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Oxford’s History of Mathematics Forum: The First Two Decades
Usually held at The Queen’s College, Oxford University (Figure 1), the topics covered are wide-ranging, from ancient Egyptian mathematics to aspects of computing, and from current research work to using history in the mathematics classroom. Besides the names already mentioned, other speakers during the Forum’s early years included David Fowler (from Warwick) on his controversial views concerning ancient Greek mathematics, Eleanor Robson and Annette Imhausen (both then in Cambridge) on the mathematics of ancient Mesopotamia and Egypt, Raymond Flood (from Oxford; see Figure 2) on nineteenth-century mathematical physicists from Ireland, Adrian Rice (from London, and later the United States) on his current research projects, and three speakers from the Open University: Jeremy Gray (trying out his forthcoming inaugural lecture; see Figure 3), June Barrow-Green (on the mathematicians of World War I; see Figure 3), and Robin Wilson (on the four-color theorem; see Figure 2). Later, in 2008–2009, during Peter’s sabbatical leave in Paris to work on Galois’s manuscripts, the meetings moved to a historic fifteenth-century wood-paneled room at All Souls College, courtesy of Benjamin Wardhaugh, before returning to Queen’s.
Journal Article
Arthur Cayley FRS and the four-colour map problem
The four-colour map problem (to prove that on any map only four colours are needed to separate countries) is celebrated in mathematics. It resisted the attempts of able mathematicians for over a century and when it was successfully proved in 1976 the 'computer proof' was controversial: it did not allow scrutiny in the conventional way. At the height of his influence in 1878, Arthur Cayley had drawn attention to the problem at a meeting of the London Mathematical Society and it was duly 'announced' in print. He made a short contribution himself and he encouraged the young A. B. Kempe to publish a paper on the subject. Though ultimately unsuccessful, the work of Cayley and Kempe in the late 1870s brought valuable insights. Using previously unpublished historical sources, of letters and manuscripts, this article attempts to piece together Cayley's contribution against the backcloth of his other deliberations. Francis Galton is revealed as the 'go-between' in suggesting Cayley publish his observations in Proceedings of the Royal Geographical Society. Of particular interest is that Cayley submitted two manuscripts prior to publication. A detailed comparison of these initial and final manuscripts in this article sheds new light on the early history of this great problem.
Journal Article
STRANGE HISTORY OF A CARTOGRAPHIC PROBLEM
\"Four Colors Suffice: How the Map Problem Was Solved\" by Oxford professor [ROBIN WILSON] appeals to the mathematical novice with an unassuming lucidity. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride: After telling his class that the problem had been wasted on third-rate minds, number- theorist Herman Minkowski took weeks at the blackboard in attempts to solve it, but finally acknowledged: \"Heaven is angered by my arrogance; my proof is also defective.\" The next failure, which convinced mathematicians worldwide for more than a decade, actually took giant steps in the right direction. Cambridge mathematician Arthur Cayley stated that any map needing more than four colors led to a contradiction: If you pretend some maps need more than four colors, and select only the smallest of these imaginary maps, then you'll have a manageable but complete set of counter-examples on your hands. (Wilson calls these the \"minimal criminals.\") If you can show, one by one, that none of these counter-examples can possibly exist, then you've shown that four colors suffice.
Newspaper Article