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University Library, University of Illinois at Urbana-Champaign

Four Color Theorem Festival: Introduction

Proving the Four-Color Theorem

A Theorem That Eluded Mathematicians for More Than a Century Was Finally Proven at Illinois


In 1852, Francis Guthrie was coloring a map of counties in England when he noticed that only four colors were needed. This led to the Four Color Theorem, stating that in distinguishing regions of any map, no more than four colors are required to ensure that no two adjacent regions will have the same color.

Sounds simple enough, right? Wrong. The theorem wasn’t proven until 1976, when the late Kenneth Appel and Wolfgang Haken, mathematics professors at the University of Illinois, finally proved the conjecture. It was the first major mathematical theorem to be solved with aid from a computer.

Haken first became interested in the theorem in 1949, but as he worked on it he realized that the breakthrough would not come without help from a computer. Thus began his collaboration with Appel, who was also an expert in computer programming.

Their solution was reported around the world, and the news was greeted with both enthusiasm and skepticism by purists who did not believe that the theorem could be proven by a machine. Subsequent efforts have confirmed the proof, however. In tribute to the professors’ work, the Department of Mathematics used the phrase “Four Colors Suffice” on its postmark for years.

In an interview more than 30 years after the proof, Haken credited mathematicians before them for most of the accomplishment.

“We were the fifth generation of people working on the problem,” he said, “so four-fifths had been done by others.”

Cited: Colleges of LAS - Gallery of Excellence

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