If I ask it a question, I try not to trust it immediately, and I independently look the answer up and I argue with it. In turn, it actually is one of my favorite learning tools, because it kind of forces me to figure out why it's wrong and explain it.
Fighting with the AI's wrongness out of spike is an unexpectedly good motivator.
I guess at some level this is almost what "prompt engineering" is (though I really hate that term), but I use it as a learning tool and I do think it's been really good at helping me cement concepts in my brain.
Interesting, that's the basic process I follow myself when learning without ChatGPT. Comparing my mental representation of the thing I'm learning to existing literature/results, finding the disconnects between the two, reworking my understanding, wash rinse repeat.
It can be hard for me to directly figure out when my mental model is wrong on something. I'm sure it happens all the time, but a lot of the time I will think I know something until I feel compelled to prove it to someone, and I'll often find out that I'm wrong.
That's actually happened a bunch of times with ChatGPT, where I think it's wrong until I actually interrogate it, look up a credible source, and realize that my understanding was incorrect.
Finally, LLMs teach us the good habits.
Arcane language is actually kind of a pet peeve of mine in theoretical CS and mathematics. Sometimes it feels like academics really obfuscate relatively simple concepts but using a bunch of weird math terms. I don't think it's malicious, I just think that there's value in having more approachable language and metaphors in the process of explaining thing.
ChatGPT (Gemini/Anthropic/etc) have the advantage of never getting sick of arguing with me. I can go back and forth and argue about any weird topic that I want for as long as I want at any time of day and keep learning until I'm bored of it.
Obviously it depends on the person but I really like it.
Beyond just subject-wise, finding people who argue in good faith seems to be an issue too. There are people I'm friends with almost specifically because we're able to consistently have good-faith arguments about our strongly opposing views. It doesn't seem to be a common skill, but perhaps that has something to do with my sample set or my own behaviors in arguments.
Politically? Yeah, nearly impossible to find anyone who argues in good faith.
Even with that, it took a process that had taken multiple hours before down to about 30-45 minutes. It was super cool.
[1] Just to be clear, I always did the homework assignments myself beforehand to make sure that a solution was solvable and fair before I assigned it.
Usually for it to get a correct answer, I have to provide it a bit of context.