The Girl Who Played with Fire Read Online Free Page B

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
(x 2 + y 2 = z 2 )
, 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 = 2 1
x
(2 2 − l)
      28 = 2 2
x
(2 3 − l)
     496 = 2 4
x
(2 5 − l)
    8,128 =
2 6 x
(2 7 − 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
(x 2 + y 2 = z 2 )
, Fermat converted the square to a cube,
(x 3 + y 3 = z 3 )
.
    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