Free Fermat's Last Theorem by Simon Singh Page A

books which made up the
Arithmetica
, only six would survive the turmoils of the Dark Ages and go on to inspire the Renaissance mathematicians, including Pierre de Fermat. The remaining seven books would be lost during a series of tragic events which would send mathematics back to the age of the Babylonians.
    During the centuries between Euclid and Diophantus, Alexandria remained the intellectual capital of the civilised world, but throughout this period the city was continually under threat from foreign armies. The first major attack occurred in 47 BC , when Julius Caesar attempted to overthrow Cleopatra by setting fire to the Alexandrian fleet. The Library, which was located near the harbour, also caught alight, and hundreds of thousands of books were destroyed. Fortunately for mathematics Cleopatra appreciated the importance of knowledge and was determined to restore the Library to its former glory. Mark Antony realised that the way to an intellectual’s heart is via her library, and so marched to the city of Pergamum. This city had already initiated a library which it hoped would provide it with the best collection in the world, but instead Mark Antony transplanted the entire stock to Egypt, restoring the supremacy of Alexandria.
    For the next four centuries the Library continued to accumulate books until in AD 389 it received the first of two fatal blows, both the result of religious bigotry. The Christian Emperor Theodosius ordered Theophilus, Bishop of Alexandria, to destroy all pagan monuments. Unfortunately when Cleopatra rebuilt and restocked the Library, she decided to house it in the Temple of Serapis, and so the Library became caught up in the destruction of icons and altars. The ‘pagan’ scholars attempted to save six centuries-worth of knowledge, but before they could do anything they were butchered by the Christian mob. The descent into the Dark Ages had begun.
    A few precious copies of the most vital books survived the Christian onslaught and scholars continued to visit Alexandria in search of knowledge. Then in 642 a Moslem attack succeededwhere the Christians had failed. When asked what should be done with the Library, the victorious Caliph Omar commanded that those books that were contrary to the Koran should be destroyed, and furthermore those books that conformed to the Koran were superfluous and they too must be destroyed. The manuscripts were used to stoke the furnaces which heated the public baths and Greek mathematics went up in smoke. It is not surprising that most of Diophantus’ work was destroyed; in fact it is a miracle that six volumes of the
Arithmetica
managed to survive the tragedy of Alexandria.
    For the next thousand years mathematics in the West was in the doldrums, and only a handful of luminaries in India and Arabia kept the subject alive. They copied the formulae described in the surviving manuscripts of Greece and then began to reinvent for themselves many of the theorems that had been lost. They also added new elements to mathematics, including the number zero.
    In modern mathematics zero performs two functions. First, it allows us to distinguish between numbers like 52 and 502. In a system where the position of a number denotes its value, a symbol is needed to confirm an empty position. For instance, 52 represents 5 times ten plus 2 times one, whereas 502 represents 5 times a hundred plus 0 times ten plus 2 times one, and the zero is crucial for removing any ambiguity. Even the Babylonians in the third millennium BC appreciated the use of zero to avoid confusion, and the Greeks adopted their idea, using a circular symbol similar to the one we use today. However, zero has a more subtle and deeper significance which was only fully appreciated several centuries later by the mathematicians of India. The Hindus recognised that zero had an independent existence beyond the mere spacing role among the other numbers – zero was a number in its own right. It represented a