I agree, needs to be ranked per capita, but I still think that Harvard would be #1.
You'd have to account for type and breadth of schools within each, in that case. Many schools don't have medical or architecture schools, so why include per capita counts?
Yale would be #1
What gives you the idea that Harvard is high population? It only has ~21000 at a time, including undergrad, grad, and professional students. Cal has 38000.
Princeton has 7,946 total undergrad and grad students. Dartmouth has just 6,298.