the chalk dropped to the floor. He looked at the place his right arm used to be. He knew before his eyes registered the truth that his right arm, too, was gone. Yet, it too, was worth the sacrifice, for this new insight was better than the Lundmire function. It must be, in fact, part of the insight that sent Vinh to the nether world.
Paul turned to Stan Shelldig, whose shocked expression revealed that he’d witnessed the loss of Paul’s appendage. “Stan,” begged Paul, “If you don’t mind, could you place the chalk between my teeth? I have something rather wondrous to share with the committee.”
Stan picked up the chalk and held it before Paul’s face. “Really, Paul,” he muttered. “Is this necessary? My God, man, you have no arms!”
“Please indulge me for just a moment, Stan. I have such a beautiful connection to show the committee, something entirely new.”
Stan nodded and placed the chalk between Paul’s front teeth. With some difficulty, Paul stepped to the board, his face but an inch away, and began to write. He talked through his teeth and around the chalk as he did so. Bobbing his head up and down he managed to finish his wondrous new connection. It would be called the Lundmire connection. He had given up much for it, but the glory would be worth it.
The committee applauded and immediately granted Paul an extension on his funding. It was the complete victory he was seeking. Afterward, Stan had to drive Paul home, for armless, Paul could no longer operate a car. “I’m sure it will be awkward,” said Paul, “but I’m sure I’ll adjust to my new situation.”
Stan seemed to have other matters on his mind. “Paul, where is Vinh? He isn’t at home or the university. His wife has been calling, and just before I left for the meeting, I got a call from the police. They asked a number of pointed questions.”
“How many” asked Paul?
“How many what?”
“Questions, how many did they ask?”
“That doesn’t matter. What matters is that they evidently think you did something with Vinh.”
The interest of the police was quickly confirmed as Stan pulled into Paul’s driveway only to find a black and white squad car. Two very large policemen were waiting for Paul. They assisted him out of Stan’s car, and then one of them began to read him his rights. The other stood by, helplessly holding a pair of handcuffs. There was no dead body yet, they explained, but it was only a matter of time before they would find it, and then it would be prison for the vile Lundmire.
“You don’t understand,” pleaded Paul. “Vinh has gone elsewhere.”
“Where?” demanded one of the policemen.
Paul noticed that the policeman’s eyes were brown. “I can’t say exactly. It’s to a different place; it’s where my arms have gone. He lives in the world of ideas.”
“Yeah, sure,” muttered the placeman as he pushed Paul toward the squad car.
“What can I do to help?” offered Stan.
“Some chalk, Stan, bring me some chalk.”
Confusion and worry dancing on his face, Stan looked at a policeman. “Can I do that? Can he have chalk?”
“Sure, bring him chalk.”
“Anything else, Paul?”
“No, just chalk. That’s all I need, and a wall of course. I must go see Vinh. I must reveal the secret he carries.”
END