The Girl Who Played with Fire Read Online Free PDF Page A

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 scientificallycorrect 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 consistedof 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