Pythagoras lived in the 500s BC. He was one of the first Greek mathematical thinkers that we know about, after Thales. He spent most of his life in the Greek colonies in Sicily and southern Italy. Pythagoras had a group of followers (like Taoists followed Lao Tzu, or Buddhists followed the Buddha). His followers learned from him and taught other people what he had taught them. Like Lao Tzu and the Buddha, Pythagoras was probably rich enough not to have to worry about money. He had plenty of money thanks to the unpaid work of enslaved people and colonized people around him.
The Pythagoreans were known for their pure lives. They didn’t eat beans, for example. They thought beans were not pure enough. Like Buddhists and Zoroastrians at the same time, Pythagoreans questioned whether it was ever right to kill animals, even for religious sacrifices. Some Pythagoreans said it wasn’t right, and they were vegetarians or vegans. Pythagoreans wore their hair long. They wore only simple clothing, and went barefoot. Both men and women were Pythagoreans.
Pythagoreans were interested in philosophy. And they were especially interested in music and mathematics. They saw music and math as two ways to create order out of chaos. Music is noise that makes sense. Mathematics is rules for how the world works.
We remember Pythagoras best for proving that the Pythagorean Theorem was true. The Sumerians and Egyptians, two thousand years earlier, already knew that the Pythagorean Theorem was generally true. Architects used it in their measurements. But Pythagoras may be the first mathematician who proved that it would always be true. We don’t really know whether it was Pythagoras that proved it. There’s no evidence for this proof until the time of Euclid, several hundred years later. Some people think that the proof must have been written around the time of Euclid, instead. But that’s the tradition.
What’s Your Angle, Pythagoras? A Math Adventure, by Julie Ellis and Phyllis Hornung (2004). For teens.
Pythagoras and the Pythagoreans: A Brief History, by Charles Kahn (2001).
History of Greek Mathematics: From Aristarchus to Diophantus, by Thomas L. Heath (1921, reprinted 1981). A lot of Euclid, but also describes who the other major Greek mathematicians were and what they did.
Episodes from the Early History of Mathematics, by Asger Aaboe (1997).