CHAPTER 1

Thursday, December 16 -- Friday, December 17

Lisbeth Salander pulled her sunglasses down to the tip of her nose and squinted from beneath the brim of her sun hat. She saw the woman from room 32 come out of the hotel side entrance and walk to one of the green-and-white-striped chaises-longues beside the pool. Her gaze was fixed on the ground and her progress seemed unsteady.

Salander had only seen her at a distance. She reckoned the woman was around thirty-five, but she looked as though she could be anything from twenty-five to fifty. She had shoulder-length brown hair, an oval face, and a body that was straight out of a mail-order catalogue for lingerie. She had a black bikini, sandals, and purple-tinted sunglasses. She spoke with a southern American accent. She dropped a yellow sun hat next to the chaise-longue and signalled to the bartender at Ella Carmichael's bar.

Salander put her book down on her lap and sipped her iced coffee before reaching for a pack of cigarettes. Without turning her head she shifted her gaze to the horizon. She could just see the Caribbean through a group of palm trees and the rhododendrons in front of the hotel. A yacht was on its way north towards St Lucia or Dominica. Further out, she could see the outline of a grey freighter heading south in the direction of Guyana. A breeze made the morning heat bearable, but she felt a drop of sweat trickling into her eyebrow. Salander did not care for sunbathing. She had spent her days as far as possible in shade, and even now was under the awning on the terrace. And yet she was as brown as a nut. She had on khaki shorts and a black top.

She listened to the strange music from steel drums flowing out of the speakers at the bar. She could not tell the difference between Sven-Ingvars and Nick Cave, but steel drums fascinated her. It seemed hardly feasible that anyone could tune an oil barrel, and even less credible that the barrel could make music like nothing else in the world. She thought those sounds were like magic.

She suddenly felt irritated and looked again at the woman, who had just been handed a glass of some orange-coloured drink.

It was not Lisbeth Salander's problem, but she could not comprehend why the woman stayed. For four nights, ever since the couple had arrived, Salander had listened to the muted terror being played out in the room next door to hers. She had heard crying and low, excitable voices, and sometimes the unmistakable sound of slaps. The man responsible for the blows -- Salander assumed he was her husband -- had straight dark hair parted down the middle in an old-fashioned style, and he seemed to be in Grenada on business. What kind of business, Salander had no idea, but every morning the man had appeared with his briefcase, in a jacket and tie, and had coffee in the hotel bar before he went outside to look for a taxi.

He would come back to the hotel in the late afternoon, when he took a swim and sat with his wife by the pool. They had dinner together in what on the surface seemed to be a quiet and loving way. The woman may have had a few too many drinks, but her intoxication was not noisome.

Each night the commotion in the next-door room had started just as Salander was going to bed with a book about the mysteries of mathematics. It did not sound like a full-on assault. As far as Salander could tell through the wall, it was one repetitive, tedious argument. The night before, Salander had not been able to contain her curiosity. She had gone on to the balcony to listen through the couple's open balcony door. For more than an hour the man had paced back and forth in the room, going on about what a shit he was, that he did not deserve her. Again and again he said that she must think him a fraud. No, she would answer, she did not, and tried to calm him. He became more intense, and seemed to give her a shake. So at last she gave him the answer he wanted . . . You're right, you are a fraud. And this he at once took as a pretext to berate her. He called her a whore, which was an accusation that Salander would have taken measures to combat if it had been directed at her. It had not been, but nevertheless she thought for a long time about whether she ought to take some sort of action.

Salander had listened in astonishment to this rancorous bickering, which all of a sudden ended with something that sounded like a slap in the face. She had been on the point of going into the hotel corridor to kick in her neighbours' door when silence descended over the room.

Now, as she scrutinized the woman by the pool, she could see a faint bruise on her shoulder and a scrape on her hip, but no other injury.

Some months earlier Salander had read an article in a Popular Science that someone had left behind at Leonardo da Vinci Airport in Rome, and she developed a vague fascination with the obscure topic of spherical astronomy. On impulse she had made her way to the university bookshop in Rome to buy some of the key works on the subject. To be able to get a grasp of spherical astronomy, however, she had had to immerse herself in the deeper mysteries of mathematics. In the course of her travels in recent months she had been to other university bookshops to seek out more books.

Her studies had been unsystematic and without any real objective, at least until she wandered into the university bookshop in Miami and came out with Dimensions in Mathematics, by Dr L. C. Parnault (Harvard University Press, 1999). That was just before she went down to the Florida Keys and began island-hopping through the Caribbean.

She had been to Guadeloupe (two nights in a hideous dump), Dominica (fun and relaxed, five nights), Barbados (one night at an American hotel where she felt terribly unwelcome), and St Lucia (nine nights). She would have considered staying longer had she not made an enemy of a slow-witted young hoodlum who haunted the bar of her backstreet hotel. Finally she lost patience and whacked him on the head with a brick, checked out of the hotel, and took a ferry to St George's, the capital of Grenada. This was a country she had never heard of before she bought her ticket for the boat.

She had come ashore on Grenada in a tropical rainstorm at 10.00 one November morning. From The Caribbean Traveller she learned that Grenada was known as Spice Island and was one of the world's leading producers of nutmeg. The island had a population of 120,000, but another 200,000 Grenadians lived in the United States, Canada, or Britain, which gave some indication of the employment market in their homeland. The terrain was mountainous around a dormant volcano, Grand Etang.

Grenada was one of many small, former-British colonies. In 1795, Julian Fedon, a black planter of mixed French ancestry, led an uprising inspired by the French Revolution. Troops were sent to shoot, hang or maim a considerable number of the rebels. What had shaken the colonial regime was that even poor whites, so-called petits blancs, had joined Fedon's rebellion without the least regard for racial boundaries. The uprising was crushed, but Fedon was never captured; he vanished into the mountainous Grand Etang and became a Robin Hood-like legend.

Some two hundred years later, in 1979, a lawyer called Maurice Bishop started a new revolution which the guidebook said was inspired by the Communist dictatorships in Cuba and Nicaragua. But Salander was given a different picture of things when she met Philip Campbell -- teacher, librarian, and Baptist preacher. She had taken a room in his guesthouse for the first few days. The gist of it was that Bishop was a popular folk leader who had deposed an insane dictator, a U.F.O. nutcase who had devoted part of the meagre national budget to chasing flying saucers. Bishop had lobbied for economic democracy and introduced the country's first legislation for sexual equality. And then in 1983 he was assassinated.

There followed a massacre of more than a hundred people, including the Foreign Minister, the Minister for Women's Affairs, and some senior trade union leaders. Then the United States invaded the country and set up a democracy. As far as Grenada was concerned, this meant that unemployment rose from around 6 per cent to almost 50 per cent, and that the cocaine trade once more became the largest single source of income. Campbell shook his head in dismay at the description in Salander's guidebook and gave her some tips on the kinds of people and the neighbourhoods she should avoid after dark.

In Salander's case, such advice normally fell on deaf ears. However, she had avoided making the acquaintance of the criminal element on Grenada by falling in love with Grand Anse Beach, just south of St George's, a sparsely populated beach that went on for miles. There she could walk for hours without having to talk to or even encounter another living soul. She moved to the Keys, one of the few American hotels on Grand Anse, and stayed for seven weeks, doing little more than walking on the beach and eating the local fruit, called chin-ups, which reminded her of sour Swedish gooseberries -- she found them delightful.

It was the off season, and barely a third of the rooms at the Keys Hotel were occupied. The only problem was that both her peace and quiet and her preoccupation with mathematical studies had been disturbed by the subdued terror in the room next door.

Mikael Blomkvist rang the doorbell of Salander's apartment on Lundagatan. He did not expect her to open the door, but he had fallen into the habit of calling at her apartment every week or so to see whether anything had changed. He lifted the flap on the letterbox and could see the same heap of junk mail. It was late, and too dark to make out how much the pile might have grown since his last visit.

He stood on the landing for a moment before turning on his heel in frustration. He returned unhurriedly to his own apartment on Bellmansgatan, put on some coffee and looked through the evening papers before the late T.V. news Rapport came on. He was irritated and depressed not to know where Salander was. He felt stirrings of unease and wondered for the thousandth time what had happened.

He had invited Salander to his cabin in Sandhamn for the Christmas holidays. They had gone for long walks and calmly discussed the repercussions of the dramatic events in which they had both been involved over the past year, when Blomkvist went through what he came to think of as an early mid-life crisis. He had been convicted of libel and spent two months in prison, his professional career as a journalist had been in the gutter, and he had resigned from his position as publisher of the magazine Millennium more or less in disgrace. But at that point everything had turned around. A commission to write a biography of the industrialist Henrik Vanger -- which he had regarded as an absurdly well-paid form of therapy -- had turned into a terrifying hunt for a serial killer.

During this manhunt he had met Salander. Blomkvist unconsciously stroked the faint scar that the noose had left beneath his left ear. Salander had not only helped him to track down the killer -- she had saved his life.

Time and again she had amazed him with her odd talents -- she had a photographic memory and phenomenal computer skills. Blomkvist considered himself virtually computer illiterate, but Salander handled computers as if she had made a pact with the Devil. He had come to realize that she was a world-class hacker, and within an exclusive international community devoted to computer crime at the highest level -- and not only to combating it -- she was a legend. She was known online only as Wasp.

It was her ability to pass freely into other people's computers that had given him the material which transformed his professional humiliation into what was to be "the Wennerström affair" -- a scoop that a year later was still the subject of international police investigations into unsolved financial crimes. And Blomkvist was still being invited to appear on T.V. talk shows.

At the time, a year ago, he had thought of the scoop with colossal satisfaction -- as vengeance and as rehabilitation. But the satisfaction had soon ebbed. Within a few weeks he was sick and tired of answering the same questions from journalists and the financial police. I am sorry, but I am not able to reveal my sources. When a reporter from the English-language Azerbaijan Times had come all the way to Stockholm to ask him the same questions, it was the last straw. Blomkvist cut the interviews to a minimum, and in recent months he relented only when the woman from She on T.V.4 talked him into it, and that had happened only because the investigation had apparently moved into a new phase.

Blomkvist's cooperation with the woman from T.V.4 had another dimension. She had been the first journalist to pounce on the story, and without her programme on the evening that Millennium released the scoop, it might not have made the impact it did. Only later did Blomkvist find out that she had had to fight tooth and nail to convince her editor to run it. There had been massive resistance to giving any prominence to "that clown" at Millennium, and right up to the moment she went on air, it was far from certain that the battery of company lawyers would give the story the all-clear. Several of her more senior colleagues had given it the thumbs down and told her that if she was wrong, her career was over. She stood her ground, and it became the story of the year.

She had covered the story herself that first week -- after all, she was the only reporter who had thoroughly researched the subject -- but some time before Christmas Blomkvist noticed that all the new angles in the story had been handed over to male colleagues. Around New Year Blomkvist heard through the grapevine that she had been elbowed out, with the excuse that such an important story should be handled by experienced financial reporters, and not some little girl from Gotland or Bergslagen or wherever the hell she was from. The next time T.V.4 called, Blomkvist explained frankly that he would talk to them only if "she" asked the questions. Days of sullen silence went by before the boys at T.V.4 capitulated.

Blomkvist's waning interest in the Wennerström affair coincided with Salander's disappearance from his life. He still could not understand what had happened.

They had parted two days after Christmas and he had not seen her for the rest of the week. On the day before New Year's Eve he telephoned her, but there was no answer.

On New Year's Eve he went twice to her apartment and rang the bell. The first time there had been lights on, but she had not answered the door. The second time there were no lights. On New Year's Day he called her again, and still there was no answer, but he did get a message from the telephone company saying that the subscriber could not be reached.

He had seen her twice in the next few days. When he could not get hold of her on the telephone, he went to her apartment in early January and sat down to wait on the steps beside her front door. He had brought a book with him, and he waited stubbornly for four hours before she appeared through the main entrance, just before 11.00 at night. She was carrying a brown box and stopped short when she saw him.

"Hello, Lisbeth," he said, closing his book.

She looked at him without expression, no sign of warmth or even friendship in her gaze. Then she walked past him and stuck her key in the door.

"Aren't you going to offer me a cup of coffee?" he said.

She turned and said in a low voice: "Get out of here. I don't want to see you ever again."

Then she shut the door in his face, and he heard her lock it from the inside. He was bewildered.

Three days later, he had taken the tunnelbana from Slussen to T-Centralen, and when the train stopped in Gamla Stan he looked out of the window and she was standing on the platform not two metres away. He caught sight of her at the exact moment the doors closed. For five seconds she stared right through him, as though he were nothing but air, before she turned and walked out of his field of vision as the train began to move.

The implication was unmistakable. She wanted nothing to do with him. She had cut him out of her life as surgically and decisively as she deleted files from her computer, and without explanation. She had changed her mobile phone number and did not answer her email.

Blomkvist sighed, switched off the T.V., and went to the window to gaze out at City Hall.

Perhaps he was making a mistake in going to her apartment from time to time. Blomkvist's attitude had always been that if a woman clearly indicated that she did not want anything more to do with him, then he would go on his way. Not respecting such a message would, in his eyes, show a lack of respect for her.

Blomkvist and Salander had slept together. It had been at her initiative, and it had gone on for half a year. If it were her decision to end the affair -- as surprisingly as she had started it -- then that was O.K. with Blomkvist. It was her decision to make. He had no difficulty with the role of ex-boyfriend -- if that is what he was -- but Salander's total repudiation of him was astonishing.

He was not in love with her -- they were about as unlike as two people could possibly be -- but he was very fond of her and really missed her, as exasperating as she sometimes was. He had thought their liking was mutual. In short, he felt like an idiot.

He stood at the window a long time.

Finally he decided. If Salander thought so little of him that she could not even bring herself to greet him when they saw each other in the tunnelbana, then their friendship was apparently over and the damage irreparable. He would make no attempt to contact her again.

Salander looked at her watch and realized that although she was sitting, perfectly still, in the shade, she was drenched with sweat. It was 10.30. She memorized a mathematical formula three lines long and closed her book, Dimensions in Mathematics. Then she picked up her key and the pack of cigarettes on the table.

Her room was on the third floor, which was also the top floor of the hotel. She stripped off her clothes and got into the shower.

A green lizard twenty centimetres long was staring at her from the wall just below the ceiling. Salander stared back but made no move to shoo it away. There were lizards everywhere on the island. They came through the blinds at the open window, under the door, or through the vent in the bathroom. She liked having company that left her alone. The water was almost ice-cold, and she stayed under the shower for five minutes to cool off.

When she came back into the room she stood naked in front of the mirror on the wardrobe door and examined her body with amazement. She still weighed only forty kilos and stood one metre twenty-four centimetres tall. Well, there was not much she could do about that. She had doll-like, almost delicate limbs, small hands, and hardly any hips.

But now she had breasts.

All her life she had been flat-chested, as if she had never reached puberty. She thought it had looked ridiculous, and she was always uncomfortable showing herself naked.

Now, all of a sudden, she had breasts. They were by no means gigantic -- that was not what she had wanted, and they would have looked ridiculous on her otherwise skinny body -- but they were two solid, round breasts of medium size. The enlargement had been well done, and the proportions were reasonable. But the difference was dramatic, both for her looks and for her self-confidence.

She had spent five weeks in a clinic outside Genoa getting the implants that formed the structure of her new breasts. The clinic and the doctors there had absolutely the best reputation in all of Europe. Her own doctor, a charmingly hard-boiled woman named Alessandra Perrini, had told her that her breasts were abnormally underdeveloped, and that the enlargement could therefore be performed for medical reasons.

Recovery from the operation had not been painless, but her breasts looked and felt completely natural, and by now the scars were almost invisible. She had not regretted her decision for a second. She was pleased. Even six months later she could not walk past a mirror with her top off without stopping and feeling glad that she had improved her quality of life.

During her time at the clinic in Genoa she had also had one of her nine tattoos removed -- a 25-centimetre-long wasp -- from the right side of her neck. She liked her tattoos, especially the dragon on her left shoulder blade. But the wasp was too conspicuous and it made her too easy to remember and identify. Salander did not want to be remembered or identified. The tattoo had been removed by laser treatment, and when she ran her index finger over her neck she could feel the slight scarring. Closer inspection would reveal that her suntanned skin was a shade lighter where the tattoo had been, but at a glance nothing was noticeable. Her stay in Genoa had cost her 190,000 kronor.1

Which she could afford.

She stopped dreaming in front of the mirror and put on her knickers and bra. Two days after she had left the clinic in Genoa she had for the first time in her twenty-five years gone to a lingerie boutique and bought the garments she had never needed before. Since then she had turned twenty-six, and now she wore a bra with a certain amount of satisfaction.

She put on jeans and a black T-shirt with the slogan: "Consider this a fair warning." She found her sandals and sun hat and slung a black bag over her shoulder.

Crossing the lobby, she heard a murmur from a small group of hotel guests at the front desk. She slowed down and pricked up her ears.

"Just how dangerous is she?" said a black woman with a loud voice and a European accent. Salander recognized her as one of a charter group from London who had been there for ten days.

Freddy McBain, the greying reception manager who always greeted Salander with a friendly smile, looked worried. He was telling them that instructions would be issued to all guests and that there was no reason to worry as long as they followed all the instructions to the letter. He was met by a hail of questions.

Salander frowned and went out to the bar, where she found Ella Carmichael behind the counter.

"What's all that about?" she said, motioning with her thumb towards the front desk.

"Matilda is threatening to visit us."

"Matilda?"

"Matilda is a hurricane that formed off Brazil a few weeks ago and tore straight through Paramaribo yesterday, that's the capital of Surinam. No-one's quite sure what direction it's going to take -- probably further north towards the States. But if it goes on following the coast to the west, then Trinidad and Grenada will be smack in its path. So it might get a bit windy."

"I thought the hurricane season was over."

"It is. It's usually September and October. But these days you never can tell, because there's so much trouble with the climate and the greenhouse effect and all that."

"O.K. But when's Matilda supposed to arrive?"

"Soon."

"Is there something I should do?"

"Lisbeth, hurricanes are not for playing around with. We had one in the seventies that caused a lot of destruction here on Grenada. I was eleven years old and lived in a town up in the Grand Etang on the way to Grenville, and I will never forget that night."

"Hmm."

"But you don't need to worry. Stay close to the hotel on Saturday. Pack a bag with things you wouldn't want to lose -- like that computer you're always playing with -- and be prepared to take it along if we get instructions to go down to the storm cellar. That's all."

"Right."

"Would you like something to drink?"

"No thanks."

Salander left without saying goodbye. Ella Carmichael smiled, resigned. It had taken her a couple of weeks to get used to this odd girl's peculiar ways and to realize that she was not being snooty -- she was just very different. But she paid for her drinks without any fuss, stayed relatively sober, kept to herself, and never caused any trouble.

The traffic on Grenada consisted mainly of imaginatively decorated minibuses that operated with no particular timetable or other formalities. The shuttle ran during the daylight hours. After dark it was pretty much impossible to get around without your own car.

Salander had to wait only a few minutes on the road to St George's before one of the buses pulled up. The driver was a Rasta, and the bus's sound system was playing "No Woman, No Cry" full blast. She closed her ears, paid her dollar, and squeezed in next to a substantial woman with grey hair and two boys in school uniform.

St George's was located on a U-shaped bay that formed the Carenage, the inner harbour. Around the harbour rose steep hills dotted with houses and old colonial buildings, with Fort Rupert perched all the way out on the tip of a precipitous cliff.

St George's was a compact and tight-knit town with narrow streets and many alleyways. The houses climbed up every hillside, and there was hardly a flat surface larger than the combined cricket field and racetrack on the northern edge of the town.

She got off at the harbour and walked to MacIntyre's Electronics at the top of a short, steep slope. Almost all the products sold on Grenada were imported from the United States or Britain, so they cost twice as much as they did elsewhere, but at least the shop had air conditioning.

The extra batteries she had ordered for her Apple PowerBook (G4 titanium with a 43 cm screen) had finally arrived. In Miami she had bought a Palm PDA with a folding keyboard that she could use for email and easily take with her in her shoulder bag instead of dragging around her PowerBook, but it was a miserable substitute for the 43 cm screen. The original batteries had deteriorated and would run for only half an hour before they had to be recharged, which was a curse when she wanted to sit out on the terrace by the pool, and the electrical supply on Grenada left a lot to be desired. During the weeks she had been there, she had experienced two long black-outs. She paid with a credit card in the name of Wasp Enterprises, stuffed the batteries in her shoulder bag and headed back out into the midday heat.

She paid a visit to Barclays Bank and withdrew $300, then went down to the market and bought a bunch of carrots, half a dozen mangos, and a 1.5-litre bottle of mineral water. Her bag was much heavier now, and by the time she got back to the harbour she was hungry and thirsty. She considered the Nutmeg first, but the entrance to the restaurant was jammed with people already waiting. She went on to the quieter Turtleback at the other end of the harbour. There she sat on the veranda and ordered a plate of calamari and chips with a bottle of Carib, the local beer. She picked up a discarded copy of the Grenadian Voice and looked through it for two minutes. The only thing of interest was a dramatic article warning about the possible arrival of Matilda. The text was illustrated with a photograph showing a demolished house, a reminder of the devastation wrought by the last big hurricane to hit the island.

She folded the paper, took a swig from the bottle of Carib, and then she saw the man from room 32 come out on to the veranda from the bar. He had his brown briefcase in one hand and a big glass of Coca-Cola in the other. His eyes swept over her without recognition before he sat on a bench at the other end of the veranda and fixed his gaze on the water beyond.

He seemed utterly preoccupied and sat there motionless for seven minutes, Salander observed, before he raised his glass and took three deep swallows. Then he put down the glass and resumed his staring out to sea. After a while she opened her bag and took out Dimensions in Mathematics.

All her life Salander had loved puzzles and riddles. When she was nine her mother gave her a Rubik's cube. It had put her abilities to the test for barely forty frustrating minutes before she understood how it worked. After that she never had any difficulty solving the puzzle. She had never missed the daily newspapers' intelligence tests; five strangely shaped figures and the puzzle was how the sixth one should look. To her, the answer was always obvious.

In primary school she had learned to add and subtract. Multiplication, division and geometry were a natural extension. She could add up the bill in a restaurant, create an invoice, and calculate the path of an artillery shell fired at a certain speed and angle. That was easy. But before she read the article in Popular Science she had never been intrigued by mathematics or even thought about the fact that the multiplication table was maths. It was something she memorized one afternoon at school, and she never understood why the teacher kept banging on about it for the whole year.

Then, quite suddenly, she sensed the inexorable logic that must reside behind the reasoning and formulae, and that led her to the mathematics section of the university bookshop. But it was not until she started on Dimensions in Mathematics that a whole new world opened to her. Mathematics was actually a logical puzzle with endless variations -- riddles that could be solved. The trick was not in solving arithmetical problems. Five times five would always be twenty-five. The trick was to understand combinations of the various rules that made it possible to solve any mathematical problem whatsoever.

Dimensions in Mathematics was not strictly a textbook, rather it was a 1200-page brick about the history of mathematics from the ancient Greeks to modern-day attempts to understand spherical astronomy. It was considered the Bible, in a class with what the Arithmetica of Diophantus had meant (and still did mean) to serious mathematicians. When she opened Dimensions in Mathematics for the first time on the terrace of the hotel on Grand Anse Beach, she was enticed into an enchanted world of figures. This was a book written by an author who was both pedagogical and able to entertain the reader with anecdotes and astonishing problems. She could follow mathematics from Archimedes to today's Jet Propulsion Laboratory in California. She had taken in the methods they used to solve problems.

Pythagoras' equation (x2 + y2 = z2), formulated five centuries before Christ, was an epiphany. At that moment Salander understood the significance of what she had memorized in secondary school from some of the rather few classes she had attended. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. She was fascinated by Euclid's discovery in about 300 B.C. that a perfect number is always a multiple of two numbers, in which one number is a power of 2 and the second consists of the difference between the next power of 2 and 1. This was a refinement of Pythagoras' equation, and she could see the endless combinations.

= 21 x (22 - 1)

8 = 22 x (23 - 1)

96 = 24 x (25 - 1)

8128 = 26 x (27 - 1)

She could go on indefinitely without finding any number that would break the rule. This was a logic that appealed to Salander's sense of the absolute. She advanced through Archimedes, Newton, Martin Gardner, and a dozen other classical mathematicians with unmixed 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 beguiling, 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 per cent 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, as was his wont, 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 to look 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 gathering 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 down the glass on the bar. She had long since realized that crappy pink drinks with stupid umbrellas were not Salander's style. She ordered always 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 which 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 O.K.?"

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 G.P.?"

"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 set-up she could send and receive email. She typed a message to

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 P.G.P. key, encrypted the message with Plague's P.G.P. 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 metres 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 metres 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 formulae.

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 on to 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 had 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 and pushed him roughly on to 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 did not give a damn what other people thought of her, 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 turned the lamp back on. She watched his reactions closely as clumsily he began to touch her. 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 had not thought of ever 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 metres behind.

He always did that. She had never slept all night 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 MacIntyre's 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 metres 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 were 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.

----------------------