[whatshisface]

>imagine a scenario in which the useful applications all involved degree 5 or higher polynomials. Would we have progressed much?

You can always approximate a polynomial around a point with a lower-degree polynomial. They will only diverge farther out. As a result whenever physics produces a high-degree polynomial we can inspect certain behaviors in a lower degree. This doesn't help with every case, but it does enough for the situation that many questions become answerable.

[sykh]

Oh definitely. Thinking it about it more it’s clear that part of my comment was I’ll thought out. I was attempting to wonder if mathematics would have developed enough theory behind it in a universe in which low degree polynomials were difficult to solve or in which most applicable problems involved high degree polynomials. I think the answer is yes.

[whatshisface]

What-if questions about the conclusions (as opposed to the axioms) of math being different rarely lead to insight, because they unpin too much. The results mostly depend on whatever else you had to change to keep your primary change from contradicting anything.

If all you changed was physics, the Taylor series thing would put quadratics right back into their position of importance.

[DoreenMichele]

I’ll thought out = ill thought out

You must be posting from a phone.

#damnauto-corrupt

[sykh]

I am! Thanks for catching that mistake.