We learn all we know about the author of the famous theorem in "chapter zero" of Kitty Ferguson's book. An Ionian Greek by origin, Pythagoras of Samos emigrated to the West when the advance of the Persian power to the Aegean threatened the liberties of the Asiatic Greek, and settled in the Italian city of Croton around 530 BC. We have no idea when he was born. But he was probably in his forties when he made his name as a teacher and religious leader in Croton, where he became entangled in local politics. Powerful enemies forced him to flee to the Greek city of Metapontum, where he died around 500 BC.
During his stay in Croton, Pythagoras thought about the structure of the world. He and his followers began to experiment with music. While playing the lyre, they noticed that some combination of string lengths produced beautiful sounds, while others did not. They also noticed a connection between lyre string lengths and human ears.
The ratios that underlie musical harmony, they realised, are rather common. In a Eureka moment, they discovered that there was order and pattern behind nature – the universe had a rational explanation. Pythagoras spent most of his life exploring numbers and their significance.
Given how little we know about Pythagoras, what can we say about his contribution to mathematics? Virtually nothing, says Ferguson. Mathematics was in use centuries before him. Most ancient cultures had more sophisticated understanding of numbers than Pythagoras and his followers. The theorem with which his name is associated was already known. Since he operated a mystical cult, and did not believe in sharing his wisdom, a great deal of what he thought was kept secret. No written works by him exist.
There are in fact not one but numerous Pythagorases. As a fervent believer in reincarnation, Pythagoras himself claimed that he could recall his previous lives. Throughout the ages, different historians, philosophers and architects have fabricated their own Pythagorases as a great mathematician, brilliant philosopher and mad mystic. Pythagoras has acquired diverse meanings for different thinkers and disciplines.
What Ferguson thus offers is not a life of Pythagoras but a biography of the idea of Pythagoras. We see how the fable was developed by Aristotle and Plato, and its influence in the Middle Ages. The Pythagorean idea influenced Kepler and Newton, as well as 20th-century figures such as Bertrand Russell and Arthur Koestler, claims Ferguson.
The main achievement of Pythagoras, the idea behind the multifaceted man, Ferguson claims, is the notion that universe is rational and can be studied with numbers. But there is a problem. If we know nothing about Pythagoras, how can we be sure that he is responsible for developing a mathematical approach to understanding the universe? What we do know is that Pythagoreanism was a sophisticated form of mystery religion in which numbers played a key part in purification of the soul.
It was more numerology than mathematics. You can't remove the numbers from the religion: the two are intimately blended. To argue that the Pythagoreans are responsible for developing a rational understanding of numbers, and their legacy played a vital part in developing the scientific method, is an inductive leap too far. Was Kepler really "knocked out" by Pythagoras when he realised he was applying two-dimensional mathematics to a three-dimensional universe? The Brethren of Purity in 10th-century Basra did believe in unity of knowledge and combined music, mathematics, medicine, astronomy and philosophy. But they were not influenced by Pythagoras, but by Ismaili gnosis, a different phenomenon.
But don't let these problems deter you. Pythagoras does two things exceptionally well. It provides a magnificent grand tour of the history of mathematics and how it has shaped our understanding of the universe. And it provides deep insight into how the West has manufactured and maintains its Greek roots. This makes it a valuable and inspiring read. As far as Pythagoras is concerned, Bertrand Russell got it partly right. He was "a serpent in the philosophic paradise". His reputation is a cleverly created mirage.
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