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Only tangenially relevant, but the exagerrated differentiation of universities, and levels of education (e.g. PhD vs. not) has always been bothering me. I only have experience in a different field (CS), and yes, those things can be indicators, but I've experienced so many outliers in both directions to know that degrees need to be taken with more than just a grain of salt.

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This differentiation is amplified in (pure) mathematics, where two different subfields can have essentially zero overlap*, making peer review and general QA difficult to scale.

* Physical sciences also have a lot of diversity, but at least you can go to their labs and see their equipment, reagents, data, etc cetera.

Yes, this is essentially because mathematics is such an old science and goes very deep into branches. That's btw also why getting a certain degree is much harder there than in any other fields I've seen (did a bunch of courses at university in various fields, and the diff between e.g. pure math and psychology is almost comical).

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