What Did Pythagoras Mean By "All Things Are Number"? by Professor Frank Wilczek

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We all know that numbers can help us understand the beauty of nature. But in this excerpt from the new book A Beautiful Question: Finding Nature’s Deep Design by Nobel Prize-winning physicist Frank Wilczek, he shows how it goes a lot deeper than that. Did the ancient mathematician Pythagoras know something we don’t?

ALL THINGS ARE NUMBER
Most of us first heard the name “Pythagoras” when we were in high school geometry class, but few recall that there was an actual person named Pythagoras who lived and died around 570–495 BCE. Very little is known about the real Pythagoras, or rather a lot is “known” about him, but most of it is surely wrong. The documentary trail is littered with contradictions. It combines the sublime, the ridiculous, the unbelievable, and the just plain weird.

Pythagoras was said to be the son of Apollo, to have a golden thigh, and to glow. He may or may not have advocated vegetarianism. Among his most notorious sayings is an injunction not to eat beans, because “beans have a soul.” Yet several early sources explicitly deny that Pythagoras said or believed anything of the sort. More reliably, Pythagoras believed in, and taught, reincarnation. Several stories—each dubious, to be sure—corroborate this...

A few things seem clear. The historical Pythagoras was born on the Greek island of Samos, traveled widely, and became the founder of and inspiration for an unusual religious movement. His cult flourished briefly in Crotone, in southern Italy, and developed chapters in several other places before being everywhere suppressed. The Pythagoreans formed secret societies, on which the initiates’ lives centered. These communities, which included both men and women, promoted a kind of intellectual mysticism that seemed marvelous, yet strange and threatening, to most of their contemporaries. Their worldview centered on worshipful admiration of numbers and musical harmony, which they saw as reflecting the deep structure of reality. (As the next two thousand years have shown, they were on to something.)...

Photo: io9

Thanks to Raphael, we know what the real Pythagoras looked like. In Raphael’s famous painting he is captured deep in concentration as he writes in a great book, surrounded by admirers. It is difficult to make out what this Pythagoras is writing, but I like to pretend it is some version of his most fundamental credo:
All Things Are Number

It is also difficult to know, at this separation in time and space, exactly what Pythagoras meant by that. So we get to use our imagination.
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Additional resources

A Beautiful Question: Finding Nature's Deep Design

Artists as well as scientists throughout human history have pondered this “beautiful question.” With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present.

Penguin Press (July 14, 2015). 

Source: io9