Fermat's Last Theorem Read Online Free Page A

explain.
    Life, Prince Leon, may well be compared with these public Games for in the vast crowd assembled here some are attracted by the acquisition of gain, others are led on by the hopes and ambitions of fame and glory. But among them there are a few who have come to observe and to understand all that passes here.
    It is the same with life. Some are influenced by the love of wealth while others are blindly led on by the mad fever for power and domination, but the finest type of man gives himself up to discovering the meaning and purpose of life itself. He seeks to uncover the secrets of nature. This is the man I call a philosopher for although no man is completely wise in all respects, he can love wisdom as the key to nature’s secrets.
    Although many were aware of Pythagoras’ aspirations nobody outside of the Brotherhood knew the details or extent of his success. Each member of the school was forced to swear an oath never to reveal to the outside world any of their mathematical discoveries. Even after Pythagoras’ death a member of the Brotherhood was drowned for breaking his oath – he publicly announced the discovery of a new regular solid, the dodecahedron, constructed from twelve regular pentagons. The highly secretive nature of the Pythagorean Brotherhood is part of the reason that myths have developed surrounding the strange rituals which they might havepractised, and similarly this is why there are so few reliable accounts of their mathematical achievements.
    What is known for certain is that Pythagoras established an ethos which changed the course of mathematics. The Brotherhood was effectively a religious community and one of the idols they worshipped was Number. By understanding the relationships between numbers, they believed that they could uncover the spiritual secrets of the universe and bring themselves closer to the gods. In particular the Brotherhood focused its attention on the study of counting numbers (1, 2, 3, …) and fractions. Counting numbers are sometimes called
whole numbers
, and together with fractions (ratios between whole numbers) are technically referred to as
rational numbers.
Among the infinity of numbers, the Brotherhood looked for those with special significance, and some of the most special were the so-called ‘perfect’ numbers.
    According to Pythagoras numerical perfection depended on a number’s divisors (numbers which will divide perfectly into the original one). For instance, the divisors of 12 are 1, 2, 3, 4 and 6. When the sum of a number’s divisors is greater than the number itself, it is called an ‘excessive’ number. Therefore 12 is an excessive number because its divisors add up to 16. On the other hand, when the sum of a number’s divisors is less than the number itself, it is called ‘defective’. So 10 is a defective number because its divisors (1, 2 and 5) add up to only 8.
    The most significant and rarest numbers are those whose divisors add up exactly to the number itself and these are the
perfect numbers.
The number 6 has the divisors 1, 2 and 3, and consequently it is a perfect number because 1 + 2 + 3 = 6. The next perfect number is 28, because 1 + 2 + 4 + 7 + 14 = 28.
    As well as having mathematical significance for the Brotherhood, the perfection of 6 and 28 was acknowledged byother cultures who observed that the moon orbits the earth every 28 days and who declared that God created the world in 6 days. In
The City of God
, St Augustine argues that although God could have created the world in an instant he decided to take six days in order to reflect the universe’s perfection. St Augustine observed that 6 was not perfect because God chose it, but rather that the perfection was inherent in the nature of the number: ‘6 is a number perfect in itself, and not because God created all things in six days; rather the inverse is true; God created all things in six days because this number is perfect. And