Don's diary: seeing the world in four colours

November 29, 2002

October 1852
University College London: while colouring the counties of a map of England, student Francis Guthrie notices that only four colours are needed. "Do four colours suffice to colour all maps?" he asks. "And if so, how can one prove it in every case?" No one seems to know.

1879
Alfred Kempe, London barrister and later treasurer of the Royal Society, discovers a "proof" that four colours are sufficient. His proof, later considered the most famous fallacious argument in the history of mathematics, is widely accepted.

1890
Durham: the mathematician Percy Heawood points out a fundamental error in Kempe's proof but salvages enough from it to prove that all maps can be coloured with five colours - still a remarkable result.

25 years ago
Illinois: after a four-year search involving consideration of 10,000 separate cases and 1,200 hours of computer time, mathematics professors Kenneth Appel and Wolfgang Haken publish their proof that four colours do suffice for all maps. Amazing that a problem so simple to state should have taken 125 years to solve.

October 2002, Sunday
Oxford: the map-colouring anniversary week has arrived. After months of planning, I anxiously await the 14 events in six venues, involving four speakers from the US.

Monday
The London launch of my book, Four Colours Suffice , at Gresham College. I speak about the history of the four-colour problem and outline its solution. Somewhat intimidated to find Ken Appel a couple of feet in front of me, but he is very encouraging.

Tuesday
At the Oxford Mathematical Institute, the Illinois professors reminisce about their solution to a large audience - a historic event as they have not lectured together about the problem for many years. This is followed by an anniversary tea for all and my Oxford book launch.

Wednesday
The highlight of the week is an 150th-anniversary meeting at University College. At this event, organised by the London Mathematical Society and the British Society for the History of Mathematics, the Illinois professors and I again outline the history and solution of the four-colour problem, while the other two US speakers describe exciting developments in the field since the problem was first solved.

Thursday
To the Open University for a seminar by one of the US speakers. I take a break from map colouring to attend a local operatic society rehearsal - next month we perform Leonard Bernstein's Candide , in which I play the judge in a garotting scene.

Friday
The final event of the week is an Oxford Mathematics Colloquium lecture on some spectacular work carried out in the past few years - an uplifting end to a most unusual, if tiring, week. The four-colour problem may be 150 years old but it is not dead yet. There is still much to discover, not least a solution that can be obtained without the aid of a computer.

Robin Wilson is senior lecturer in mathematics at the Open University and fellow of Keble College, Oxford.

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