Kenneth Appel
Encyclopedia
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. 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.
The proof has been one of the most controversial of modern mathematics because of its heavy dependence on computer "number-crunching" to sort through possibilities, which drew criticism from many in the mathematical community for its inelegance: "a good mathematical proof is like a poem — this is a telephone directory!" Appel and Haken agreed in a 1977 interview that it was not "elegant, concise and completely comprehensible by a human mathematical mind".
However, the proof was the start of a sea-change in mathematicians' attitudes toward computers – which they had largely disdained as a tool for engineers rather than for theoreticians - leading to the creation of what is sometimes called "experimental mathematics
".
Appel studied at Queens College
and the University of Michigan
, followed by research at the Institute for Defense Analyses
in Princeton before he became a faculty member at the University of Illinois at Urbana-Champaign
in 1961.
From 1993 through 2002, Appel was chair of the mathematics department at the University of New Hampshire
in Durham, New Hampshire
. Although retired now, he still works and occasionally teaches there and has an office on campus. As emeritus faculty Appel works with local schools in implementing and maintaining WeBWorK
, a web-based open source mathematics-assignment system developed at the University of Rochester.
Kenneth Appel is the father of Andrew Appel
, a noteworthy computer scientist.
Wolfgang Haken
Wolfgang Haken 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...
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...
, solved one of the most famous problems in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, 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.
The proof has been one of the most controversial of modern mathematics because of its heavy dependence on computer "number-crunching" to sort through possibilities, which drew criticism from many in the mathematical community for its inelegance: "a good mathematical proof is like a poem — this is a telephone directory!" Appel and Haken agreed in a 1977 interview that it was not "elegant, concise and completely comprehensible by a human mathematical mind".
However, the proof was the start of a sea-change in mathematicians' attitudes toward computers – which they had largely disdained as a tool for engineers rather than for theoreticians - leading to the creation of what is sometimes called "experimental mathematics
Experimental mathematics
Experimental mathematics is an approach to mathematics in which numerical computation is used to investigate mathematical objects and identify properties and patterns...
".
Appel studied at Queens College
Queens College, City University of New York
Queens College, located in Flushing, Queens, New York City, is one of the senior colleges of the City University of New York. It is also the fifth oldest of the City University's twenty-three institutions of higher learning. The college's seventy seven acre campus is located in the heart of the...
and the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, followed by research at the Institute for Defense Analyses
Institute for Defense Analyses
The Institute for Defense Analyses is a non-profit corporation that administers three federally funded research and development centers to assist the United States government in addressing important national security issues, particularly those requiring scientific and technical expertise...
in Princeton before he became a faculty member 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...
in 1961.
From 1993 through 2002, Appel was chair of the mathematics department at the University of New Hampshire
University of New Hampshire
The University of New Hampshire is a public university in the University System of New Hampshire , United States. The main campus is in Durham, New Hampshire. An additional campus is located in Manchester. With over 15,000 students, UNH is the largest university in New Hampshire. The university is...
in Durham, New Hampshire
Durham, New Hampshire
As of the census of 2000, there were 12,664 people, 2,882 households, and 1,582 families residing in the town. The population density was 565.5 people per square mile . There were 2,923 housing units at an average density of 130.5 per square mile...
. Although retired now, he still works and occasionally teaches there and has an office on campus. As emeritus faculty Appel works with local schools in implementing and maintaining WeBWorK
WeBWorK
WeBWorK is an online homework delivery system primarily used for mathematics and science. It allows students to complete their homework over the web, and receive instantaneous feedback as to the correctness of their responses...
, a web-based open source mathematics-assignment system developed at the University of Rochester.
Kenneth Appel is the father of Andrew Appel
Andrew Appel
Andrew Wilson Appel is the Eugene Higgins Professor of computer science at Princeton University, New Jersey. He is especially well-known because of his compiler books, the Modern Compiler Implementation in ML series, as well as Compiling With Continuations...
, a noteworthy computer scientist.