My kid (an actual rocket scientist) told me the AI he had access too was pretty bad at linear algebra. I’ve had eigenvalues on my mind lately, so I thought that would be a good opportunity for a test. I asked Copilot about a conjecture, that a subset of stocks in a system having nontrivial participation factors should correspond with a feedback loop or loops.
TLDR; Copilot decided to proceed by contradiction (which is smart) and constructed a series of alleged counterexamples that violated the assumptions in my question in obvious ways (which is dumb). I’d say this is a poor showing, because it’s hallucinating, making overconfident proclamations, and doing it all with a smarty-pants superior attitude. I’d say this was a net waste of electrons. I did get some useful thoughts out of the process, but overall it took me longer to check and reject the incorrect answers than it would have for me to dig deeper on my own.
Interestingly, this is not my experience with linear algebra coding using Claude Code CLI. If I have a very concrete spec for operations I’d like to perform to realize a particular analysis, Claude is very good at building the data structures and library calls needed to make it work. I think the key difference is that the code is testable, with verification in the loop. This is also the difference between quantitative modeling and making predictions from verbal or intuitive models.
