Would you hire a doctor by insisting they perform surgery in front of you? Would you hire a lawyer by demanding they filling out legal paperwork in front of you?

My background is a mix of neuroscience/biology and machine learning, and it's always funny to me how jobs right on that margin interview totally differently, depending on how the organization started.

If they think of themselves as "tech", you're at the whiteboard, reversing strings in C and playing games with trees. When I interviewed for nearly identical job in a "science" department, someone spent 45 minutes chatting with me about the coding behind projects I had mentioned. I even offered to show or write soome code and got told "Nah, we already looked at your github and it's fine."

I imagine doctors are rarely hired "cold" - they have some sort of prior relationship with the hiring institution or someone working there. E.g. they are already consulting there, or another doctor who works there has worked with them closely on a case etc.

Same for lawyers. You'd be targeting someone whom you've dealt or worked with in prior lawsuits (maybe they were the opposition counsel), deals (counsel for the other party), or complex cases involving multiple law firms working for the same side.

Would you judge a jazz musician by asking him where Miles Davis learned to play music?

No but I absolutely would have them audition.

It is only a false equivalence in that programming literally != sculpting. It is a relevant analogy, however.

It's still not - we would not ask someone to make a painting or drawing or animation or maquette or 3d model on the spot during an on site/video interview ( maybe you might personally but that generally not practiced) - that is directly analogous.

I don't get what is wrong with expecting a candidate to have carefully read an algorithms book at some point in their lives. Most software engineering jobs expect a degree in CS, that implies 3-4 years of study. You should be able to remember important information related to CS.