> This is no different than how math textbooks present the history of any particular mathematical abstraction or theorem: they don't go in depth on all the fals

> This is no different than how math textbooks present the history of any particular mathematical abstraction or theorem: they don't go in depth on all the false starts and dead ends people explored before making real progress. That's certainly something interesting but it has no place—and no room—in textbooks dedicated to explaining abstractions. The simplified story of how something could have been developed is, I believe, more relevant to understanding the importance of an idea than the way it was actually developed. Unfortunately, textbooks rarely do even this. That is, they don't supply nearly enough justification/motivation for the complicated definition they posit and the structures they develop. For the canonical (and accessible) bit of philosophy of mathematics on this, I highly recommend Lakatos’ "Proof and refutations" [1]. As a demonstration, it gives a very non-historical and exhaustive explanation for the definition of an "honest" polyhedron with respect to Euler characteristics [2], and is liberally footnoted with the actual history. Unfortunately, textbooks have not improved much since it was written in 1963. [1]: https://math.berkeley.edu/~kpmann/Lakatos.pdf https://math.berkeley.edu/~kpmann/Lakatos.pdf [2]: https://en.wikipedia.org/wiki/Euler_characteristic https://en.wikipedia.org/wiki/Euler_characteristic