Part 4 (2/2)

Yes? Humboldt leafed in the astronomical almanac, took up his pencil, and began to calculate. So what was it now?

Did one always have to be so German?

NUMBERS.

On the day everything changed, one of his molars was hurting so much he thought he'd go insane. In the night he had lain on his back, listening to the landlady snoring next door. At about six thirty in the morning, as he blinked wearily into the dawn light, he discovered the solution to one of the oldest problems in the world.

He went staggering through the room like a drunk. He must write it down immediately, he must not forget it. The drawer didn't want to open, suddenly the paper had hidden itself from him, his quill broke off and made blotches, and then the next thing to trip him up was the chamber pot. But after half an hour of scribbling there it all was on some crumpled piece of paper, the margins of a Greek textbook, and the tabletop. He laid his pen aside. He was breathing heavily. He realized that he was naked, and registered the dirt on the floor and the stink with surprise. He was freezing. His toothache was almost unbearable.

He read. Worked his way through it, followed the proof line by line, looked for errors, and didn't find any. He roamed over the last page and looked at his distorted, smeared, seventeen-sided figure. For more than two thousand years, people had been constructing regular triangles and pentangles with ruler and compa.s.ses. To construct a square or to double the angles of a polygon was child's play. And if one combined a triangle and a pentangle, what one got was a fifteen-sided figure. More was impossible.

And now: seventeen. And he had a hunch there was a method that would allow him to go further. But he would have to find it.

He went to the barber, who tied his hands tight, promised it really wouldn't be bad, and with one quick movement pushed his pincers into his mouth. The very touch of them, a blinding flash of pain, almost made him faint. He tried to gather his thoughts, but then the pincers took hold, something went click click in his head, and it was the taste of blood and the pounding in his ears that brought him back to the room and the man with the ap.r.o.n, who was saying it hadn't been so bad, had it? in his head, and it was the taste of blood and the pounding in his ears that brought him back to the room and the man with the ap.r.o.n, who was saying it hadn't been so bad, had it?

On his way home he had to lean against walls, his knees were weak, his feet weren't under control, and he felt dizzy. In another few years there would be doctors for teeth, then it would be possible to cure this kind of pain and you wouldn't have to have every inflamed tooth pulled. Soon the world would no longer be full of the toothless. And everybody wouldn't have pockmarks, and n.o.body would lose their hair. He was amazed that n.o.body else ever thought about these things. People thought everything was naturally the way it was. Eyes glazed, he made his way to Zimmerman's rooms.

Entering without knocking, he laid the pieces of paper out in front of him on the dining table.

Oh, said the professor sympathetically, teeth, bad? He himself had been lucky, he'd only lost five, Professor Lichtenberg was left with a mere two, and Kastner had been toothless for years. With the tips of his fingers, because of a bloodstain, he picked up the first sheet. His brow furrowed. His lips moved.It went on so long that Gauss could hardly believe it any more. n.o.body could take that long to think!

This is a great moment, said Zimmerman finally.

Gauss asked for a gla.s.s of water.

He felt like praying. This must be printed, and it would be best if it appeared under the name of a professor. It wasn't the done thing for students to be publis.h.i.+ng on their own.

Gauss tried to reply, but when Zimmerman brought him the gla.s.s of water, he could neither speak nor drink. He made a gesture of apology, wobbled home, lay down in bed, and thought about his mother up there in Brunswick. It had been a mistake to come to Gottingen. The university here was better, but he missed his mother, and even more so when he was ill. At about midnight, when his cheek had swollen still further and every movement in every part of his body hurt, he realized the barber had pulled the wrong tooth.

Luckily the streets were still empty in the early morning so n.o.body saw him stopping continually to lean his head against the house walls and sob. He would have given his soul to live a hundred years later when there would be medications for pain and doctors who deserved the name. Nor was it that hard. All that was necessary was to numb the nerves in the right spot, the best thing would be little doses of poison. Curare needed to be researched better! There was a flask of it in the Inst.i.tute of Chemistry, he would go and have a look. But his thoughts slid away from him and he was only more aware of his own groaning.

It happens, said the barber cheerfully. Pain spread itself wide, but Nature was intelligent and man came with plenty of teeth. At the moment when he pulled the tooth, everything around Gauss went black.

As if the pain had wiped the event from his memory or from time itself, he found himself hours or days later-how could he tell-back in the chaos of his bed, with a half-empty bottle of schnapps on the night table and at his feet the Universal Advertiser Universal Advertiser and and Literary Supplement Literary Supplement, in which Privy Councilor Zimmerman laid out the latest method for constructing a regular seventeen-sided figure. And sitting beside the bed was Bartels, who had come to congratulate him.

Gauss fingered his cheek. Oh, Bartels. He knew all about it. He himself came out of poverty, had been considered a wunderkind, and believed himself chosen for great things. Then he had met him, Gauss. And he knew, meanwhile, that for the next two nights after they met, Bartels had lain awake and thought about whether he should go back to the village, milk cows, and muck out stalls. Sometime during the third night, he had realized that there was only one way to save himself: he would have to like Gauss. He would have to help him, no matter where it led. From that moment on, he had thrown all his strength into working with Gauss, he had talked to Zimmerman, written letters to the duke, and one difficult evening, by means of threats none of them wanted to remember, he had got Gauss's father to agree to let his son go to high school. And the next summer he had gone with Gauss to visit his parents in Brunswick. Suddenly the mother had taken him aside, her face small with worry and shyness, to ask if there was any future for her son at the university with all the educated people. Bartels hadn't understood. What she meant was, did Carl have any future researching things? She was asking in confidence, and promised not to repeat anything. As a mother, one always had worries. Bartels had remained silent for a while, before asking with a contempt which shamed him later if she didn't know that her son was the greatest scientist in the world. She had wept and wept, and it had been extremely embarra.s.sing. Gauss had never succeeded in forgiving Bartels.

He had come to a decision, said Gauss.

For what? Bartels looked up distractedly.

Gauss gave an impatient sigh. For mathematics. Until now he had wanted to concentrate on cla.s.sical philology, and he still liked the idea of writing a commentary on Virgil, in particular Aeneas' descent to the underworld. He felt that n.o.body yet had correctly understood this chapter. But there would still be time for that, after all he had only just turned nineteen. But above all he had realized that he could achieve more in mathematics. If one had to be born, even if n.o.body had bothered to ask, then one could at least try to accomplish something. For example, solving the question of what a number is. The foundation of arithmetic.

A life's work, said Bartels.

Gauss nodded. With a little luck he'd be finished in five years.

But soon he realized it would go faster than that. Once he had begun, ideas came crowding in with a force he hadn't experienced before. He barely slept, he stopped going to the university, ate the bare minimum, and rarely went to visit his mother. When he wandered through the streets murmuring to himself, he felt he had never been so awake. Without looking where he was going, he avoided b.u.mping into people, he never stumbled, once he leapt to one side for no reason at all and wasn't even surprised when a roof tile landed in the same second at his feet and shattered. Numbers didn't seduce one away from reality, they brought reality closer, made it clearer and more meaningful in a way it had never been before.

Numbers were his constant companions now. He thought of them even when he was visiting wh.o.r.es. There weren't that many in Gottingen, they all knew him, greeted him by name, and sometimes gave him a discount because he was young, good-looking, and well-mannered. The one he liked best was called Nina and came from a distant town in Siberia. She lived in the old lying-in house, was dark-haired, with big dimples in her cheeks and broad shoulders that smelled of the earth; when he was holding her tight, looking up at the ceiling as he felt her rocking on him, he promised he would marry her and learn her language. She laughed at him, and when he swore that he meant it, she answered that he was still very young.

The examination for his doctorate was supervised by Professor Pfaff In response to his scribbled request, he was exempted from the oral exam, as it would have been quite risible. When he went to collect the doc.u.ment itself, he had to wait in the corridor. He ate a piece of dry cake and read the Gottingen Scholars' Bulletin Gottingen Scholars' Bulletin, which contained a report by a German diplomat about his brother's visit to New Andalusia. A white house on the edge of town, evenings cooling off in the river, women who came frequently to visit to have their lice counted. He turned the pages with a vague excitement. Naked Indians in the Chaymas mission, birds that lived in caves and used their voices to see, the way other creatures use eyesight. The great eclipse of the sun, then the departure for the Orinoco. The man's letter had taken eighteen months to arrive, and only G.o.d knows whether he was still alive. Gauss lowered the newspaper, Zimmerman and Pfaff were standing in front of him. They hadn't dared to disturb him.

That man, he said, impressive! But crazy too, as if truth was something you found out there and not here. Or as if you could run away from yourself.

Pfaff hesitantly handed him the doc.u.ment: pa.s.sed, summa summa c.u.m laude. c.u.m laude. Of course. People were saying, said Zimmerman, that some great work was in progress. He was delighted that Gauss had found something that could occupy his interest and dispel his melancholy. Of course. People were saying, said Zimmerman, that some great work was in progress. He was delighted that Gauss had found something that could occupy his interest and dispel his melancholy.

Yes, he was working on something of the kind, said Gauss, and when it was done, he would be going.

The two professors exchanged glances. Leaving the Electorate of Hannover? They did hope not.

No, said Gauss, please not to worry. He would be going far, but not out of the Electorate of Hannover.

The work advanced quickly. The law of quadratic reciprocity was worked out, and the riddle of the frequency of prime numbers came closer to a solution. He had completed the first three sections and was already into the main part. But again and again he laid his quill aside, propped his head in his hands, and wondered whether there was a proscription against what he was doing. Was he digging too deep? At the base of physics were rules, at the base of rules there were laws, at the base of laws there were numbers; if one looked at them intently, one could recognize relations.h.i.+ps between them, repulsions or attractions. Some aspects of their construction seemed incomplete, occasionally hastily thought out, and more than once he thought he recognized roughly concealed mistakes-as if G.o.d had permitted Himself to be negligent and hoped n.o.body would notice.

Then the day came when he had no more money. As he was no longer a student, his stipendium had run out. The duke had never been pleased that he had gone to Gottingen, so there was no question of an extension.

He could get relief, said Zimmerman. By chance there was a job, a temporary one; they needed an industrious young man to help with land surveying.

Gauss shook his head.

It wouldn't last long, said Zimmerman. And fresh air never hurt anybody.

Which was how he found himself unexpectedly stumbling through the countryside in the rain. The sky was low and dark, the earth was muddy. He climbed over a hedge and landed panting, sweating, and strewn with pine needles in front of two girls. Asked what he was doing here, he nervously expounded the technique of triangulation: if you knew one side and two angles of a triangle, you could work out the other sides and the unknown angle. So you picked a triangle somewhere out here on G.o.d's good earth, measured the side that was most easily accessible, and then used this gadget to establish the angle of the third corner. He lifted the theodolite and turned it this way, and then this way, and do you see, like this, with awkward fingers, as if doing it for the first time. Then you fit together a whole series of these triangles. A Prussian scientist was in the process of doing exactly this among all the fabulous creatures in the New World.

But a landscape isn't a flat surface, retorted the bigger of the two.

He stared at her. There had been no pause. As if she had needed no time to think it over. Certainly not, he said, smiling.

A triangle, she said, had one hundred and eighty degrees as the sum of its angles on a flat surface; but it was on a sphere, so this was no longer true. Everything would stand or fall based on that.

He looked her up and down as if seeing her for the first time. She returned his look with raised eyebrows. Yes, he said. So. In order to even things out, you had to scrunch the triangles, so to speak, after measuring them until they were infinitely small. In and of itself, a simple exercise in differentials. Although in this form ... He sat down on the ground and took out his pad. In this form, he murmured, as he began making notes, it's never been worked out in this form yet. When he looked up, he was alone.

For several weeks he went on crisscrossing the region with the geodetic implements, ramming stakes into the ground and measuring their relative distances. Once he rolled down a slope and dislocated his shoulder, more than once he fell into stinging nettles, and one afternoon when winter had almost arrived, a horde of children hurled dirty s...o...b..a.l.l.s at him. When a sheepdog bounded out of a wood, bit into his calf almost gently, and vanished again like a ghost, he decided this must stop. He was ill-suited to such dangers.

But he saw Johanna quite often now. It seemed as if she had always been somewhere nearby, only hidden from him by camouflage or lapses in his attention span. She walked ahead of him in the street, and it was as if his wish that she stop was enough to make her slow her step. Or she sat in church three rows behind him looking tired but concentrated as the pastor laid out their future d.a.m.nation if they failed to make Christ's suffering their own, his cares their cares, his blood their blood; Gauss had long since given up wondering what this was supposed to mean, and was quite aware of how sarcastically she would look at him if he turned around now.

Once they went for a walk outside the town with her silly, perpetually sn.i.g.g.e.ring friend Minna. They talked about new books he didn't know, how often it rained, the future of the Directory in Paris. Johanna often answered him before he'd finished speaking. He thought about seizing her and pulling her down onto the ground, and knew for sure that she could read his thoughts. Did they have to go through all this hypocrisy? Of course it was necessary, and when he accidentally touched her hand, he made a deep bow, as the n.o.bility did, and she made a curtsey. On the way home he wondered if the day would ever come when people could deal with one another without lying. But before he could pursue that thought, he realized that every number could be expressed as the sum of three triangular numbers. Hands shaking, he groped for his pad, but he had left it at home by accident, and had to keep murmuring the formula softly to himself until they reached the next inn, where he tore a slate pencil out of the waiter's hand and scrawled it down on the tablecloth.

After that he never left his rooms. The days turned to evenings, the evenings to nights, which soaked up watery light in the early hours until day began again, all of it apparently as a matter of course. But it wasn't, death could arrive in a flash, he had to hurry. Sometimes Bartels came, bringing food. Sometimes his mother came. She stroked his head, looked at him with eyes swimming with love, and flushed with joy if he kissed her on the cheek. Then Zimmerman appeared, asked if he needed help with his work, saw his look, and went his way, mumbling in embarra.s.sment. Letters from Lichtenberg, b.u.t.tner, and the secretary of the duke arrived; he didn't read any of them. Twice he had diarrhea, toothache three times, and one night such violent colic that he thought here it was, G.o.d wouldn't permit him to do this, the end was near. Another night, science, his work, his whole life all suddenly seemed strange and superfluous to him because he had no friend and no one apart from his mother to whom he meant anything. But that too pa.s.sed, like everything else.

And then one rainy day, he was finished. He laid down his pen, blew his nose with extreme precision, and ma.s.saged his forehead. Already the memories of the last months, all the struggles, the decisions, the intellectual effort, were a thing of the past. They were the experiences of someone he suddenly no longer was. In front of him was the ma.n.u.script that this previous self had left behind, hundreds of tightly written pages. He leafed through it and asked himself how he could have pulled it off. He recalled no inspiration, no flashes of illumination. Just work.

The costs of having it printed meant he had to borrow from Bartels, who was almost penniless himself. Then there were problems when he insisted on reproofing the typeset pages personally; the idiot of a bookseller simply didn't understand that no one else was capable. Zimmerman wrote to the duke, who disgorged a little more money, and the Disquisitiones Arithmeticae Disquisitiones Arithmeticae could appear. He had just turned twenty and his life's work was done. He knew: however long he remained on earth, he would never be able to achieve something comparable again. could appear. He had just turned twenty and his life's work was done. He knew: however long he remained on earth, he would never be able to achieve something comparable again.

He wrote a letter requesting Johanna's hand in marriage, and was refused. It was nothing to do with him personally, she wrote, it was just that she doubted anyone could exist side by side with him. She suspected he absorbed life and strength from the people around him the way the earth absorbed the sun or the sea absorbed the rivers, and that his company would condemn her to the pallid semi-unreality of a ghostly existence.

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