Kenneth Appel
American mathematician (1932–2013)
Appel, Kenneth Ira
(1932-10-08)October 8, 1932
Brooklyn, New York Died April 19, 2013(2013-04-19) (aged 80)
Dover, New Hampshire Citizenship American Alma mater B.S. – Queens College, CUNY Ph.D. – University of Michigan Known for Proving the Four-color theorem with Wolfgang Haken Children Andrew Appel Peter H. Appel Awards Fulkerson Prize [1979] • Scientific career Fields Graph theory, combinatorics, topology Institutions University of Illinois at Urbana–Champaign, University of New Hampshire Doctoral advisor Roger Lyndon
Kenneth Ira Appel, a man whose intellect carved its name into the very fabric of mathematics, was born on October 8, 1932, in the sprawling embrace of Brooklyn, New York. He departed this world on April 19, 2013, in the quietude of Dover, New Hampshire, at the age of 80. Appel, an American mathematician, is etched in history for his monumental achievement in 1976: the proof of the four-color theorem. This wasn't a solitary endeavor; he forged this path alongside his colleague Wolfgang Haken at the esteemed University of Illinois at Urbana–Champaign. Their proof, a landmark in graph theory, combinatorics, and topology, asserted that any map drawn on a two-dimensional surface could be colored using only four colors, such that no two adjacent regions share the same hue. This was, and remains, a profound statement about the fundamental nature of spatial representation.
The proof itself, however, was a double-edged sword. It was revolutionary, yes, but also controversial. It leaned heavily, and unprecedentedly, on an exhaustive set of computer calculations – thousands upon thousands of them. This reliance on computational power, so vast it defied manual verification, marked a turning point, a digital ghost in the machine of pure mathematical thought. It was the first prominent instance where human intuition and rigorous proof were augmented, or perhaps even supplanted, by the brute force of algorithms.
Biography
Appel's journey began in Brooklyn, but his formative years were spent in Queens, New York. He was the son of Irwin and Lillian Sender Appel, a Jewish couple whose influence, though perhaps unspoken in the sterile halls of academia, undoubtedly shaped his path. Before immersing himself in the abstract world of numbers, Appel briefly navigated the practical realm as an actuary. His life took a turn toward service when he joined the U.S. Army, a two-year stint that saw him stationed at Fort Benning, Georgia, and later in Baumholder, Germany.
The year 1959 was pivotal. He completed his doctoral program at the prestigious University of Michigan and married Carole S. Stein in Philadelphia. The couple then relocated to Princeton, New Jersey, where Appel engaged in research in cryptography at the Institute for Defense Analyses from 1959 to 1961. His later years saw him recognized for his contributions; in 2012, he was elected a Fellow of the American Mathematical Society. His final years were spent in Dover, New Hampshire, where he passed away on April 19, 2013, following a diagnosis of esophageal cancer the previous October.
Beyond the theorems and proofs, Appel was a man of diverse interests. He served as the treasurer for the Strafford County Democratic Committee, a testament to his engagement with the civic sphere. He pursued tennis with vigor until his early fifties and maintained a lifelong passion for collecting stamps. The strategic depths of the game of Go also captivated him, as did the simple, fundamental act of baking bread. He and Carole were parents to two sons, Andrew W. Appel, a distinguished computer scientist, and Peter H. Appel, and a daughter, Laurel F. Appel, whose life was tragically cut short on March 4, 2013. Appel also contributed to his community as a member of the Dover school board from 2010 until his death.
Schooling and Teaching
Appel's academic journey began at Queens College, where he earned his bachelor's degree in 1953. His pursuit of higher learning continued at the University of Michigan, where he obtained his M.A. in 1956 and, subsequently, his Ph.D. in 1959. His doctoral advisor, Roger Lyndon, was a significant figure in group theory, a field that would later intersect with Appel's own research.
After his tenure at the Institute for Defense Analyses, Appel joined the Mathematics Department at the University of Illinois in 1961, initially as an assistant professor. His research there delved into group theory and computability theory. He ascended the academic ranks, becoming an associate professor in 1967 and a full professor in 1977. It was during this period, amidst the intellectual currents of the University of Illinois, that he and Wolfgang Haken embarked on their groundbreaking work on the four-color theorem. The significance of their proof was recognized with the Delbert Ray Fulkerson prize in 1979, awarded jointly by the American Mathematical Society and the Mathematical Programming Society.
During his time at Illinois, Appel guided five doctoral students, each contributing to the vast tapestry of mathematical knowledge documented in the Mathematics Genealogy Project.
In 1993, Appel transitioned to New Hampshire, taking on the role of chairman in the Mathematics Department at the University of New Hampshire. He retired in 2003, holding the title of professor emeritus. Even in retirement, his passion for mathematics remained undimmed. He dedicated his time to volunteer work, fostering mathematical enrichment in public schools in Dover and southern Maine. His philosophy was clear and unwavering: "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's name is inextricably linked to topology, the abstract study of shapes and spaces. His most profound contribution, however, was the definitive resolution of the four-color theorem in 1976, a puzzle that had tantalized mathematicians for over a century. This monumental proof, undertaken with Wolfgang Haken, was described by The New York Times in 1976 as a triumph achieved with the aid of "modern computers." The article noted the astonishing scale of the computation: "1,200 hours of computer calculation during which about ten billion logical decisions had to be made." While acknowledging the lack of immediate "applied significance," the report lauded it as "a major intellectual feat" offering "important new insight into the nature of two-dimensional space."
The use of computers in a mathematical proof was, at the time, a radical departure. Appel himself observed the prevailing sentiment: "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 proof, detailed in an article titled Every Planar Map is Four Colorable (Contemporary Mathematics, vol. 98, American Mathematical Society, 1989), was a testament to this computational approach.
This reliance on machine calculation did invite criticism. Many mathematicians found the proof lacking in the aesthetic elegance they associated with pure mathematics, with one commentator lamenting, "a good mathematical proof is like a poem—this is a telephone directory!" Appel and Haken themselves conceded in a 1977 interview that their proof was not "elegant, concise, and completely comprehensible by a human mathematical mind." Yet, despite these reservations, their work served as a catalyst, shifting the perception of computers from mere tools for engineers to instruments for theoretical exploration, paving the way for what is now known as experimental mathematics.
Group Theory
Beyond the celebrated four-color theorem, Appel made other significant contributions. His work with P.E. Schupp on "Artin Groups and Infinite Coxeter Groups" is notable. In this paper, they introduced and proved four theorems concerning Coxeter groups, demonstrating their applicability to Artin groups. The proofs themselves drew upon the sophisticated "results and methods of small cancellation theory," further solidifying Appel's expertise in abstract algebra.