Pythagoras and the Pythagoreans: A Brief History by Charles H. KahnMy rating: 3 of 5 stars
The focus of this book is primarily on how Pythagoreanism influenced thinkers from ancient times up through Kepler in the 17th century. My main take away is that Pythagoras and Pythagoreanism really become a catch-all symbol of a sage-like, mystical philosophical/mathematical musings. It's not even really clear to me that the ideas later referred to as something called Pythagoreanism is all that connected to the historical Pythagoras--of whom we seem to know very little. Pythagoras seems to become a kind of omniscient sage symbol rather than a philosopher of distinct ideas and arguments.
Kahn argues for some influence on Plato and his Academy and through this and Neoplatonism gets picked up by others in later antiquity and in the Renaissance. The content of this influence on Plato is somewhat opaque, and seems centered on two main ideas: the cosmological role of numbers and geometry and the transmigration of souls. But it's also not entirely clear where these ideas really come from and how they find their way (and the extent that they really do) into Plato (though I think they are there in Academic Platonism and later Neoplatonism -- I'm less sure about Plato himself).
The book doesn't really get into the ideas themselves as such, it's more focus on tracing the lines of influence from thinker to thinker. It won't really be of interest to someone looking for a precis of Pythagoras or his ideas. I found it enlightening at times but not really what I was looking for.
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