In 1976 together with colleague Kenneth Appel at the University of Illinois at Urbana-Champaign, Haken solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color.
Haken has introduced several important ideas, including Haken manifolds, Kneser-Haken finiteness, and an expansion of the work of Kneser into a theory of normal surfaces. Much of his work has an algorithmic aspect, and he is one of the influential figures in algorithmic topology. One of his key contributions to this field is an algorithm to detect if a knot is unknotted.
Haken is the father of six children. His eldest son Armin Haken proved that there exist propositional tautologies that require resolution proofs of exponential size. Lippold Haken, the inventor of the Continuum fingerboard, is also his son. Wolfgang Haken is the cousin of Hermann Haken, a physicist well known for laser theory and Synergetics.
- Haken, W. "Theorie der Normalflachen." Acta Math. 105, 245-375, 1961.
- Wolfgang Haken at the Mathematics Genealogy Project
- Haken's faculty page at UIUC
- Wolfgang Haken biography from World of Mathematics
- Lippold Haken's life story
- Haken, Armin (1985), "The intractability of resolution", Theoretical Computer Science 39: 297–308, doi:10.1016/0304-3975(85)90144-6
- Appel, Kenneth; Haken, Wolfgang (1989), Every Planar Map is Four Colorable, AMS, p. xv, ISBN 0-8218-5103-9