In 1984, Celso Costa wrote down a formula for a minimal surface that would awaken the slumbering mathematical discipline of minimal surfaces. Up to then, the known complete, embedded minimal surfaces of finite topology, were just the plane, the catenoid and the helicoid, and many mathematicians believed that that was that. 

Hoffman and Meeks used then-cutting edge computer graphics to make crude images of the surface. The pictures suggested symmetries not obvious from the formulas, which allowed them to prove that this was the first embedded example in 200 years. Since then, the theory has exploded, providing dozens of new types of examples unimaginable before, and a wealth of classification results.- Matthias Weber