Basically an equivalent of simple algorithmic questions. Not "real" because it's impossible to share enough context of a real problem in an interview to make it practical. Short, testing principles, but most importantly basic thinking and problem solving facilities.
I've been an engineer in the past (physics undergrad -> aerospace job -> grad school/ml). I have never seen or heard of an engineer being expected to solve math equations on a whiteboard during an interview. It is expected that you already know these things. Honestly, it is expected that you have a reference to these equations and you'll have memorized what you do most.
As an example, I got a call when I was finishing my undergrad for a job from Raytheon. I was supposedly the only undergrad being interviewed but first interview was a phone interview. I got asked an optics question and I said to the interviewer "you mind if I grab my book? I have it right next to me and I bookmarked that equation thinking you might ask and I'm blanking on the coefficients (explain form of equation while opening book)". He was super cool with that and at the end of the interview said I was on his short list.
I see no problem with this method. We live in the age of the internet. You shouldn't be memorizing a bunch of stuff purposefully, you should be memorizing by accident (aka through routine usage). You should know the abstractions and core concepts but the details are not worth knowing off the top of your head (obviously you should have known at some point) unless you are actively using them.
For a proper engineering question (as in not software), I'd expect the expected answer to be naming the reference book where you'd look up the formula. Last thing you want is someone overconfident in their from memory version of physics.
Honestly, having been in both worlds, there's not too much of a difference. Physics is harder but coding you got more things to juggle in your brain. So I really do not think it is an issue to offload infrequent "equations"[0] to a book/google/whatever.
[0] And equations could be taken out of quotes considering that math and code are the same thing.
"How do you know your memory was infallible at that moment? Would you stake other people's lives on that memory?"
So what you did on that phone interview was probably the biggest green-flag they'd seen all day.
You still can't get GPT to understand and give nuanced responses without significant prompt engineering (usually requiring someone that understands said nuance of the specific problem). So... I'm not concerned. If you're getting GPT to pass your interviews, then you should change your interviews. LLMs are useful tools, but compression machines aren't nuanced thinking machines, even if they can mascaraed as such in fun examples.
Essentially ask yourself this: why in my example was the engineer not only okay with me grabbing my book but happy? Understand that and you'll understand my point.
Edit: I see you're the founder of Archipelago AI. I happen to be an ML researcher. We both know that there's lots of snakeoil in this field. Are you telling me you can't frequently sniff that out? Rabbit? Devon? Humane Pin? I have receipts for calling several of these out at launch. (I haven't looked more than your profile, should I look at your company?)
> I see you're the founder of Archipelago AI.
I don't know where you got that from, but I'm not.
Being asked a theoretical chemistry question at a job interview would be...odd.
You can be asked about your proficiency with some lab equipment, your experience with various procedures and what not.
But the very thought of being asked theoretical questions is beyond ridiculous.
What would be the point of asking theoretical questions?
There's just no way in hell people can remember even 10% of what they studied in college, book knowledge isn't really the goal, rather than teaching you how to learn and master the topics.
My degree is in computational/theoretical chemistry. Even before I went into software engineering, it would have been really odd for me to be asked questions about wet chemistry.
Admittedly it would have been odd to be quizzed on theory out of the blue as well.
What would not have been odd was to give a job talk and be asked questions based on that talk; in my case this would have included aspects of theory relevant to the simulation work and analysis I presented.
