Proof by Bureaucracy

March 16, 2025
By Aathreya Kadambi

I’ve been reading Lee’s Riemannian geometry book, and I thought it was funny, because I kind of skipped over reading smooth manifolds, so now I have to experience what I like to call “proofs by bureaucracy”. For example, see his proofs of Existence and Uniqueness of Geodesics and Properties of the Exponential Map. At the end of the day, the bulk of the proof is just calling a result from the appendix: A.42. All right Lee, I know you’ve already written up the proof in your smooth manifolds book, but now I have to go reference that one to understand the deeper meaning behind this result! 🤦‍♂️ The only words I have are: what a proof by bureaucracy 😩.

I guess I should have read smooth manifolds. But at the same time, it’s been much more fun reading Riemannian manifolds first and referring to his smooth manifolds book as needed tbh. I feel the same way about classes like measure theory and commutative algebra. They’re alright, but if you refer to them while you’re going through functional analysis, probability theory, or algebraic geometry… I just think it’s much more fun that way!