One of the most famous mathematicians of the ancient world was Pythagoras of Samos (570 – 495 BCE). Much mystery surrounds the early life of Pythagoras and it is sometimes difficult to separate fact from legend. It is believed that around the age of nine, Pythagoras may have traveled to Miletos where he was taught by the famous Greek philosopher Thales and his pupil Anaximander. Later on, around 535 BCE, it is likely that he traveled to Egypt and Babylon where he was taught geometrical principles that laid the foundation for many of his theorems.
In about 518 BCE Pythagoras settled in Cronton, a Greek seaport in southern Italy, where he founded a school dedicated to studying mathematics. The school provided a way of life for him and his followers that included rules on diet and behavior, but also placed a primacy on mathematics and numbers. They believed that everything in the universe was related to numbers. Therefore symmetries and sequences held deep meaning where they turned up in nature, including in the study of music. Since Pythagoras traveled widely in the ancient world it likely that he incorporated many ideas of the Egyptians and Babylonians into his school’s philosophy. Indeed, the school was part philosophy, part mysticism, but its influence was profound and was clearly a source of inspiration for future generations of Greek mathematicians and thinkers.
During his lifetime Pythagoras made several discoveries in mathematics. The one which he is most famous for and bears his name is the Pythagorean Theorem. It states that for any right sided triangle the square of the length of the hypotenuse is equal to the sum of the square of the length of the two legs. He is also alleged to have been one of the first people to teach that the Earth was a sphere. The exact details of his death are unclear but his school expanded rapidly after 500 BC preserving his philosophy, ideas, and legacy for future generations.