On Eponymous Erasure

While slumming on the Internet I came across a woman complaining. Imagine my astonishment! The lady¹, let’s call her Karen, had an esoteric complaint, it was:

The Pythagorean Theorem was known long before his birth. Calling the theorem “Pythagorean” is a form of erasure.

Oh my!

Apparently, attributing a well-known mathematical result to a person or school associated with its long history erases others, and by “others” Karen means BIPOC’ky people.

Ok, Karen, I’ll play.

You are correct that specific cases of the “Pythagorean Theorem” were known long before Pythagoras. The most famous Babylonian mathematical tablet YBC 7289 shown below demonstrates that the Babylonians were aware of the square case at least a thousand years before Pythagoras.

Other tablets indicate they also knew about Pythagorean triples: natural number solutions of a² + b² = c².

a	b	c
3	4	5
5	12	13
7	24	25
	…

The Babylonians weren’t the only culture aware of the “Pythagorean Theorem.” The Egyptians, Chinese, and Indians were all aware of special cases and some, particularly the ancient Chinese and Indians, even came up with sort-of-ok proofs for particular cases like equilateral right triangles. This is hardly surprising. I submit that anyone building square houses or laying out rectangular fields is likely to stumble on special cases of the Pythagorean theorem. It’s a simple matter to pace off the sides of a rectangular field and compare the result to the diagonal. The Pythagorean Rule-of-Thumb, to distinguish it from the theorem, has been known forever. I wouldn’t be surprised if it was found in ice age cave paintings or aboriginal rock art one day. But, as anyone that’s ever-studied mathematics knows, there’s a big difference between a rule-of-thumb and a general proof, and the first sort-of-ok surviving general proof of the Pythagorean Theorem has been attributed to none other than Euclid². Karen, it’s a shame that Euclid, the most famous name in mathematics, has been erased.

I know that didn’t go the way you wanted, but your complaint, when divorced from postering, has merit. The custom of naming things after alleged progenitors has a long-checkered history. Misattributions, or “erasures” using your term, are so common they have their own law: Stigler’s law of eponymy. “Stigler’s law states that no scientific discovery is named after its original discoverer.” In a nice bit of self-reference, Stigler’s Law applies to Stigler’s Law. The “law” was known before Stigler claimed it. It seems we naked apes love “erasing” others.

Now, Karen, it would be so-so nice if we could rename the Pythagorean theorem after its “first discover,” but I suspect we will never know who or when this occurred. If we opt for “first prover” then we have to nail down what we mean by proof. If we’re going to insist on general ultra-anal formal axiomatic proofs then you can make a good case that the Pythagorean Theorem was not really “proven” until modern times as the Pythagorean Theorem is a good test case for computer proof assistants: see Formalizing 100 Theorems. Rechristening the “Pythagorean Theorem” is, to use an annoying cliché, problematic.

The only thing that makes sense is to strip away all eponymous names and call the Pythagorean Theorem something forgettable like the Right-Angle Triangle Side Length Theorem. Fortunately, renaming things will not damage mathematics. David Hilbert once famously remarked,  “One must be able to say all times – instead of points, straight lines, and planes – tables, chairs, and beer mugs.” It’s the mathematical content that matters, not the language used to discuss the content. So maybe the answer to eponymous Stiglerian erasure is extreme erasure. Let’s purge all traces of humanity from mathematics. Some cynics might add that formal axiomatics has been pursuing this for over a century already.

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1. The complainer identified as female.↩︎

2. The Pythagorean Wikipedia page describes Euclid’s proof as axiomatic. I consider this an overstatement.↩︎