As a math professor, I care much more about the key idea, heuristics, and motivation than the proof. With the others in place the proof is clear, something an AI or a student can do.
As a math professor, I care much more about the key idea, heuristics, and motivation than the proof. With the others in place the proof is clear, something an AI or a student can do.
Well, it's knowing when to push and when to not. You probably have an intuition for, I don't know, abstract algebra objects (I don't know your field of specialty :P), without needing to symbolically manipulate all of it, but you developed a deep intuition for them through many proofs and attempts at proofs with them.
Im glad you brought up abstract algebra—that was the one class in my math undergrad that I never developed an intuition for. I learned to do the proofs by pushing symbols around and putting bars on top of them but I never felt like I understood what was happening.
That's leaning into engineering, away from math. Heuristics aren't always accurate. Math history before proof is the history of delusion. Idea, heuristics, and motivation aren't nearly enough for correctness outside of a sandbox.