"It’s difficult to support undergrad without good researchers and an accompanying grad school. Or rather, it is superficially possible, but in a couple generati

"It’s difficult to support undergrad without good researchers and an accompanying grad school. Or rather, it is superficially possible, but in a couple generations (academic ones, i.e. in a decade or two), as graduates of the school assume teaching positions, a kind of vicious circle of degeneration sets in [...]" I don't agree with this. First, because there are a bunch of elite liberal arts colleges in the US that serve as direct counterexamples. Second, because the teachers at these schools are not typically drawn from graduates of the school, but from PhD graduates of mid- to high-ranking research programs. To give one example, Francis Su (who writes a lot about math education) teaches at Harvey Mudd – an excellent institution with no graduate program – and earned a PhD from Harvard. Also: "Unfortunately, the amount of places in the world doing fundamental maths, places diverse enough that you can stand in the hallway and find someone who can explain to you a subject far removed from your own (that’s essentially what counts as “world-class”), is perhaps a couple dozen, certainly not in the hundreds." This is just wrong. Diversity is not really essential to the ranking or quality of a department. Plenty of top places eschew certain subjects (logic, combinatorics) or have relatively narrow tastes (NYU Courant, Princeton ORFE). Building strong groups in a few focus areas is much more important for research productivity. It sucks to be the only person doing Subject X at a certain place.