Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

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 in 1976, with colleague

Wolfgang Haken Wolfgang Haken (June 21, 1928 – October 2, 2022) was a German American mathematician who specialized in topology, in particular 3-manifolds. Biography Haken was born in Berlin, Germany. His father was Werner Haken, a physicist who had Max ...

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 Universit ...

, solved one of the most famous problems in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, 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.

Biography

Appel was born in

Brooklyn, New York Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...

, on October 8, 1932. He grew up in

Queens, New York Queens is a borough of New York City, coextensive with Queens County, in the U.S. state of New York. Located on Long Island, it is the largest New York City borough by area. It is bordered by the borough of Brooklyn at the western tip of Long I ...

, and was the son of a Jewish couple, Irwin Appel and Lillian Sender Appel. He worked as an

actuary An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset man ...

for a brief time and then served in the

U.S. Army The United States Army (USA) is the land service branch of the United States Armed Forces. It is one of the eight U.S. uniformed services, and is designated as the Army of the United States in the U.S. Constitution.Article II, section 2, cl ...

for two years at Fort Benning, Georgia, and in

Baumholder, Germany Baumholder () is a town in the Birkenfeld district in Rhineland-Palatinate, Germany, in the Westrich, an historic region that encompasses areas in both Germany and France. The town of Baumholder is the administrative seat of the like-named ''Verb ...

. In 1959, he finished his doctoral program at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

, and he also married Carole S. Stein in

Philadelphia Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...

. The couple moved to

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

, where Appel worked for the

Institute for Defense Analyses The Institute for Defense Analyses (IDA) is an American non-profit corporation that administers three federally funded research and development centers (FFRDCs) – the Systems and Analyses Center (SAC), the Science and Technology Policy Institute ...

from 1959 to 1961. His main work at the Institute for Defense Analyses was doing research in

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

. Toward the end of his life, in 2012, he was elected a

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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, ...

. He died in

Dover, New Hampshire Dover is a city in Strafford County, New Hampshire, United States. The population was 32,741 at the 2020 census, making it the largest city in the New Hampshire Seacoast region and the fifth largest municipality in the state. It is the county se ...

, on April 19, 2013, after being diagnosed with

esophageal cancer Esophageal cancer is cancer arising from the esophagus—the food pipe that runs between the throat and the stomach. Symptoms often include difficulty in swallowing and weight loss. Other symptoms may include pain when swallowing, a hoarse voice ...

in October 2012.Obituary For: Kenneth I. Appel http://www.meaningfulfunerals.net/fh/obituaries/obituary.cfm?o_id=2069700&fh_id=12298 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. He and Carole had two sons, Andrew W. Appel, a noted

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

, 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.

Schooling and teaching

Kenneth Appel received his bachelor's degree from

Queens College Queens College (QC) is a public college in the Queens borough of New York City. It is part of the City University of New York system. Its 80-acre campus is primarily located in Flushing, Queens. It has a student body representing more than 170 ...

in 1953. After serving the army he attended the

where he earned his M.A. in 1956, and then later his Ph.D. in 1959.

Roger Lyndon Roger Conant Lyndon (December 18, 1917 – June 8, 1988) was an American mathematician, for many years a professor at the University of Michigan.. He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation a ...

, his doctoral advisor, was a mathematician whose main mathematical focus was in

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

. After working for the

, in 1961 Appel joined the Mathematics Department faculty at the

University of Illinois 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 University ...

as an Assistant Professor. While there Appel researched in

and

computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since e ...

. In 1967 he became an

Associate Professor Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''. Overview In the ''North American system'', used in the United States and many other countries, it is a ...

and in 1977 was promoted to

Professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

. It was while he was at this university that he and

proved the four color theorem. From their work and proof of this theorem they were later awarded the

Delbert Ray Fulkerson Delbert Ray Fulkerson (; August 14, 1924 – January 10, 1976) was an American mathematician who co-developed the FordFulkerson algorithm, one of the most well-known algorithms to solve the maximum flow problem in networks. Early life and educa ...

prize, in 1979, by the

and the

Mathematical Programming Society The Mathematical Optimization Society (MOS), known as the Mathematical Programming Society until 2010,World of Mathematics. N.p.: Thomson Corporation, 2005-2006. Kenneth I. Appel Biography , Bookrags.com 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 The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a ty ...

."Mathematics Genealogy Project." The Mathematics Genealogy Project - Kenneth Appel http://genealogy.math.ndsu.nodak.edu/id.php?id=5059 In 1993 Appel moved to

New Hampshire New Hampshire is a U.S. state, state in the New England region of the northeastern United States. It is bordered by Massachusetts to the south, Vermont to the west, Maine and the Gulf of Maine to the east, and the Canadian province of Quebec t ...

as Chairman of the

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Department at the

University of New Hampshire The University of New Hampshire (UNH) is a public land-grant research university with its main campus in Durham, New Hampshire. It was founded and incorporated in 1866 as a land grant college in Hanover in connection with Dartmouth College, mo ...

. In 2003 he retired as

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

. 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."

Contributions to mathematics

The four color theorem

Kenneth Appel is known for his work 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 ...

, the branch of mathematics that explores certain properties of geometric figures."Kenneth I. Appel." Science and Its Times (2005–2006) His biggest accomplishment was proving 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 sh ...

in 1976 with

. The ''

New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid d ...

'' wrote in 1976:

Now the four-color conjecture has been proved by two University of Illinois mathematicians, Kenneth Appel and
Wolfgang Haken Wolfgang Haken (June 21, 1928 – October 2, 2022) was a German American mathematician who specialized in topology, in particular 3-manifolds. Biography Haken was born in Berlin, Germany. His father was Werner Haken, a physicist who had Max ...
. 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.

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." 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. 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".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 Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the l ...

s rather than for theoreticians—leading to the creation of what is sometimes called

experimental mathematics Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with th ...

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 In mathematics, a Coxeter group, named after Harold Scott MacDonald Coxeter, H. S. M. Coxeter, is an group (mathematics), abstract group that admits a group presentation, formal description in terms of Reflection (mathematics), reflections (or Kal ...

and then proved them to be true for Artin groups. The proofs of these four theorems used the "results and methods of small cancellation theory."

References

External links

*
Kenneth I. Appel Biography

Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...

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