[WhitneyLand]

You stress the importance of having a Phd - How much of that is because it's really needed and how much of it is a filter / credibility signal?

[user5994461 → WhitneyLand]

You need to learn the maths and for that there is nothing close to sitting down in a master/phd classroom for years, doing hard exercises for the whole duration of it, that could get you fired of the school if you ever get a single one wrong at an exam.