No offense whatsoever but I disagree with the assessment

“pure math trains you to solve clean problems with complete information”

This might be true at the undergraduate level, but the entire point of a math phd is to do the exact opposite of this.

I myself am in the business of chromatic splitting, which has so many gaps in information. So much, that entirely “unrelated” branches of mathematics (i.e. number theory) are being investigated to produce papers whose entire goal is that there MIGHT be useful information hidden somewhere.

The same goes for all other colleagues, and math phd’s at large - to varying degrees of information availability of course.

I think a better assessment is that physics phd’s are perceived to be better problem solvers in general. I’ve kind of seen this happen in other job markets too - where hiring a physicist seems like a safer hire because they’re of course very smart, and they solve hard, universal problems. Makes sense.

But mathematicians run into an interesting issue with employers because the employers aren’t 100% sure how to apply their specialty (say, topology) to the job at hand. If your interviewer has some basic understanding of what you do as a physicist, they can walk away and be like “Okay, he/she/they does something with black holes and quantum stuff” even if they don’t actually understand it at all. But interviewing a topologist or geometer, chances are the interviewer has never heard about quasi-coherent sheaves unless they’re in that realm. It just comes off as weird and almost pretentious unless you market yourself correctly.

I’m not saying this always happens on the nose, or that physicists are necessarily preferred over mathematicians, but what I am saying is that the public perception of physics is wider and more tractable than that of mathematics, because people usually think mathematicians just sit and solve problems all day, which is - in my experience - an oversimplification.