My rating: 3 of 5 stars
Everyone knows that Pythagoras was an early Greek mathematician, that he proved the Pythagorean theorem, and that he was one of the first to glimpse our modern conception of the world– that the universe can be described by numbers. Everyone “knows” this, but is there actually any historical basis to these claims? What do we really know about Pythagoras and what he did, and how much of what is taught about him in math classes is actually myth? Apparently quite a bit, according to Alberto Martinez.
The Cult of Pythagoras could have as easily been titled The Myths of Pythagoras. Martinez, a historian of science at the University of Texas, Austin, convincingly argues in the first two chapters of this work that the foundation on which we’ve built the myth of Pythagoras and his accomplishments is very thin indeed. Martinez does what generations of math historians and popularizers of science have failed to do: drill down to the source material and examine what ancient authorities actually have to say about the man. What he finds is that the earliest accounts are vague, contradictory, and emphasize Pythagoras’s mythical attributes– his teachings as a religious figure and his reported miracles– as much as they do his mathematics. What fascinates Martinez is the way that these accounts have been distorted and magnified over the centuries until we get the Pythagoras of modern conception today: the veritable father of mathematics.
Pythagoras actually takes up only fraction of this book. The subtitle, “Math and Myths,” gives a better indication of the bulk of the work. Besides Pythagoras, Martinez debunks other famous myths from the history of mathematics. Gauss finding the sum of all integers from 1 to 100 during a grade school exercise. Euler getting imaginary numbers wrong. Galois’ tragic tale. The golden ratio popping up everyone where in nature and art and architecture. If the book was simply a historian of science plumbing the depths of the historical source material and making modern promulgators of these stories look foolish, it would be worth the admission alone.
But Martinez has a deeper program here. There’s a fundamental myth about mathematics that he uses many of these other minor myths to explode. And that is the Platonic conception of mathematics as something somehow independent of the physical world itself, existing beyond our own mental constructions. This is the perception of mathematics existing eternal and unchanging, of mathematical discovery as not inventing new systems but instead discovering truths that were there all along. What Martinez sees instead, when he looks at the history of mathematics, is the story of things being formalized and formulated, not discovered. In particular, Martinez examines the nature of imaginary numbers, the problem of dividing by zero, and the rules regulating multiplication by negatives. These are not mathematical properties written in stone, Martinez argues, though they’re often taught that way. They are instead conventions that developed slowly over time.
Against a mathematical Platonism on the one hand and a radical constructivism on the other, Martinez ventures into philosophy and poses his own system of mathematical pluralism. Some fundamental tenants of mathematics are true independent of human though. 2 + 2 will always equal 4, for instance, whether or not there is anyone around to see or discover this fact. But other mathematical principles are constructed, like William Hamilton’s quaternions. The problem is, Martinez doesn’t provide us with any way of distinguishing which portions of mathematics fall into which category. Are the principles of Euclidean geometry independent of human thought? Would the Pythagorean theorem hold for all right triangles, regardless of whether there were humans around to mentally construct them? Or does the construction of self-consistent non-Euclidean geometries argue against this? There’s fertile ground for philosophical speculation there, which I would have liked to have seen Martinez follow up on.
At the end of the book, Martinez returns to Pythagoras. Why is it so easy to hang accomplishments on this man’s name without any secure historical basis? Beyond mathematics, Martinez explains, Pythagoras also gets attributions from religion, new age thought, philosophy, alchemy, astronomy, and more. Here Martinez ventures into sociology, explaining how accomplishments (whether actual or not) tend to accrue to people who are already “famous.” The very paucity of real data regarding Pythagoras, Martinez concludes, makes him a sort of vessel in which all these attributes can be poured, a well-known cipher from antiquity for our own values that we wish to project into the past.
In sum, The Cult of Pythagoras, though the prose is in places is uneven and the book itself wanders in the multiple points it makes, is a powerful argument for expelling myth from the teaching of mathematics. The history of mathematics itself, based not on unfounded stories but on the real historical events and accomplishments, is far more interesting and compelling than the unhelpful myths that are propagated regarding mathematicians and the practice of mathematics itself. Martinez’s scholarship is grounded on what the texts actually tell us, and I heartily recommend to anyone teaching mathematics. The chapters on Pythagoras alone make this worth any mathematician’s bookshelf.