You check it's work. I used it to calculate efficiency in a factory game and went through and made corrections to inconsistencies I spotted. Always check it's work.

I use it for explaining stuff when studying for uni and I do it like this: If I don't understand e.g. a definition, I ask an LLM to explain it, read the original definition again and see if it makes sense.

This is an informal approach, but if the definition is sufficiently complex, false answers are unlikely to lead to an understanding. Not impossible ofc, so always be wary.

For context: I'm studying computer science, so lots of math and theoretical computer science.

I'm not at all confident in the answers directly. I've gotten plenty of wrong answers form AI and I've gotten plenty of correct answers. If anything it's just more practice for critical thinking skills, separating what is true and what isn't.

When it comes to math though, it's pretty straightforward, I'm just looking for context on some steps in the problems, maybe reminders of things I learned years ago and have forgotten, that sort of thing. As I said, I'm interested in actually understanding the stuff that I'm learning because I am using it for the things I'm working on so I'm mainly reading through textbooks and using AI as well as other sources online to round out my understanding of the concepts. If I'm getting the right answers and the things I am doing are working, it's a good indicator I'm on the right path.

It's not like I'm doing cutting edge physics or medical research where mistakes could cause lives.

I personally use it's answers as a jumping off point to do my own research, or I ask it for sources directly about things and check those out. I frequently use LLMs for learning about topics, but definitely don't take anything they say at face value.

For a personal example, I use ChatGPT as my personal Japanese tutor. I use it discuss and break down nuances of various words or sayings, names of certain conjugation forms etc. etc., and it is absolutely not 100% correct, but I can now take the names of things that it gives me in native Japanese that I never would have known and look them up using other resources. Either it's correct and I find confirming information, or it's wrong and I can research further independently or ask it follow up questions. It's certainly not as good as a human native speaker, but for $20 a month and as someone who likes enjoys doing their own research, I fucking love it.

I, like the OP, was also studying math from a textbook and using GPT4 to help clear things up. GPT4 caught an error in the textbook.

The LLM doesn't have a theory of mind, it wont start over and try to explain a concept from a completely new angle, it mostly just repeats the same stuff over and over. Still, once I have figured something out, I can ask the LLM if my ideas are correct and it sometimes makes small corrections.

Overall, most of my learning came from the textbook, and talking with the LLM about the concepts I had learned helped cement them in my brain. I didn't learn a whole lot from the LLM directly, but it was good enough to confirm what I learned from the textbook and sometimes correct mistakes.

He is cross checking

I mean, why are you confident the work in textbooks is correct? Both have been proven unreliable, though I will admit LLMs are much more so.

The way you verify in this instance is actually going through the work yourself after you’ve been shown sources. They are explicitly not saying they take 1+1=3 as law, but instead asking how that was reached and working off that explanation to see if it makes sense and learn more.

Math is likely the best for this too. You have undeniable truths in math, it’s true, or it’s false. There are no (meaningful) opinions on how addition works other than the correct one.