Four Color Fest

Visit the Four Color Theorem Festival library guide and Schedule of events to watch videos and learn more about the Four Color Theorem.

Can a map on a plane or a sphere be colored in with only four distinct colors such that neighboring countries do not share a color? In 1976, roughly 40 years ago, Kenneth Appel and Wolfgang Haken of the University of Illinois announced a proof of the Four Color Theorem.

The problem began nearly 150 years ago when a law student in England discovered that four colors were needed to color a map of English counties. English mathematician, Arthur Cayley, later presented the problem to the mathematical society in London, in 1878. What followed were a number of proofs that turned out to be wrong. Alfred Kempe proposed a solution in 1879, but he was disproved eleven years later by Percy Heawood. Peter Tait found a proof in 1880, but his proof was also disproved in 1891. Although Alfred Kempe’s proof was wrong, some of his ideas were used later in the correct proof. Many years later, in the 1960s and 1970s, a computer-based proof was developed by a Heinrich Heesch. It was that sketch that Kenneth Appel and Wolfgang Haken improved and used to test a number of cases.

The 40th anniversary of the proof of the Four Color Theorem will take place at the University of Illinois at Urbana-Champaign in November. The event will begin on Thursday, November 2nd at 4 p.m. in room 314 of Altgeld Hall with a lecture, Four Colors Suffice, by Robin Wilson. In his talk, Wilson will discuss the history and solution to the Four Color Theorem. A solution that took 124 years to find in addition to relying on computers to check a large number of cases. Is it really a solution? Robin Wilson, Professor Emeritus of Pure Mathematics at the Open University and at Gresham College, London will discuss what it involved and what role the University of Illinois played.

There will be a lecture on Friday, November 3rd at 4 p.m. in the Spurlock Museum Auditorium on Graph Coloring and Machine Proofs in Computer Science from 1977 to 2017. This lecture on the assistance of computer programs to check the proof will be followed by a reception from 5 – 7 p.m. in the Ballroom of the Alice Campbell Alumni Center.

Starting at 10 a.m. on Saturday, November 4th in the Ballroom of the Alice Campbel Center the Illinois Geometry Lab will host an open house with Four Color Theorem activities for students and the community. Following the four color activities will be a musical performance to celebrate the 150th anniversary of the University as well as the 40th anniversary of the Four Color Theorem. Please note that the musical entertainment event requires registration and fee to attend. Attend a concert in the evening, starting at 7:30 p.m., in the Music Building Auditorium. A Portrait in Four Colors will feature the Haken Continuum, an instrument invented by Wolfgang Haken’s son. Enjoy classical, jazz, blues, and rock genres (four music genres) during the performance.

Online Activities:

• Map from Simon Tatham’s Portable Puzzle Collection
• Four Color Problem Coloring Sheets
• Four Color Theorem Coloring Patterns
• Four Color Online Game

Resources:

• Print and electronic copies of items on the proof of the Four Color Theorem that are available in full-text online and at the Mathematics Library:
  – items displayed during the Four Color Theorem Festival
  – additional items
• Additional full-text of papers received from authors and made available online by the University of Illinois at Urbana-Champaign Mathematics Library:
  – W. Haken (1971), Notes on Shimamoto’s Construction
  – U. Schmidt (1982), Überprüfung des beweises für den Vierfarbensatz

 

A special thanks to Walker Babich and Rachel Smith, Grainger Graduate Assistants, for creating this Mathematics Library exhibit.