Free Fermat's Last Theorem by Simon Singh Page B

quantity of nothing. For the first time the abstractconcept of nothingness had been given a tangible symbolic representation.
    This may seem a trivial step forward to the modern reader, but the deeper meaning of the zero symbol had been ignored by all the ancient Greek philosophers, including Aristotle. He had argued that the number zero should be outlawed because it disrupted the consistency of the other numbers – dividing any ordinary number by zero led to an incomprehensible result. By the sixth century the Indian mathematicians no longer brushed this problem under the rug, and the seventh-century scholar Brahmagupta was sophisticated enough to use division by zero as a definition for infinity.
    While Europe had abandoned the noble search for truth, India and Arabia were consolidating the knowledge which had been smuggled out of the embers of Alexandria and were reinterpreting it in a new and more eloquent language. As well as adding zero to the mathematical vocabulary, they replaced the primitive Greek symbols and cumbersome Roman numerals with the counting system which has now been universally adopted. Once again, this might seem like an absurdly humble step forward, but try multiplying CLV by DCI and you will appreciate the significance of the breakthrough. The equivalent task of multiplying 155 by 601 is a good deal simpler. The growth of any discipline depends on the ability to communicate and develop ideas, and this in turn relies on a language which is sufficiently detailed and flexible. The ideas of Pythagoras and Euclid were no less elegant for their awkward expression, but translated into the symbols of Arabia they would blossom and give fruit to newer and richer concepts.
    In the tenth century the French scholar Gerbert of Aurillac learnt the new counting system from the Moors of Spain and through his teaching positions at churches and schools throughout Europe he was able to introduce the new system to the West.In 999 he was elected Pope Sylvester II, an appointment which allowed him to further encourage the use of Indo-Arabic numerals. Although the efficiency of the system revolutionised accounting and was rapidly adopted by merchants, it did little to inspire a revival in European mathematics.
    The vital turning point for Western mathematics occurred in 1453 when the Turks ransacked Constantinople. During the intervening years the manuscripts which had survived the desecration of Alexandria had congregated in Constantinople, but once again they were threatened with destruction. Byzantine scholars fled westward with whatever texts they could preserve. Having survived the onslaught of Caesar, Bishop Theophilus, Caliph Omar and now the Turks, a few precious volumes of the
Arithmetica
made their way back to Europe. Diophantus was destined for the desk of Pierre de Fermat.
Birth of a Riddle
    Fermat’s judicial responsibilities occupied a great deal of his time, but what little leisure he had was devoted entirely to mathematics. This was partly because judges in seventeenth-century France were discouraged from socialising on the grounds that friends and acquaintances might one day be called before the court. Fraternising with the locals would only lead to favouritism. Isolated from the rest of Toulouse’s high society, Fermat could concentrate on his hobby.
    There is no record of Fermat ever being inspired by a mathematical tutor; instead it was a copy of the
Arithmetica
which became his mentor. The
Arithmetica
sought to describe the theory of numbers, as it was in Diophantus’ time, via a series of problemsand solutions. In effect Diophantus was presenting Fermat with one thousand years worth of mathematical understanding. In one book Fermat could find the entire knowledge of numbers as constructed by the likes of Pythagoras and Euclid. The theory of numbers had stood still ever since the barbaric burning of Alexandria, but now Fermat was ready to resume study of the most fundamental of