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Pythagoras: Life, work and achievements

Pythagoras, a pioneer of early Greek philosophy, mathematics and natural science
(Image credit: Getty Images)

Born in Samos in around 570 B.C, Pythagoras is commonly said to be the first pure mathematician who proposed that everything is a number.

Although he is most famous for his mathematical theorem, Pythagoras also made extraordinary developments in astronomy and geometry. He also developed a theory of music while and founded a philosophical and religious school in Croton, Italy. It was here he taught that "the whole cosmos is a scale and a number", according to the University of St Andrews (opens in new tab) .

While playing on his lyre, which was an ancient Greek stringed instrument, Pythagoras discovered that the vibrating strings created a beautiful sound when the ratios of the lengths of the wires were whole numbers, and that this was also true of other instruments. He combined this discovery with his understanding of the planets, conceiving the theory that when the planets were in harmony, it created beautiful music that man was incapable of hearing. 

Pythagoras concluded that mathematics and music were interconnected and that knowledge of one area led to an understanding of the other, according to the University of Connecticut (opens in new tab). He also believed that music had healing properties and would often play his lyre for the sick and dying.

Little is known about the life of Pythagoras and, as a result, many bizarre myths have sprung up around the man.

It was claimed amongst other things that he had taken part in the Olympics and was awarded laurels for pugilism, or boxing, when he was a young man. It was also said that he had fought in the Trojan Wars during a previous life.

This last myth reflects Pythagoras' genuine belief in metempsychosis, which argues that all souls are everlasting and, when the physical body dies, it simply floats away and finds a new body to live in, according to Stanford University (opens in new tab). Later reports stated that he had been able to clearly recall four previous lives.

His fascination with astronomy (opens in new tab) ,as with many ancient Greeks, combined with his deep understanding of numbers led Pythagoras to confirm that the Earth was in fact a sphere and, through patient study, he discovered that the Evening Star (opens in new tab) and the Morning Star were the same planet, Venus (opens in new tab).

Pythagoras Theory

Pythagoras' Theory states that in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides, according to Encyclopedia Britannica. 

In other words, when a triangle has a right angle and squares are made of each of the three sides, then the biggest square has the same area as the other two squares combined. The equation can be used to work out the length of a third side if only two measurements are given. 

Pythagoras theorem

Children are taught Pythagoras’ Theory all over the world. (Image credit: Getty Images)

The Babylonians discovered this mathematical phenomena circa 1900 – 1600 BC but Pythagoras may have been first to prove it, according to New Scientist (opens in new tab).

Although Pythagoras’ Theory is still taught in every classroom today, no one would recognise his original school of thought as it combined his mathematical teachings with philosophy and religion. His followers, the Pythagoreans 

created a secret commune, filled with strange rules and regulations, according to Encyclopaedia Britannica (opens in new tab)

Much of his written work was stored in the Great Library of Alexandria. Far from being the master mathematician that we think of today, Pythagoras was known for his belief in reincarnation, religious rituals and almost magical abilities, according to Stanford University. For example, it was said that he could be in two places at the same time. Today, these mystical elements have been almost forgotten and he is now looked upon as a founding father of science and mathematics.

In his footsteps


Greek philosopher Plato created the world's first university, known as the Platonic Academy, in ancient Athens. Although different from a modern day university, the Academy was a place where people could meet and share their academic beliefs. Plato based a large proportion of his teachings on the thoughts of Pythagoras and his Pythagorean disciples, according to Stanford University.

An illustration of Plato

The Greek Philosopher and Mathematician Plato studied the teachings of Pythagoras. (Image credit: Getty Images)


Like Pythagoras, Aristotle was interested in the concept of a soul, according to the University of Washington (opens in new tab). He wrote "On the Soul", which set out to examine the psychology of mankind, the principles of which are still referred to by psychologists today. Aristotle combined metaphysics with scientific investigation just as Pythagoras had achieved with metaphysics and the Number Theory. He was also inspired by Pythagoras’ interest in astronomy, ultimately developing the physical model of the heavens.

An illustration of Aristotle

Having read the works of Pythagoras, Aristotle went on to teach Alexander the Great. (Image credit: Getty Images)

Additional resources

To find out more about Pythagoras, check out “Pythagoras: His Life, Teaching, and Influence (opens in new tab)”, by Christoph Riedweg and “Pythagoras: His Lives And The Legacy Of A Rational Universe (opens in new tab)”, by Kitty Ferguson.


Jo is a freelance journalist, academic lawyer and lecturer specialising in criminal law and forensics. Jo has written for several magazines, including Real Crime and All About History. She is also the author of a number of true crime books and horror anthologies, such as "Murderous East Anglia" and "Strangers".