Enumerative geometry is a branch of geometry concerned with questions like the following: “Given four lines in 3-space, how many lines are there which intersect all four of them?”. In the late 19th century, Hermann Schubert introduced Schubert Calculus, which gives answers to some of these questions with surprising efficiency. The intrinsic beauty of the subject led to David Hilbert asking for a rigorous foundation for it as the 15th of his famous 23 problems. We will discuss how this was achieved in an accessible way, focusing on the example question above. No prior knowledge of Grassmannians or cohomology theories will be assumed.