Math is a belief system

I have resisted the siren call of TikTok. But some of its videos are so powerful they leave their orbit and end up on other platforms and catch my attention. Case in point is the “I don’t think math is real” video. I enjoyed Hank Green’s response to its response.

This young woman is asking all of the right questions that don’t just lead to a greater understanding of math, but actually joyous understanding of math.

And I get frustrated that often the way we teach math right now ignores these questions. How did Pythagoras, a dude who didn’t even have a flushable toilet, figure out an equation that we still use and is still useful today? Thousands of years later!

A truth so true that it’s more true than reality is. Every point in our universe has some bluntness. Every line has some wiggle. But in Pythagoras’ mind, there was a perfect triangle that, one that no matter how far in you zoomed in, the lines were straight, the points were pointy. One in which for every right triangle the area of the square made by the hypotenuse was exactly the same as the area of the squares made by the legs of the two triangles added together. Exactly!…

The idea that we teach people the pythagorean theorem without teaching them that mathematicians build universes in their minds that are more perfect than the one that we live in, in some ways, that’s wild! Sometimes it is brought up, and sometimes the fact that Pythagoras built a CULT promising SECRET KNOWLEDGE about this stuff and then actually delivered on that secret knowledge that was extremely powerful and wild that you can create a universe in your mind, that also is sometimes taught but not always! I mean come on! This young woman asks, does math exist? I don’t know. Did Pythagoras discover his theorem, or did he invent it? Does math both exist and not exist? Is it an artifact of our minds, or of reality? No one knows the answer to that question! But let’s let people ask it!

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Speaking of Pythagorus, some years ago I heard an episode of The Theory of Everything that kind of blew my mind when it suggested to me that math is a belief system.

Philosopher Daniel Heller-Roazen tells us the story of Pythagoras and the fifth hammer and how Kant and Kepler both tried (and failed) to record the universal harmonies Pythagoras once heard.

An ancient tradition holds that Pythagoras invented harmony. It is said that one day, he wandered by a forge and, hearing a wondrous sound come from within, ventured in to investigate. He found five men hammering with five hammers. To his astonishment, he discovered that four of the five hammers stood in a marvelous set of proportions, which, when combined, allowed him to reconstruct the laws of music. But there was also a fifth hammer. Pythagoras saw and heard it, but he could not measure it; nor could he reason its discordant sound. He therefore discarded it.

What was this hammer, such that Pythagoras chose so decidedly to reject it? In The Fifth Hammer, Daniel Heller-Roazen lucidly shows how that fabled gesture offers a key for understanding ideas of harmony in the broadest sense of the term. Since antiquity, “harmony” has been a name for more than a theory of musical sounds; it has constituted a paradigm for the scientific understanding of the sensible world. Nature, through harmony, has been transcribed in the ideal elements of mathematics. But, time and again, the transcription has run up against one fundamental limit: something in nature resists being written down in a set of ideal units. A fifth hammer, obstinately, continues to sound.

The Fifth Hammer: Pythagoras and the Disharmony of the World by Daniel Heller-Roazen, Zone Books

So much of nature is ignored when it is decided that it is not elegant.

See also: women’s bodies.

See also: music.

So much of music is not considered music by white Western music critics if it doesn’t match white Western European music theory. Western European Music theory’s foundation is based on the work of Pythagoras.

When the foundation of math erases so much, perhaps the question of whether math even is real, is exactly the question we should be asking in this moment.