Marshall Penfield (Colin Hanks) has built much of a successful mathematical career around dissecting the Eppes Convergence, looking to prove it is flawed. He comes to CalSci to lecture on the crack in its foundation which he has uncovered, pushing Charlie to reconsider his work, and strive to improve it.
Marshall returns later as a somewhat grudging ally, but proves an excellent yardstick, against which Charlie can measure his own growth, both inside and beyond the field of mathematics. When he rides off into the sunset, a detente at least has been achieved.