Mathematics

f : ℂ → ℂ, z ↦ z²

In case you couldn't tell, I really like geometry. What ends up here: complex analysis done with pictures, differential forms and where they lead, the occasional bit of curvature. Mostly things I wanted to understand properly and only did once I wrote them down.

Cauchy-Riemann = Maxwell??! Part 1.July 2026
Yep, you read the title correctly. Maxwell's equations are actually the CAUCHY-RIEMANN equations in Minkowski space. That is some weird shit.
The Jacobian - Fortney §3.3July 2026
Where does the Jacobian determinant come from? Here's a nice proof using the wedgeproduct of forms.
Christoffel SymbolsJuly 2026
What are Christoffel symbols, and why can we use their derivatives to measure curvature?
The Power of Index NotationJuly 2026
Index notation looks like a different language, but it makes life a lot easier when working with tensors. Here's an example of why.
The Riemann Tensor - Fleisch §6.3, pp. 183–187July 2026
The EFEs are just as much a statement about geometry as about gravity. Here, we look at how the Einstein tensor is built from the Riemann tensor, and how it measures curvature.