Wolfgang Haken (June 21, 1928 – October 2, 2022) was a

German American German Americans (german: Deutschamerikaner, ) are Americans who have full or partial German ancestry. With an estimated size of approximately 43 million in 2019, German Americans are the largest of the self-reported ancestry groups by the Unite ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who specialized in

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

, in particular

3-manifold In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds lo ...

Biography

Haken was born in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. His father was Werner Haken, a physicist who had

Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...

as a doctoral thesis advisor. In 1953, Haken earned a Ph.D. degree in mathematics from Christian-Albrechts-Universität zu Kiel (Kiel University) and married Anna-Irmgard von Bredow, who earned a Ph.D. degree in mathematics from the same university in 1959. In 1962, they left Germany so he could accept a position as visiting professor at the

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

. He became a full professor in 1965, retiring in 1998. In 1976, together with colleague

Kenneth Appel Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American 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-c ...

at the

, Haken solved the

four-color theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...

. 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 ideas, including

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. Sometimes one considers only orientable Haken manifolds, in w ...

s, Kneser-Haken finiteness, and an expansion of the work of Kneser into a theory of

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'' (see figure). A triangle cuts off a vertex of the tetrahedron wh ...

s. Much of his work has an algorithmic aspect, and he is a figure in

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. A primary concern of algorithmic topology, as its ...

. One of his key contributions to this field is an algorithm to detect if a knot is unknotted. Haken's eldest son, Armin, proved that there exist

propositional In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

tautologies that require

resolution Resolution(s) may refer to: Common meanings * Resolution (debate), the statement which is debated in policy debate * Resolution (law), a written motion adopted by a deliberative body * New Year's resolution, a commitment that an individual mak ...

proofs of exponential size. Haken's eldest daughter, Dorothea Blostein, is a professor of computer science, known for her discovery of the master theorem for divide-and-conquer recurrences. Haken’s second son, Lippold, is the inventor of the

Continuum Fingerboard The Continuum Fingerboard or Haken Continuum is a music performance controller and synthesizer developed by Lippold Haken, a professor of Electrical and Computer Engineering at the University of Illinois, and sold by Haken Audio, located in Cham ...

. Haken’s youngest son, Rudolf, is a professor of music, who established the world's first Electric Strings university degree program at the

. Wolfgang is the cousin of

Hermann Haken Hermann Haken (born 12 July 1927) is physicist and professor emeritus in theoretical physics at the University of Stuttgart. He is known as the founder of synergetics. He is a cousin of the mathematician Wolfgang Haken, who proved the Four ...

, a physicist known for laser theory and synergetics. In 1978, Haken delivered an

invited address at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in Helsinki. He was a recipient of the 1979

Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...

of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

for his solution with Appel of the

.Delbert Ray Fulkerson Prize

. Accessed May 29, 2011 Wolfgang Haken with Marshall Pangilinan

References

* Haken, W. "Theorie der Normalflachen." ''Acta Math''. 105, 245–375, 1961. *

External links

Wolfgang Haken memorial website
*
Haken's faculty page at the University of Illinois at Urbana-Champaign

Wolfgang Haken biography from World of Mathematics

Lippold Haken's life story
* * {{DEFAULTSORT:Haken, Wolfgang 1928 births 2022 deaths Topologists University of Illinois Urbana-Champaign faculty University of Kiel alumni German emigrants to the United States

Biography

See also

References

External links