Who was Pythagoras and what did he teach? He lived from 570 to 495 BC, born on the island of Samos in the Aegean Sea, and is best known for the "Pythagorean Theorem" which is about the sum of the square of two sides of a right triangle equaling the square of the hypotenuse. Such discovery of the ways of numbers was central to Pythagoras' teachings, as mathematics, geometry and theology blended in what he called "philosophy" - a first use of the term, which adds to the word "sophos" meaning wisdom. Phythagoras went beyond wisdom to seeking an understanding of the universe and everything in it.
This book is a modern edited edition of a book first published in 1687 by Thomas Stanley, and it is a collection of information from a number of sources, including a biography of Pythagoras. What stands out for me is that Pythagoras founded a school of sorts that was also a bit of a cult. Full members of the school gave all their possessions to the organization and devoted themselves to study. According to sources in this book, initiates had to spend five years in silence. Pythagoras also had other disciples who studied, but did not devote their lives and money to the school. But why the influence down through the ages? First, Pythagoras was extremely well esteemed during his lifetime and many regarded him as a god because his wisdom and knowledge went so far beyond that of ordinary people. Second, the Pythagorean schools (they spread to other parts of the ancient world) lasted for many generations, and those who were called "Pythagoreans" played important roles in the governing of the power centers of the ancient world over a long period of time.
What impressed me in reading this material was both the spiritual content of his teachings and how much of the science he actually got right. Pythagoras believed in the preexistence of and immortality of the soul. Yes, his religion centers on the gods of the world of his time, but he adopted a policy of peaceful friendship among all people, he did not accept bloody sacrifice, and he revered plant and animal life as well. In one story, he told some strangers on the bank of a river how many fish they would catch. When their catch was exactly as he had foretold, they were amazed, but Pythagoras asked them to return the fish to the waters so they could live and he paid them the value of their catch. From these ancient sources, it appears that Pythagoreans were vegetarians who did not think killing animals honored the gods.
It also appears that Pythagoras taught that the earth and planets go round the sun and that the sun consists of fire. He taught that there were other worlds like the earth and that the universe is infinite. His work on geometry, mathematics, and music is amazing and full of insights into the nature of things. To Pythagoras, everything had numbers behind it. All existence derived from the Monad, the One. Each type of number has significance, not just for counting things, but intrinsically. Numbers as abstractions is the very stuff of the universe.
Much of the Pythagorean teachings are clouded by the passage of thousands of years and the inevitable reformulating and misunderstanding of what he taught. The concepts are sometimes difficult to grasp and, even with the editing for a modern audience, much of the content here is steeped in the worldviews of both the middle ages when Thomas Stanley was writing and that of 500 BC when Pythagoras lived. But if you make your way slowly through this material, you will find instances of interesting insights into the world we inhabit and how we ought to live. The concepts of Pythagoras still have something to teach us. Here are two examples of sayings attributed to Pythagoras:
--- "We ought to be slient or speak things that are better than silence."
--- "Comprehend not few things in many words, but many things in few words."
Pythagoras taught his disciples to live a life of moderation in all things, to value the unseen over what can be seen and felt and to understand the invisible numbers and geometry behind everything. For an easier reading explanation of how numbers construct everything, I recommend A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science by Michael S. Schneider. This book is full of illustrations and information about the mathematics and geometry of our world, much of which mirrors the Pythagorean teachings. You might also try another interesting and somewhat unorthodox book, Quantum Pythagoreans by Mike Ivsin.
Modern thinkers continue to seek out the true teachings of Pythagoras, and this book -- "A Compendium of Classical Sources" -- is a good addition to that effort.