Wolfgang Haken
Encyclopedia
Wolfgang Haken is a mathematician
who specializes in topology
, in particular 3-manifold
s.
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 manifold
s, Kneser-Haken finiteness, and an expansion of the work of Kneser
into a theory of normal surface
s. 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.
Haken delivered an invited address at the 1978 International Congress of Mathematicians
in Helsinki.
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.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who specializes in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, in particular 3-manifold
3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
s.
In 1976 together with colleague Kenneth Appel
Kenneth Appel
Kenneth Ira Appel is a mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem...
at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
, 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 manifold
Haken manifold
In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface...
s, Kneser-Haken finiteness, and an expansion of the work of Kneser
Hellmuth Kneser
Hellmuth Kneser was a German mathematician, who made notable contributions to group theory and topology. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds...
into a theory of normal surface
Normal surface
In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron so that each component of intersection is a triangle or a quad . A triangle cuts off a vertex of the tetrahedron while a quad separates pairs of vertices...
s. Much of his work has an algorithmic aspect, and he is one of the influential figures in algorithmic topology
Algorithmic topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular computational geometry and computational complexity theory....
. 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
Propositional formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value...
tautologies
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...
that require resolution
Resolution (logic)
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic...
proofs of exponential
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
size. Lippold Haken, the inventor of the Continuum fingerboard
Continuum (instrument)
The Continuum Fingerboard or Haken Continuum is a music performance controller developed by Lippold Haken, a professor of Electrical and Computer Engineering at the University of Illinois, and sold by Haken Audio, located in Champaign, Illinois....
, is also his son.
Haken delivered an invited address at the 1978 International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Helsinki.
Wolfgang Haken was a recipient of the 1979 Fulkerson Prize
Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Programming Society and the American Mathematical Society . Up to three awards of $1500 each are presented at each International Symposium of the MPS...
of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
for his solution with Appel of the four-color problem.