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 Plague_xyz_666@hotmail.com: