**Alfred Kempe** published a false "proof" of the four colour theorem in 1879 which stood until Heawood showed the mistake 11 years later. The 'proof' is however still the basis for the computer aided proof discovered 100 years later.

- Alfred attended St Paul's School which, at this time, stood in the churchyard of St Paul's Cathedral in the City of London.
- Kempe had a very fine counter-tenor voice and as a member of St Paul's School Choral Society he sang the treble parts as a young boy, while later in his school career he sang alto.
- Kempe was taught mathematics by Cayley and graduated in 1872 with distinction in mathematics and in the same year he published his first mathematical paper A general method of solving equations of the nth degree by mechanical means.
- Despite his love of mathematics and music, Kempe chose a profession which involved neither of these, becoming a barrister.
- Soon Kempe became an authority on ecclesiastical law and this led to him holding many Chancellorships.
- A Chancellorship is a lay office of legal advisor to an Anglican diocese, and Kempe held a number of these through his career: he was legal advisor to the diocese of Newcastle, Southwell, St Albans, Peterborough, Chichester, Chelmsford and finally the most important Chancellorship of all, namely that of the diocese of London to which he was appointed in 1912.
- It would be true to say that he so conducted his own side of a case as always to win the respect of an opponent, while if one had much to do with Kempe, respect inevitably ripened into a warm regard an affection.
- Most of Kempe's early contributions to mathematics were on linkages, involving applications of geometry.
- But only in 1876 did Kempe prove a theorem on the possibility of reproducing any plane curve of degree nnn by means of an articulated mechanism.
- In 1926 Gersgorin, basing his work on Kempe's considerations and using the complex variable method, proved a more general theorem on the possibility of constructing similar mechanisms for an arbitrary algebraic function.
- Kempe's work on straight line linkages was inspired by a lecture On recent discoveries in mechanical conversion of motion given by Sylvester in January 1874 at the Royal Institution.
- Kempe worked on the topic and presented a series of lectures at the Royal Institution on How to draw a straight line: A lecture on linkages in 1877.
- Kempe published a false "proof" of the four colour theorem in 1879 which stood until Heawood found an error eleven years later.
- Clearly in 1923 this error by Kempe was considered an embarrassment, something which the authors pretended never existed.
- Yet this is a totally false assessment of Kempe's paper, as has since been shown, for Kempe's 'proof' is the basis of the computer aided proof discovered 100 years later.
- Kempe introduced two fundamental ideas in his paper which were to provide the basis of the proof by Kenneth Appel and Wolfgang Haken in 1976.
- Kempe showed if a map MMM requires at least five colours and MMM contains a region with four or fewer neighbours, then there must be a map M′M'M′ which requires five colours yet M′M'M′ has fewer regions than MMM.
- From this Kempe was able to prove that any map could be five coloured.
- Kempe's short list of unavoidable configurations had to be extended and the 1976 proof analysed 1,936 distinct cases with a computer to show that each was reducible.
- Kempe was proposed for election to the Royal Society in the year he published his "proof" of the four colour theorem.
- Kempe was President of the London Mathematical Society from 1872 to 1874.
- Kempe did not find any of these definitions satisfactory since, he said, they did not help to push forward the boundaries of mathematical research.
- As scientific circles are not free from the irritability and combativeness that affect other coteries of man, Sir Alfred was again and again appealed to as the irresistible peacemaker.
- Kempe had one further interest which we have not yet mentioned, namely his love of the mountains.
- Kempe's health began to deteriorate in around 1912 and he began to wind down his extraordinarily busy life.
- Giving up some of his many duties seemed to give Kempe a few more years when his health did not deteriorate any further but in 1922 he developed pneumonia which led to his death.

Born 6 July 1849, Kensington, London, England. Died 21 April 1922, London, England.

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Origin England, Puzzles And Problems, Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive