
‘Infinitesimal,’ a Look at a 16th-Century Math Battle - igravious
http://www.nytimes.com/2014/04/08/science/infinitesimal-looks-at-an-historic-math-battle.html
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ciot1CDM
If you're interested in a modern rigorous treatment of the classical
infinitesimal, check out "smooth infinitesimal analysis"
([https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis](https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis))

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igravious
Should have checked sooner for replies to my post, sorry!

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

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

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twangist
This review proves a very counterintuitive result: It's possible to review a
book about the history of infinitesimals without once mentioning either
Leibniz or Newton.

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igravious
Ha, just so, yes. Let's bring the term `fluxions' back into vogue!

