News for hackers. Stuff that matters.

A comment on Using calculus to do number theory.

Re:Using calculus to do number theory by pfortuny on Wednesday March 18, 2026 @11:39AM (#47427143)
In some sense the title is a bit misleading (one is led to think of Analytic Number Theory). I'd rather use the title "Using differentials to...", which is more precise, as there is not exactly any "calculus" going on but there is indeed differential algebra and differential "number theory", so to speak.

But great and elegant article. Thanks.

[ Parent | on HN ]
Re:Using calculus to do number theory by measurablefunc on Wednesday March 18, 2026 @02:10PM (#47429199)
The technical term is "formal derivative" b/c there are no limits involved, it's basically a rewrite rule for changing x^n to nx^(n-1).
[ Parent | on HN ]
Re:Using calculus to do number theory by pfortuny on Wednesday March 18, 2026 @03:15PM (#47430178)
I know, yes, but did not want to digress. Thanks though. Actually, it is the "extension" to K[e] with e^2=0, as "usual".
[ Parent | on HN ]
Re:Using calculus to do number theory by measurablefunc on Wednesday March 18, 2026 @04:06PM (#47430762)
The infinitesimally thickened point.
[ Parent | on HN ]
Re:Using calculus to do number theory by ne38 on Wednesday March 18, 2026 @03:41PM (#47430471)
Actually it is Calculus in p-adic numbers!
[ Parent | on HN ]
Re:Using calculus to do number theory by pfortuny on Wednesday March 18, 2026 @03:49PM (#47430563)
Mmmmhhhh, sure? Because p-adic numbers have characteristic 0, AFAIK.
[ Parent | on HN ]