by Неизвестный
6 = 21x (22 − l)
28 = 22x (23 − l)
496 = 24x (25 − l)
8,128 = 26x (27 − l)
She could go on indefinitely without finding any number that would break the rule. This was a logic that appealed to her sense of the absolute. She advanced through Archimedes, Newton, Martin Gardner, and a dozen other classical mathematicians with unmitigated pleasure.
Then she came to the chapter on Pierre de Fermat, whose mathematical enigma, “Fermat’s Last Theorem,” had dumbfounded her for seven weeks. And that was a trifling length of time, considering that Fermat had driven mathematicians crazy for almost four hundred years before an Englishman named Andrew Wiles succeeded in unravelling the puzzle, as recently as 1993.
Fermat’s theorem was a beguilingly simple task.
Pierre de Fermat was born in 1601 in Beaumont-de-Lomagne in southwestern France. He was not even a mathematician; he was a civil servant who devoted himself to mathematics as a hobby. He was regarded as one of the most gifted self-taught mathematicians who ever lived. Like Salander, he enjoyed solving puzzles and riddles. He found it particularly amusing to tease other mathematicians by devising problems without supplying the solutions. The philosopher Descartes referred to Fermat by many derogatory epithets, and his English colleague John Wallis called him “that damned Frenchman.”
In 1621 a Latin translation was published of Diophantus’ Arithmetica which contained a complete compilation of the number theories that Pythagoras, Euclid, and other ancient mathematicians had formulated. It was when Fermat was studying Pythagoras’ equation that in a burst of pure genius he created his immortal problem. He formulated a variant of Pythagoras’ equation. Instead of (x2 + y2 = z2), Fermat converted the square to a cube, (x3 + y3 = z3).
The problem was that the new equation did not seem to have any solution with whole numbers. What Fermat had thus done, by an academic tweak, was to transform a formula which had an infinite number of perfect solutions into a blind alley that had no solution at all. His theorem was just that—Fermat claimed that nowhere in the infinite universe of numbers was there any whole number in which a cube could be expressed as the sum of two cubes, and that this was general for all numbers having a power of more than 2, that is, precisely Pythagoras’ equation.
Other mathematicians swiftly agreed that this was correct. Through trial and error they were able to confirm that they could not find a number that disproved Fermat’s theorem. The problem was simply that even if they counted until the end of time, they would never be able to test all existing numbers—they are infinite, after all—and consequently the mathematicians could not be 100 percent certain that the next number would not disprove Fermat’s theorem. Within mathematics, assertions must always be proven mathematically and expressed in a valid and scientifically correct formula. The mathematician must be able to stand on a podium and say the words This is so because …
Fermat, true to form, sorely tested his colleagues. In the margin of his copy of Arithmetica the genius penned the problem and concluded with the lines Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet. These lines became immortalized in the history of mathematics: I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.
If his intention had been to madden his peers, then he succeeded. Since 1637 almost every self-respecting mathematician has spent time, sometimes a great deal of time, trying to find Fermat’s proof. Generations of thinkers had failed until finally Andrew Wiles came up with the proof everyone had been waiting for. By then he had pondered the riddle for twenty-five years, the last ten of which he worked almost full-time on the problem.
Salander was at a loss.
She was actually not interested in the answer. It was the process of solution that was the point. When someone put a riddle in front of her, she solved it. Before she understood the principles of reasoning, the number mysteries took a long time to solve, but she always arrived at the correct answer before she looked it up.
So she took out a piece of paper and began scribbling figures when she read Fermat’s theorem. But she failed to find a proof for it.
She disdained the idea of looking at the answer key, so she bypassed the section that gave Wiles’ solution. Instead she finished her reading of Dimensions and confirmed that none of the other problems formulated in the book presented any overwhelming difficulties for her. Then she returned to Fermat’s riddle day after day with increasing irritation, wondering what was Fermat’s “marvellous proof.” She went from one dead end to another.
She looked up when the man from room 32 stood and walked towards the exit. He had been sitting there for two hours and ten minutes.
Ella Carmichael set the glass on the bar. She had long since realized that crappy pink drinks with stupid umbrellas were not Salander’s style. She always ordered the same drink, rum and Coke. Except for one evening when she had been in an odd mood and got so drunk that Ella had to call the porter to carry her to her room, her normal consumption consisted of caffè latte and a few drinks. Or Carib beer. As always, she sat at the far right end of the bar and opened a book that looked to have complicated lines of numbers in it, which in Ella’s eyes was a funny choice of reading for a girl of her age.
She also noticed that Salander did not appear to have the least interest in being picked up. The few lonely men who had made advances had been rebuffed kindly but firmly, and in one case not very kindly. Chris MacAllen, the man dispatched so brusquely, was a local wastrel who could have used a good thrashing. So Ella was not too bothered when he somehow stumbled and fell into the pool after bothering Miss Salander for an entire evening. To MacAllen’s credit, he did not hold a grudge. He came back the following night, all sobered up, and offered to buy Salander a beer, which, after a brief hesitation, she accepted. From then on they greeted each other politely when they saw each other in the bar.
“Everything OK?”
Salander nodded and took the glass. “Any news about Matilda?”
“Still headed our way. It could be a real bad weekend.”
“When will we know?”
“Actually not before she’s passed by. She could head straight for Grenada and then decide to swing north at the last moment.”
Then they heard a laugh that was a little too loud and turned to see the lady from room 32, apparently amused by something her husband had said.
“Who are they?”
“Dr. Forbes? They’re Americans from Austin, Texas.” Ella Carmichael said the word Americans with a certain distaste.
“I could tell they’re Americans, but what are they doing here? Is he a GP?”
“No, not that kind of doctor. He’s here for the Santa Maria Foundation.”
“What’s that?”
“They support education for talented children. He’s a fine man. He’s discussing a proposal for a new high school in St. George’s with the Ministry of Education.”
“He’s a fine man who beats his wife,” Salander said.
Ella gave Salander a sharp look and went to the other end of the bar to serve some local customers.
Salander stayed for ten minutes with her nose in Dimensions. She had known that she had a photographic memory since before she reached puberty, and because of it she was very different from her classmates. She had never revealed this to anyone—except to Blomkvist in a moment of weakness. She already knew the text of Dimensions in Mathematics by heart and was dragging the book around mainly because it represented a physical link to Fermat, as if the book had become some kind of talisman.
But this evening she could not concentrate on Fermat or his theorem. Instead she saw in her mind Dr. Forbes sitting motionless, gazing at the same distant point in the sea at the Carenage.
She could not have explained why she knew that something was not right.
Finally she closed the book, went back to her room, and booted up her PowerBook. Surfing the Internet did not call for
any thinking. The hotel did not have broadband, but she had a built-in modem that she could hook up to her Panasonic mobile phone and with that setup she could send and receive email. She typed a message to [email protected]:
No broadband here. Need info on a Dr. Forbes with the Santa Maria Foundation, and his wife, living in Austin, Texas. $500 to whoever does the research. Wasp.
She attached her public PGP key, encrypted the message with Plague’s PGP key, and sent it. Then she looked at the clock and saw that it was just past 7:30 p.m.
She turned off her computer, locked her door, and walked four hundred yards along the beach, past the road to St. George’s, and knocked on the door of a shack behind the Coconut.
George Bland was sixteen and a student. He intended to become a lawyer or a doctor or possibly an astronaut, and he was just as skinny as Salander and only a little taller. Salander had met him on the beach the day after she moved to Grand Anse. She had sat down in the shade under some palms to watch the children playing football by the water. She was engrossed in Dimensions when the boy came and sat in the sand a few yards away from her, apparently without noticing she was there. She observed him in silence. A thin black boy in sandals, black jeans, and a white shirt.
He too had opened a book and immersed himself in it. Like her, he was reading a mathematics book—Basics 4. He began to scribble in an exercise book. Five minutes later, when Salander cleared her throat, he jumped up with a start. He apologized for bothering her and was on the brink of being gone when she asked him if what he was working on were complicated formulas.
Algebra. After a minute she had shown him an error in his calculation. After half an hour they had finished his homework. After an hour they had gone through the whole of the next chapter in his textbook and she had explained the trick behind the arithmetical operations as though she were his tutor. He had looked at her awestruck. After two hours he told her that his mother lived in Toronto, that his father lived in Grenville on the other side of the island, and that he himself lived in a shack a little way along the beach. He was the youngest in the family, with three older sisters.
Salander found his company surprisingly relaxing. The situation was unusual. She hardly ever began conversations with strangers just to talk. It was not a matter of shyness. For her, a conversation had a straightforward function. How do I get to the pharmacy? or How much does the hotel room cost? Conversation also had a professional function. When she worked as a researcher for Dragan Armansky at Milton Security, she had never minded having a long conversation if it was to ferret out facts.
On the other hand, she disliked personal discussions, which always led to snooping around in areas she considered private. How old are you? Guess. Do you like Britney Spears? Who? What do you think of Carl Larsson’s paintings? I’ve never given them a thought. Are you a lesbian? Piss off.
This boy was gawky and self-conscious, but he was polite and tried to have an intelligent conversation without competing with her or poking his nose into her life. Like her, he seemed lonely. He appeared to accept without puzzlement that a goddess of mathematics had descended onto Grand Anse Beach, and with pleasure that she would keep him company. They got up as the sun sank to the horizon. They walked together towards her hotel, and he pointed out the shack that was his student quarters. Shyly he asked if he might invite her to tea.
The shack contained a table that was cobbled together, two chairs, a bed, and a wooden cabinet for clothes. The only lighting was a desk lamp with a cable that ran to the Coconut. He had a camp stove. He offered her a meal of rice and vegetables, which he served on plastic plates. Boldly he even offered her a smoke of the local forbidden substance, which she also accepted.
Salander could not help noticing that he was affected by her presence and did not know how he should treat her. She, on a whim, decided to let him seduce her. It developed into a painfully roundabout procedure in which he certainly understood her signals but had no idea how to react to them. Finally she lost patience, pushed him roughly onto the bed, and took off her shirt and jeans.
It was the first time she had shown herself naked to anyone since the operation in Italy. She had left the clinic with a feeling of panic. It took her a long while to realize that no-one was staring at her. Normally she didn’t give a damn what other people thought, and she did not worry about why she felt nervous now.
Young Bland had been a perfect initiation for her new self. When at last (after some encouragement) he managed to unfasten her bra, he immediately switched off the lamp before undressing himself. Salander could tell that he was shy, and she turned the lamp back on. She watched his reactions closely as he began to touch her clumsily. Only much later did she relax, certain that he thought her breasts were natural. On the other hand, it was unlikely he had much to compare them to.
She had not planned to get herself a teenage lover on Grenada. It had been an impulse, and when she left him late that night she didn’t consider going back. But the next day she ran into him on the beach and realized that the clumsy boy was pleasant company. For the seven weeks she lived on Grenada, George Bland became a regular part of her life. They did not spend time together during the day, but they spent the hours before sundown on the beach and the evenings alone in his shack.
She was aware that when they walked together they looked like two teenagers. Sweet sixteen.
He evidently thought that life had become much more interesting. He had met a woman who was teaching him about mathematics and eroticism.
He opened the door and smiled delightedly at her.
“Would you like company?” she said.
Salander left the shack just after two in the morning. She had a warm feeling in her body and strolled along the beach instead of taking the road to the Keys Hotel. She walked alone in the dark, knowing that Bland would be a hundred yards behind.
He always did that. She had never slept over at his place, and he often protested that she, a woman all alone, should not be walking back to her hotel at night. He insisted it was his duty to accompany her back to the hotel. Especially when it was very late, as it often was. Salander would listen to his objections and then cut the discussion off with a firm no. I’ll walk where I want, when I want. And no, I don’t want an escort. The first time she caught him following her she was really annoyed. But now she thought his wanting to protect her was rather sweet, so she pretended that she did not know he was there behind her or that he would turn back when he saw her go in the door of the hotel.
She wondered what he would do if she were attacked.
She would make use of the hammer she had bought at a hardware store and kept in the outside pocket of her shoulder bag. There were not so many physical threats that could not be countered with a decent hammer, Salander thought.
There was a full moon and the stars were sparkling. Salander looked up and identified Regulus in Leo near the horizon. She was almost at the hotel terrace when she stopped short. She had caught sight of someone near the waterline below the hotel. It was the first time she had seen a living soul on the beach after dark. He was almost a hundred yards off, but Salander knew at once who it was there in the moonlight.
It was the fine Dr. Forbes from room 32.
She took three quick steps into the shadow of a tree. When she turned her head, Bland was invisible too. The figure at the water’s edge was walking slowly back and forth. He was smoking a cigarette. Every so often he would stop and bend down as if to examine the sand. This pantomime continued for twenty minutes before he turned and with rapid steps walked to the hotel’s beach entrance and vanished.
Salander waited for a few minutes before she went down to where Dr. Forbes had been. She made a slow semicircle, inspecting the sand. All she could make out was pebbles and some shells. After a few minutes she broke off her search and went back to the hotel.
On her balcony, she leaned over the railing and peered in her neighbours’ door. All was quiet. The evening’s argument was obviously over. After a
while she took from her shoulder bag some papers to roll a joint from the supply that Bland had given her. She sat down on a balcony chair and gazed out at the dark water of the Caribbean as she smoked and thought.
She felt like a radar installation on high alert.
CHAPTER 2
Friday, December 17
Advokat Nils Erik Bjurman set down his coffee cup and watched the flow of people outside the window of Café Hedon on Stureplan. He saw everyone passing in an unbroken stream, but observed none of them.
He was thinking of Lisbeth Salander. He thought often about Salander.
What he was thinking made him boil with rage.
Salander had crushed him. He was never going to forget it. She had taken command and humiliated him. She had abused him in a way that had left indelible marks on his body. On an area the size of a book below his navel. She had handcuffed him to his bed, abused him, and tattooed him with I AM A SADISTIC PIG, A PERVERT, AND A RAPIST.
Stockholm’s district court had declared Salander legally incompetent. He had been assigned to be her guardian, which made her inescapably dependent on him. From the first time he met her he had fantasized about her. He could not explain it, but she seemed to invite that response.
What he had done—he, a fifty-five-year-old lawyer—was reprehensible, indefensible by any standard. He knew that, of course. But from the moment he’d laid eyes on Salander in December two years earlier, he had not been able to resist her. The laws, the most basic moral code, and his responsibility as her guardian—none of it mattered at all.