MachuPikacchu on Nostr: In one of my first courses on linear algebra we were taught how to do things by hand ...

In one of my first courses on linear algebra we were taught how to do things by hand initially but from there we did everything in Mathematica.

That may seem like "cheating" or that the students wouldn't retain the lesson since a computer was doing all the work. I strongly disagree with that view in hindsight.

We were able to explore visually what matrices did to the inputs. For example, eigenvectors are the axes along which some action would happen and the eigenvalues determine the quality and degree (ie. reflection, expansion, contraction, etc.). If you're doing calculations by hand it's hard to get enough examples to build intuition and without spending a lot of time you can't "tinker with" the numbers to the same extent.

The same is going to be true of LLMs and similar tech. Sure, they can do a lot of "thinking" for you and some will argue it leads to brain rot (and maybe it will!) but it also enables you to explore many more possibilities in your finite time than you otherwise could.