‘Infinitesimal,’ a Look at a 16th-Century Math Battle

I actually posted the above review/link in the hope that somebody would mention nilpotent infinitesimals and smooth infinitesimal analysis.

Interesting, in my opinion, is that homotopy type theory (HoTT)[0] has taken Conway's surreal numbers[1] approach. Given that I think HoTT is the correct _foundational_ tack and at the same time I also think that smooth infinitesimal analysis is the correct _calculus_ tack I'd very much like to see the two methods combined.

[0] http://homotopytypetheory.org/book/ Part II Mathematics, 11 Real numbers, 11.6 The surreal numbers

[1] https://en.wikipedia.org/wiki/Surreal_number