Fermat's Last Theorem by Simon Singh

as eagles sustain themselves in the wind.’
    Leonhard Euler was born in Basle in 1707, the son of a Calvinist pastor, Paul Euler. Although the young Euler showed a prodigious talent for mathematics, his father was determined that he should study theology and pursue a career in the Church. Leonhard dutifully obeyed and studied theology and Hebrew at the University of Basle.
    Fortunately for Euler the town of Basle was also home to the eminent Bernoulli clan. The Bernoullis could easily claim to be the most mathematical of families, creating eight of Europe’s most outstanding minds within only three generations – some have said that the Bernoulli family was to mathematics what the Bach family was to music. Their fame spread beyond the mathematical community and one particular legend typifies the profile of the family. Daniel Bernoulli was once travelling across Europe and had struck up a conversation with a stranger. After a while he modestlyintroduced himself: ‘I am Daniel Bernoulli.’ ‘And I,’ said his companion sarcastically, ‘am Isaac Newton.’ Daniel fondly recalled this incident on several occasions, considering it the most sincere tribute he had ever received.
    Daniel and Nikolaus Bernoulli were close friends of Leonhard Euler, and they realised that the most brilliant of mathematicians was being turned into the most mediocre of theologians. They appealed to Paul Euler and requested that Leonhard be allowed to forsake the cloth in favour of numbers. Euler senior had in the past been taught mathematics by Bernoulli senior, Jakob, and had a tremendous respect for the family. Reluctantly he accepted that his son had been born to calculate, not preach.
    Leonhard Euler soon left Switzerland for the palaces of Berlin and St Petersburg, where he was to spend the bulk of his creative years. During the era of Fermat, mathematicians were considered amateur number-jugglers, but by the eighteenth century they were treated as professional problem-solvers. The culture of numbers had changed dramatically, and this was partly a consequence of Sir Isaac Newton and his scientific calculations.
    Newton believed that mathematicians were wasting their time teasing each other with pointless riddles. Instead he would apply mathematics to the physical world and calculate everything from the orbits of the planets to the trajectories of cannon-balls. By the time Newton died, in 1727, Europe had undergone a scientific revolution, and in the same year Euler published his first paper. Although the paper contained elegant and innovative mathematics, it was primarily aimed at describing a solution to a technical problem regarding the masting of ships.
    The European powers were not interested in using mathematics to explore esoteric and abstract concepts; instead they wanted to exploit mathematics to solve practical problems, and they competedto employ the best minds. Euler began his career with the Czars, before being invited to the Berlin Academy by Frederick the Great of Prussia. Eventually he returned to Russia, under the rule of Catherine the Great, where he spent his final years. During his career he tackled a multitude of problems, ranging from navigation to finance, and from acoustics to irrigation. The practical world of problem-solving did not dull Euler’s mathematical ability. Instead tackling each new task would inspire him to create innovative and ingenious mathematics. His single-minded passion drove him to write several papers in a single day, and it is said that between the first and second calls for dinner he would attempt to dash off a complete calculation worthy of publication. Not a moment was wasted and even when he was cradling an infant in one hand Euler would be outlining a proof with the other.
    One of Euler’s greatest achievements was the development of the algorithmic method. The point of Euler’s algorithms was to tackle apparently impossible problems. One such problem