# Have there been attempts to base early math education on category theory?

The New Math curriculum built math eduction on set theory. Have there been any attempts to do something similar with category theory?

I was fortunate to grow up in a relatively enlightened spacetime, such that I got New Math in my earliest primary education. It Worked For Me in the sense that, as a child, math seemed both interesting and straightforward. Though I retained a continuing interest in math (which I tend to attribute to that primary-math pedagogy), my formal study ended with the undergraduate engineering curriculum (differential equations and calculus-based probability) and the more-fascinating-to-me introduction to discrete math taught in undergraduate informatics (misnamed "computer science" in too much of the world).

I have a longer-standing interest in logics and the history and philosophy of logic, and started learning about attempts to "found mathematics" (where found is a verb, not an adjective) via philosophy of math. Hence when I learned about efforts to found math on set theory, I wasn't able to "go too deep" (lacking much pure math), but found it fairly tractable--that was how I was first taught math.

I later learned a bit more about category theory, which I had previously encountered (less than a bit, and much too briefly) in a programming-language-theory class. Lately I've been reading a bit more about category theory; I seem to understand it well enough (though of course without testing, that's just my quale), but (aside from the applications of CT to sets) I still find CT less immediate or intuitive than set theory. My hypothesis is, even though I didn't get taught formal ST until college (which, in my case, was decades after secondary school), New Math wired some deep and persistent neural networks.

Which motivates my question: has anyone attempted a primary-math pedagogy mostly based on category theory, similar to the way New Math was mostly based on set theory? If so, does it have any empirical advantages (in terms of educational outcomes) other than making category theory more intuitive?

• I have edited your post for clarity. Titles should be descriptive, and should not require a paragraph of explanation. I seem to have saved some words by actually spelling out the thing you sought to abbreviate. – Xander Henderson May 20 '20 at 12:02
• I have added the (category-theory) tag. – J W May 20 '20 at 12:46
• So we will teach children to regard a light switch as a $\mathbb{Z}/2$ torsor? – Dan Fox May 22 '20 at 10:19
• New Math failed because it was too abstract for young kids. Do you want to fall into the same pit again? – Rusty Core May 22 '20 at 20:44
• @RustyCore, no, it failed because it was too abstract for the teachers. Young kids would be fine with it. – Kostya_I May 23 '20 at 15:12