Thanks for making my point more clearly than I did!
As an aside, regarding whether people actually do PhD-level math at these jobs, the answer is indeed often no. However, the jobs can still require PhD-level experience. This is because for the average person, there is a lag between being able to merely learn concepts at a given level versus being able to actually synthesize those concepts to solve novel problems. It is relatively easy to learn a subject and solve exercises in that subject that you know pertain to the concepts you just studied, as you would encounter in a course. It is much harder to be given a problem out of the blue and realize what concepts are required to solve it, as you would encounter in a scientific career.
As a concrete example, I once was explaining neural networks to a bright college freshman. I showed him the forward pass equation, then asked him how he would optimize the network weights given said equation. Even though he learned the chain rule in his courses, he didn’t think to apply it to derive the backpropagation step. By contrast, a talented junior or senior can easily figure this out.
In my experience, for the average person, the learning/synthesis gap is usually a few years. Hence, your average new PhD-level data scientist would be capable of synthesizing advanced undergraduate material towards solving novel problems in their job. And there are a hell of a lot of data science jobs that require that.
As an aside, regarding whether people actually do PhD-level math at these jobs, the answer is indeed often no. However, the jobs can still require PhD-level experience. This is because for the average person, there is a lag between being able to merely learn concepts at a given level versus being able to actually synthesize those concepts to solve novel problems. It is relatively easy to learn a subject and solve exercises in that subject that you know pertain to the concepts you just studied, as you would encounter in a course. It is much harder to be given a problem out of the blue and realize what concepts are required to solve it, as you would encounter in a scientific career.
As a concrete example, I once was explaining neural networks to a bright college freshman. I showed him the forward pass equation, then asked him how he would optimize the network weights given said equation. Even though he learned the chain rule in his courses, he didn’t think to apply it to derive the backpropagation step. By contrast, a talented junior or senior can easily figure this out.
In my experience, for the average person, the learning/synthesis gap is usually a few years. Hence, your average new PhD-level data scientist would be capable of synthesizing advanced undergraduate material towards solving novel problems in their job. And there are a hell of a lot of data science jobs that require that.