Landmarks of subjects of mathematics
Differential Geometry: the Gauss-Bonnet theorem.
I took a one-semester intro course on differential geometry class and we got to this towards the end of the semester, so I feel that a couple of months is an appropriate time frame for this theorem.
In Analytic Number Theory, the Prime Number Theorem is a great result.
Riemann's 1859 paper, which outlined a possible approach to proving the PNT, is credited with motivating a large amount of the research done in Complex Analysis in the 19th century.