You only need to do Big-O proofs at work if your job is thinking up entirely new algorithms. But that *is* your CS theory professor's other job (besides teaching), so they think it's really important to know.https://twitter.com/EmilyKager/status/967165799071809536 …
Generally BA/BS should prepare you to locate & make practical use of results in your field of study, PhD should prepare you to develop new results.

