I agree, it can be incredibly frustrating at times. My rule is that if it “compiles” in my brain as an understood idea then i accept it. I also push back a lot (sometimes it points out good errors in my thinking, sometimes it admits it hallucinated). Real humans hallucinate a lot as well or confidently state subtly wrong ideas, it’s a good habit anyway. It’s basically the same approach when presented with a “formula” for something in school. If i dont know how to derive/prove it then i dont accept it as part of my memorized or accepted toolkit/things i use (and try to forget it). If it fits with the rest of my network of understood ideas i do. It’s annoying but still more time efficient than trawling through lecture slides with domain specific language etc