>>68012910

CS, as a field, is math. It’s taught well at astonishingly few schools, all of which are research institutions. Hell, all your continuous math shows up again alongside discrete mathematics. If you take graduate level CS, this much is apparent

List of topics being

Randomized algorithms

Proof of their concentration bounds (gives you a better description of runtime than an expected value asymptotic)

Analytical combinatorics

Quantum information and computation theory

Complexity theory (used to study everything from circuit design to folding of proteins and and black hole behavior)

Homotopic type theory (foundations of mathematics)

Computability

Analog computation

Non ML AI

Systems design and proof of correctness (think things like paxos proof made to solve distributed consensus, which was a landmark result)

Computational medicine

Algorithmic game theory

Convex optimization

Compiler and language theory

The huge volume of geometry and topology research

Graphics theory and development

The list goes on. CS, as a proper mathematical science, intersects with every theory we’ve built up so far, and it’s exciting to see it carry it forward past “let’s just run this program simulation for a day.” If you’re at all interested in this, I highly suggest double majoring in math and CS (physics and CS is fine too, but you get way less pure math that shows up in CS at the grad level anyway)

t. double majored in math and CS