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Wolfgang Haken (born June 21, 1928 in Berlin, Germany) is a mathematician who specializes in topology, in particular 3-manifolds. 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. In 1978 Haken delivered an invited address at the International Congress of Mathematicians in Helsinki.〔(International Congress of Mathematicians 1978 ). International Mathematical Union. Accessed May 29, 2011〕 Wolfgang Haken was a recipient of the 1979 Fulkerson Prize of the American Mathematical Society for his solution with Appel of the four-color problem.〔(Delbert Ray Fulkerson Prize ), American Mathematical Society. Accessed May 29, 2011〕 ==See also== * Unknotting problem 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wolfgang Haken」の詳細全文を読む スポンサード リンク
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