I have experience with both mathematics and CS departments, and I have exactly the opposite opinion. I think the Old School Mathematics model is absolute garbage and often explicitly and intentionally exploitative.
1. It's not like those math Ph.D.s are sitting around reading textbooks with their advisors.
They are TA'ing service courses. A lot of TA'ing. In addition to TA'ing, they are prepping for a high-stakes exam.
The exam will wash out the 50-70% of people who are needed as temp TA labor but whom the department has no intention of advising through to a Ph.D.
After 2 or 3 years, you pass the exam. Yay! But wait. Reading textbooks with your advisor? No! you need to take a whole slew of courses. Why? Because course enrollment == money and easy/interesting teaching assignments. And good luck getting tons of research done in-between your TA'ing and courses...
Now you're done with courses! Yay! After TA duties, you can spend 100% of your time on research (aka 50% of a 40 hour work week aka 80% of a grad student work week). Except you only have 2 years left :-(
So now it's on to 1-3 postdocs so that you can start doing, after 5 years, what that CS phd student was doing when they "hit the ground running": build a research agenda that resonates with a large enough set of researchers that it translates into a research job.
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Also, the "one singular result" style of research is unique not just to mathematics, but to a particular subset of mathematics. It's just not a good fit for most research problems, even in Mathematics. I've seen tons of well-composed dissertations focused on a singular, pointless problem.
The hodgepodge dissertations don't have a "beautiful singular result" feel, but almost invariably contribute at least one piece of useful, new knowledge.
Finally, worth noting that the best and brightest don't leave research; they might leave academia, but typically not research.
TL;DR: If you can find an advisor who isn't a slave driver (the majority of them at good places), the CS model is 1000% better than the Math model. You might be hired as a researcher for someone else's research agenda, but at least you don't spend the first 1/3rd of the phd as temp teaching labor stressing over high-stakes exams.
> The exam will wash out the 50-70% of people who are needed as temp TA labor but whom the department has no intention of advising through to a Ph.D.
At which department?
Speaking as a math professor in an American research university -- this is unusual. Pass rates at most places are reasonably high, and professors hope that as many people as possible pass.
It is true that grad students are expected to TA (if they want funding); usually grant funding is not available to support them. But generally the teaching burdens are relatively modest, around ~15 hours a week including grading and office hours.
If you really believe this, pressure USC's department to start publishing their pass rates each year and pressure your peers at other institutions to do the same. IME departments outright lie on visit days and/or change their definition of "reasonable" any time they accidentally over-admit.
E.g., Berkeley -- one of the few places to actually reveal information of any sort on prelim pass rates -- describes their pass rate as "reasonable" and in the same sentence goes on to clarify that they typically pass 2/3rds of students but of course don't make any promises or anything.
Maybe us Ph.D.s are so damn battle-scarred we don't realize that a 1/3rd attrition rate on a poverty salary is actually really unacceptable and absolutely not normal? Can you name a single software company that works like that?
1. It's not like those math Ph.D.s are sitting around reading textbooks with their advisors.
They are TA'ing service courses. A lot of TA'ing. In addition to TA'ing, they are prepping for a high-stakes exam.
The exam will wash out the 50-70% of people who are needed as temp TA labor but whom the department has no intention of advising through to a Ph.D.
After 2 or 3 years, you pass the exam. Yay! But wait. Reading textbooks with your advisor? No! you need to take a whole slew of courses. Why? Because course enrollment == money and easy/interesting teaching assignments. And good luck getting tons of research done in-between your TA'ing and courses...
Now you're done with courses! Yay! After TA duties, you can spend 100% of your time on research (aka 50% of a 40 hour work week aka 80% of a grad student work week). Except you only have 2 years left :-(
So now it's on to 1-3 postdocs so that you can start doing, after 5 years, what that CS phd student was doing when they "hit the ground running": build a research agenda that resonates with a large enough set of researchers that it translates into a research job.
--
Also, the "one singular result" style of research is unique not just to mathematics, but to a particular subset of mathematics. It's just not a good fit for most research problems, even in Mathematics. I've seen tons of well-composed dissertations focused on a singular, pointless problem.
The hodgepodge dissertations don't have a "beautiful singular result" feel, but almost invariably contribute at least one piece of useful, new knowledge.
Finally, worth noting that the best and brightest don't leave research; they might leave academia, but typically not research.
TL;DR: If you can find an advisor who isn't a slave driver (the majority of them at good places), the CS model is 1000% better than the Math model. You might be hired as a researcher for someone else's research agenda, but at least you don't spend the first 1/3rd of the phd as temp teaching labor stressing over high-stakes exams.