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Topic: Kenneth I. Appel, Mathematician Who Harnessed Computer Power, Dies at 80
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
Kenneth I. Appel, Mathematician Who Harnessed Computer Power, Dies at 80
Posted: Apr 30, 2013 3:27 PM
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From The New York Times, Sunday, April 28, 2013. See
Kenneth I. Appel, Mathematician Who Harnessed Computer Power, Dies at 80

By Dennis Overbye DENNIS OVERBYE

Kenneth I. Appel, who helped usher the venerable mathematical proof
into the computer age, solving a longstanding problem concerning
colors on a map with the help of an I.B.M. computer making billions
of decisions, died on April 19 in Dover, N.H. He was 80.

The cause was esophageal cancer, which was diagnosed in October, his
son Andrew said.

Since the time of Euclid and Pythagoras, proofs of mathematical
theorems had consisted of long strings of equations or geometric
notations that any mathematician could read and quibble with, all
marching logically, step by step, toward a conclusion. But the proof
that Dr. Appel and a colleague, Wolfgang Haken, established in 1976
was of a different order.

Their conclusion, that four colors would suffice for any map,
depended on 1,200 hours of computer time - the equivalent of 50 days
- and 10 billion logical decisions all made automatically and out of
sight by the innards of an I.B.M. computer at the University of
Illinois in Urbana.

Hailed in some circles, including this newspaper, as "a major
intellectual feat," the proof shepherded computers toward a greater
role in higher math. But it made many mathematicians uneasy; they
worried about computer bugs and wondered how they could check or
understand a "proof" they could not see. And it ignited a
long-running debate about what constitutes a mathematical proof.

"Like a landmark Supreme Court case, the proof's legacy is still felt
and hotly debated," said Edward Frenkel, a mathematician at the
University of California, Berkeley.

Kevin Short, a mathematician at the University of New Hampshire,
where Dr. Appel spent his later years, called the feat "a watershed
for modern mathematics."

"It has spawned whole fields of study," he said.

Kenneth Ira Appel (pronounced ah-PEL) was born on Oct. 8, 1932, in
Brooklyn and grew up in Queens, where he graduated from Queens
College with a degree in mathematics in 1953. His father, Irwin, was
an electrical engineer, and his mother, the former Lillian Sender,
had been an office worker.

After a short stint as an actuary and two years in the Army, Kenneth
Appel enrolled at the University of Michigan, where he earned a Ph.D.
in math in 1959. During the summers, he programmed computers for
Douglas Aircraft.

Dr. Appel soon went to work for the Institute for Defense Analyses in
Princeton, N.J., doing research in cryptography and number theory for
the federal government. He joined the University of Illinois as a
professor in 1961. Long interested in Democratic politics, he also
served a term on the Urbana City Council.

Some of the thorniest problems in math are simple to state but
hideously complex under the surface. Such is the case with the
four-color theorem, first enunciated by an English mapmaker, Francis
Guthrie, in 1852. He asserted that to create a map in which no
adjacent countries are the same color, only four colors are needed.
Although everyone believed it was true, proof had eluded a century of
mathematicians until Dr. Appel attended a lecture in 1972 by Dr.

Because of the bewildering variety of map configurations, Dr. Haken
was contemplating using computers to solve the problem, but as he
related in his lecture that evening, experts had convinced him that
it was not possible.

Dr. Appel, familiar with computers from his defense and government
work, was more optimistic.

"I don't know of anything involving computers that can't be done;
some things just take longer than others," he said to Dr. Haken
afterward, according to an account in the journal Social Studies of
Science by Donald MacKenzie of the University of Edinburgh. "Why
don't we take a shot at it?"

The two started off by showing that the universe of all possible maps
must contain what mathematicians call an "unavoidable set" of 1,936
different configurations. One configuration might be a country
surrounded by four neighbors, for example.

Their task, then, was to prove that each of these configurations
could be rendered on a map using only four colors in such a way that
no two adjacent land areas were of the same color. That was where the
heaviest computation would come in. To help, they recruited a
computer science graduate student, John Koch, and Dr. Appel persuaded
the university to let them use its I.B.M. 370-168 computer, newly
acquired for administrative services.

Those were the days when computers filled an entire room, although
their memory capacities were minuscule compared with a modern
smartphone. Dr. Short recounted an occasion, as described by Dr.
Appel, when the computer gave an unexpected answer.

"Oh, that wire must have fallen out again," Dr. Appel said.

Dr. Appel began to think of the computer as a partner, though with a
different kind of brain, with almost "an artificial intelligence," he
told Dr. MacKenzie.

"The computer was, to the best of my feeling about the subject, not
thinking like a mathematician," he said. "And it was much more
successful, because it was thinking not like a mathematician."

In the summer of 1976, Dr. Appel and Dr. Haken announced their result
to their colleagues by leaving a note on the department blackboard:
"Four colors suffice." Their work was published in 1977 in the
Illinois Journal of Mathematics.

Their four-color proof earned newspaper headlines and a prestigious
award in mathematics, the Delbert Ray Fulkerson Prize. But the notion
of computer proofs drew skepticism in some academic circles. In a
visit to one university, Dr. Appel and Dr. Haken said, professors
barred them from meeting graduate students lest the students' minds
become contaminated.

Dr. Appel became the chairman of the mathematics department at the
University of New Hampshire in 1993. He retired in 2003. He also
served on the Dover School Board and for a time was the treasurer of
the Strafford County Democratic Party.

Before their revolutionary work was published, Dr. Appel and Dr.
Haken enlisted their entire families to check hundreds of pages of
calculations, making sure that diagrams of map configurations matched
the computer printouts and did not have typos. Andrew Appel said his
sister, Laurel, found some 800 mistakes, most of which she could fix

Laurel F. Appel, a biology professor at Wesleyan University, died
this year. Besides his son Andrew, a computer science professor at
Princeton, Dr. Appel is survived by his wife, the former Carole S.
Stein; another son, Peter; a sister, Lois Green; and five

Despite the criticism in more traditionalist quarters, Dr. Appel
never agonized about his reliance on a computer to arrive at the
four-color theorem, his son Andrew said. The mathematician Alan
Turing, he noted, had shown long ago that even very short theorems
could have very long proofs, running hundreds of pages. As his son
recalled, Dr. Appel used to say, "Without computers, we would be
stuck only proving theorems that have short proofs."
This article has been revised to reflect the following correction:
Correction: April 30, 2013. An obituary on Monday about the
mathematician Kenneth I. Appel contained several errors. The author
of an article in the journal Social Studies of Science that discussed
Dr. Appel's work was Donald MacKenzie, not Douglas MacKenzie. The
agency in Princeton, N.J., for which Dr. Appel worked is the
Institute for Defense Analyses, not Analysis. And Dr. Appel's wife is
Carole S. Appel, not Carole S. Stein. (Stein was her surname before
she married, but she took her husband's name.)
PHOTO SIDEBAR: Kenneth Ira Appel
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244

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