Have you ever done of the interviews? Or given? I've done both, multiple times and currently work there. Generally speaking the interviews are not "regurgitate academic CS" on demand. It does test your algorithmic and data structure thinking. Reason being is it's hard to find questions that are complex enough to be hard, yet easy to explain in just a few minutes, AND has richness of details. Those kinds of problems tend to be mathematical, algorithmic, etc. Stuff that, yes, is unlike what you do 80% of the time, but that is expected to be able to do.

I made it thru my interviews without remembering obscure things, only knowing basic O-notation, and generally not being a math genius.

I'm not sure where this perception comes from -- my guess is it's a mix of cognitive dissonance and overgeneralizing from bad experiences.

The majority of interview questions I've encountered (at Google and elsewhere) are of the form: here's a data structure or API, can you use it to solve some problem? Nobody's ever asked me to prove A* from scratch. Even in cases where the question does revolve around a specific algorithm or CS concept they've always taken the time to explain it. I used to ask a question based around LZ77 encoding and I always went over the algorithm whether or not the candidate was familiar with it.

That's when I think there's some difference in the way mathematics is being taught in engineering and the way it is taught to mathematicians.

It is very different to attend a calculus class and learn to apply some formulas and that's all. You vaguely remember the formulas some years later, and the algebraic abilities are all you have, but they are still very powerful tools.

However, if you do a mathematics course like advanced linear algebra then you realize that for this particular teacher knowing the formulas doesn't matter, at all. You have to write proofs for everything. And these proofs require all of your imagination, all of your experience and then some.

It changes the way you approach every single problem from that moment.

Now, most people have never needed that ability. Most people will never exert themselves to the stress, the lost nights of sleep and the sheer single mindedness that drives everything out of your mind for days, until you get that proof. That damned proof you will never forget for months, if ever.

The end result is that it makes your mind work in overdrive for solving the same kind of problems.

So the issue is that some people have memorized stuff (and that never works well for too long), while other people has taken that stuff as the first step, and then through a long process of proving every single step of one or more theorems, have tattooed that stuff in some part of their minds, and are simply trying to find someone having a similar tattoo, to find someone with whom they can relate about their shared experience.

Anyway, the people I know that can do that, don't really like to program computers.

You have said that you haven't interviewed with them, and don't work there. You seem to be spouting a lot of bullshit for someone who hasn't had these experiences.