Ask HN: The most beautiful applied mathematics
What is the most beautiful piece of mathematics that has practical applications that you have come across while working in software (including ML/modelling)?
This is on the simpler side of applied math but I think it leads well to thinking about interesting things like encodings of geometric objects (vector versus rank-constrained tensor) and to geometric algebra which is becoming more popular in game development.
https://en.wikipedia.org/wiki/Dimensional_analysis
The classic example is the derivation of the Reynolds number (mentioned in link under examples);
If you take all the things that matter about a pipe and a fluid: speed, density, length, viscosity .. and arrange those so that all dimensions cancel out you're left with a quantity that expresses a key property of the system.
This has had repeated practical applications when thinking about new systems over the past decades I've been working.
Another nugget of thought from applied mathematics was the notion that any iterated dynamic systems will end up in one of five places (subject to scaling by a constant)
-1, 0, 1, infinity, or sin()
It'll flip, diminish to nothing, stabilise, exponentiate, or wobble.
( or combinations thereof, subject to caveats, etc. YMMV )