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 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 elementary 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 math. It was something she memorized one afternoon at school, and she never understood why the teacher kept going on about it for the whole year.
Then, suddenly, she sensed the inexorable logic that must reside behind the reasoning and the formulas, 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 to solve 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 but rather a 1,200-page brick about the history of mathematics from the ancient Greeks to modern-day attempts to understand spherical astronomy. It was considered the bible of math, 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 few classes she had attended. In a right 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 BC 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.
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