Still, it may be surprising to learn that these weren't doing their famous work within the university system: Copernicus, Tycho Brahe, Descartes, Pascal, Huygens, Leibniz, Euler, Lagrange, Laplace, Leeuwenhoek, Halley, Spinoza, Hobbes, Cavendish.
Kepler didn't get a professorship and did his most famous work (elliptical orbits, Kepler's Laws) later in Prague as imperial mathematician.
Newton is the main one who indeed was a prof in Cambridge during his main works.
It could be that interest in research itself is a relatively recent development. A lot of scholarship amounted to study of past scholarship, until science came along. Empirical science as we know it was barely a century old when Newton came along.
Kepler didn't get a professorship and did his most famous work (elliptical orbits, Kepler's Laws) later in Prague as imperial mathematician.
Newton is the main one who indeed was a prof in Cambridge during his main works.