Editing Kenneth Appel (section)

===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]].