Professor Haken was completing work on the Recognition Problem of the 3-dimensional Sphere and on a new, faster algorithm for the Knotting Problem. His earlier solution of the Knotting Problem—an open problem since 1847—used radically unconventional methods to find an algorithm to determine whether a given closed polygon in 3-space is knotted. These same methods led to the solution of the Decision Problem in a great variety of cases. With Kenneth Appel, he completed a proof of the Four Color Conjecture that had been considered the major outstanding problem in graph theory, open since its formulation in 1852. For this work, he and Appel received the Delbert Ray Fulkerson Prize in Discrete Mathematics awarded by the American Mathematical Society and the Mathematical Programming Society.

In Memoriam