Editing Kenneth Appel

{{short description|American mathematician (1932–2013)}}
{{Infobox scientist
| birth_name        = Kenneth Ira Appel
| image             = Kenneth appel 1970.jpg
| caption           = Appel in 1970
| birth_date        = {{Birth date|1932|10|8}}
| birth_place       = [[Brooklyn]], [[New York (state)|New York]]
| death_date        = {{death date and age|2013|04|19|1932|10|8}}
| death_place       = [[Dover, New Hampshire]]
| citizenship       = [[United States of America|American]]
| ethnicity         = 
| fields            = [[Graph theory]], [[combinatorics]], [[topology]]
| workplaces        = [[University of Illinois at Urbana–Champaign]], [[University of New Hampshire]]
| alma_mater        = [[B.S.]] – [[Queens College, City University of New York|Queens College, CUNY]]<br />[[Doctor of Philosophy|Ph.D.]] – [[University of Michigan]]
| doctoral_advisor  = [[Roger Lyndon]]
| doctoral_students = <!-- [[Weldon Bliss]]<br />[[Jo Ann Fellin]]<br />[[Everett Gibson]]<br />[[Zhu-Xin Hu]]<br />[[John Koch]] -->
| known_for         = Proving the [[Four-color theorem]] with [[Wolfgang Haken]]
| influences        = 
| influenced        = 
| awards            = [[Fulkerson Prize]] [1979]
| signature         = <!--(filename only)-->
| footnotes         = 
| children          = [[Andrew Appel]]<ref name="memoriam">{{Cite web|last=|first=|date=|title=In Memoriam: Kenneth Appel|url=https://math.illinois.edu/resources/department-history/faculty-memoriam/kenneth-appel|archive-url=https://web.archive.org/web/20211201130155/https://math.illinois.edu/resources/department-history/faculty-memoriam/kenneth-appel|archive-date=2021-12-01|access-date=2020-09-07|website=math.illinois.edu}}</ref><br />
[[Peter H. Appel]]<ref name="memoriam" />
}}

'''Kenneth Ira Appel''' (October 8, 1932 – April 19, 2013) was an [[Americans|American]] [[mathematician]] who in 1976, with colleague [[Wolfgang Haken]] at the [[University of Illinois at Urbana–Champaign]], solved the [[four-color theorem]], one of the most famous problems in [[mathematics]]. 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 was controversial because it depended on thousands of computer calculations that could not be double-checked by hand, the first prominent example of such a process.

==Biography==
Appel was born in [[Brooklyn, New York]], on October 8, 1932. He grew up in [[Queens, New York]], and was the son of a Jewish<ref name=jinfo>{{cite web |url=http://www.jinfo.org/Mathematics_Comp.html |title=Jewish Mathematicians |website=Jinfo.org |accessdate=29 June 2018}}</ref> couple, Irwin Appel and Lillian Sender Appel. He worked as an [[actuary]] for a brief time and then served in the [[U.S. Army]] for two years at Fort Benning, Georgia, and in [[Baumholder, Germany]]. In 1959, he finished his doctoral program at the [[University of Michigan]], and he also married Carole S. Stein in [[Philadelphia]]. The couple moved to [[Princeton, New Jersey]], where Appel worked for the [[Institute for Defense Analyses]] from 1959 to 1961. His main work at the Institute for Defense Analyses was doing research in [[cryptography]]. Toward the end of his life, in 2012, he was elected a [[Fellow]] of the [[American Mathematical Society]]. He died in [[Dover, New Hampshire]], on April 19, 2013, after being diagnosed with [[esophageal cancer]] in October 2012.<ref name="Obituary">{{Cite web|last=|first=|date=|title=Kenneth Appel Obituary (1932 - 2013) - Dover, NH|url=https://www.legacy.com/us/obituaries/fosters/name/kenneth-appel-obituary?id=20368248|archive-url=https://web.archive.org/web/20240101094706/https://www.legacy.com/us/obituaries/fosters/name/kenneth-appel-obituary?id=20368248|archive-date=2024-01-01|access-date=2024-01-01|website=www.legacy.com}}</ref>

Kenneth Appel was also the treasurer of the Strafford County Democratic Committee. He played tennis through his early 50s. He was a lifelong stamp collector, a player of the game of Go and a baker of bread.<ref name="memoriam" /> He and Carole had two sons, [[Andrew W. Appel]], a noted [[computer scientist]], and [[Peter H. Appel]], and a daughter, Laurel F. Appel, who died on March 4, 2013. He was also a member of the Dover school board from 2010 until his death.<ref name="Obituary" />

==Schooling and teaching==
Kenneth Appel received his bachelor's degree from [[Queens College]] in 1953.  After serving the army he attended the [[University of Michigan]] where he earned his M.A. in 1956, and then later his Ph.D. in 1959. [[Roger Lyndon]], his doctoral advisor, was a mathematician whose main mathematical focus was in [[group theory]].

After working for the [[Institute for Defense Analyses]], in 1961 Appel joined the Mathematics Department faculty at the [[University of Illinois]] as an assistant professor. While there Appel researched in [[group theory]] and [[computability theory]]. In 1967 he became an [[associate professor]] and in 1977 was promoted to [[professor]]. It was while he was at this university that he and [[Wolfgang Haken]] proved the four color theorem. From their work and proof of this theorem they were later awarded the [[Delbert Ray Fulkerson]] prize, in 1979, by the [[American Mathematical Society]] and the [[Mathematical Programming Society]].<ref name="Bookrags">World of Mathematics. N.p.: Thomson Corporation, 2005-2006. Kenneth I. Appel Biography | Bookrags.com</ref>

While at the University of Illinois Appel took on five students during their doctoral program.  Each student helped contribute to the work cited on the [[Mathematics Genealogy Project]].<ref name="Genealogy Project">"Mathematics Genealogy Project." The Mathematics Genealogy Project - Kenneth Appel http://genealogy.math.ndsu.nodak.edu/id.php?id=5059</ref>

In 1993 Appel moved to [[New Hampshire]] as chairman of the [[Mathematics]] Department at the [[University of New Hampshire]]. In 2003 he retired as [[professor emeritus]]. During his retirement he volunteered in mathematics enrichment programs in Dover and in southern Maine public schools. He believed "that students should be afforded the opportunity to study mathematics at the level of their ability, even if it is well above their grade level."<ref name="Obituary" />

==Contributions to mathematics==

===The four color theorem===
Kenneth Appel is known for his work in [[topology]], the branch of mathematics that explores certain properties of geometric figures.<ref name="Article">"Kenneth I. Appel." Science and Its Times (2005–2006)</ref> His biggest accomplishment was proving the [[four color theorem]] in 1976 with [[Wolfgang Haken]]. The ''[[New York Times]]'' wrote in 1976:

<blockquote>Now the four-color conjecture has been proved by two University of Illinois mathematicians, Kenneth Appel and [[Wolfgang Haken]]. They had an invaluable tool that earlier mathematicians lacked—modern computers. Their present proof rests in part on 1,200 hours of computer calculation during which about ten billion logical decisions had to be made. The proof of the four-color conjecture is unlikely to be of applied significance. Nevertheless, what has been accomplished is a major intellectual feat. It gives us an important new insight into the nature of two-dimensional space and of the ways in which such space can be broken into discrete portions.<ref name="Obituary" /></blockquote>

At first, many mathematicians were unhappy with the fact that Appel and Haken were using computers, since this was new at the time, and even Appel said, "Most mathematicians, even as late as the 1970s, had no real interest in learning about computers. It was almost as if those of us who enjoyed playing with computers were doing something non-mathematical or suspect."<ref name="Magazine">{{cite web |last=Brooks |first=David |title=Math Pioneers |work=UNH Magazine Online |url=http://unhmagazine.unh.edu/sp02/mathpioneers.html }}</ref> The actual proof was described in an article as long as a typical book titled ''Every Planar Map is Four Colorable'', Contemporary Mathematics, vol. 98, American Mathematical Society, 1989.<ref name="Bookrags" />

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".<ref>[http://glassrcalc3.wordpress.com/2006/10/19/the-four-color-map-problem-by-sharon-murray/ Four Color Map Problem]</ref>

Nevertheless, the proof was the start of a change in mathematicians' attitudes toward computers—which they had largely disdained as a tool for [[engineer]]s rather than for theoreticians—leading to the creation of what is sometimes called [[experimental mathematics]].

===Group theory===
Kenneth Appel's other publications include an article with P.E. Schupp titled ''Artin Groups and Infinite Coxeter Groups''. In this article Appel and [[Schupp]] introduced four theorems that are true about [[Coxeter groups]] and then proved them to be true for [[Artin group]]s. The proofs of these four theorems used the "results and methods of small cancellation theory."<ref name="Artin">{{cite journal |last1=Appel |first1=Kenneth I. |first2=P. E. |last2=Schupp |title=Artin Groups and Infinite Coxeter Groups |journal=[[Inventiones Mathematicae]] |volume=72 |issue=2 |year=1983 |pages=201–220 |doi=10.1007/BF01389320 |bibcode=1983InMat..72..201A |s2cid=15886682 }}</ref>

==References==
{{Reflist}}

==External links==
* {{MathGenealogy|id=5059}}
* [http://www.bookrags.com/biography/kenneth-i-appel-wom/ Kenneth I. Appel Biography]
* [https://zbmath.org/authors/?q=ai:appel.kenneth-i Author profile] in the database [[Zentralblatt MATH|zbMATH]]

{{Authority control}}

{{DEFAULTSORT:Appel, Kenneth}}
[[Category:1932 births]]
[[Category:University of Michigan alumni]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Graph theorists]]
[[Category:University of Illinois Urbana-Champaign faculty]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:2013 deaths]]
[[Category:Mathematicians from New York (state)]]
[[Category:Scientists from Brooklyn]]