rham

That phrase is generally attributed to Rham Emanuel [1], and the sentiment is discussed in Saul Alinsky's Rules for Radicals (page 89, Communications).

For instance, you can interpret Maxwell equations as certain statements about de Rham cohomology classes of certain 2-forms on 4-manifolds.

More generally, see also the Laplace-Beltrami and Laplace-de Rham operators, both defined on (pseudo-)Riemannian manifolds not necessarily embedded in ℝ³.

Div, grad, and curl are a manifestation of de Rham cohomology that make use of a lot of lucky coincidences.

On the other hand, the standard course will also prepare you for mathematical topics like lie derivatives, differential geometry and de Rham cohomology.

It was very refreshing to see students compute De Rham cohomology and discuss Galois theory (if I recall correctly) in a major Hollywood production.

Differential forms, de Rham cohomology...

Unfortunately we did not cover De Rham cohomology.

Even more generally, see the huge body of beautiful mathematics that has arisen from the study of elliptic differential operators in general (de Rham cohomology, Hodge theory, the Atiyah-Singer index theorem, …).

(Especially nice if you like complex analysis, differential geometry and de Rham theory.) David Eisenbud and Joseph Harris, The Geometry of Schemes, Springer, 2010.

You see electromagnetism, realize that electromagnetic field is just 2-form on 4-manifold, and see that Maxwell equations just state that both this form and its Hodge dual are closed, so that they represent de Rham cohomology classes.

I admire how they build from nothing but elementary linear algebra and calculus, and end up at quite advanced topics like De Rham cohomology, of which I never imagined it had any application in computer science at all.

(Possibly dumb question) As a topologist, not a computer scientist - is "discrete differential forms" just the practice of computing things in De Rham cohomology by passing to simplicial homology via Poincare duality?

"De Rham cohomology", "simplicial homology" and "Poincare duality?" might all be simple concepts -- but the jargon will need to be unpacked for most readers of HN.

Claudia de Rham had a talk a month or so back in which she said something along the lines of (this is how I remember it) "We are quite good at excluding effective gravitational models, but we are however better at constructing new ones.".

It contained references to de Rham, Dijkstra, Carlitz, Neil Sloane, Stern (of Stern-Brocot trees fame), Eisenstein, Conway, Zagier, Schönhage, Hardy, Ramanujan, and so forth.