## Cayley's attitude to 'colour'

Tony Crilly has written a fascinating paper on Arthur Cayley and the four colour problem: T Crilly, Arthur Cayley FRS and the four-colour map problem, Notes and Records Roy. Soc. London 59 (3) (2005), 285-304. We quote below a very brief extract from this paper in which Crilly examines Cayley's attitude to 'colour':

Why was Cayley attracted to the problem? One aspect lay in his attitude to 'colour.' In the years 1877-79, in particular, Cayley exploited the uses of colour in mathematics, something not usually associated with the subject. His water-colour sketches taken into the lecture room could show off polyhedra to advantage, but he also found colour useful in the investigative process itself. His attempt to construct a theory of colour (based on linear equations) came to little, but his graphical group theory, in which he introduced the notion of the graph of a group, which he later termed a colourgroup (Gruppenbild, now called a 'Cayley colour graph'), suggested a geometric approach to group theory that has proved fruitful. In his hands the Newton-Fourier method of mathematical analysis also made use of colour. Originally motivated by the practical root-finding of equations, the method was extended to functions of a complex variable by Cayley, and his work can now be interpreted as research in fractals. Here he was in a 'grey-scale' phase, in which regions of the complex plane were labelled white, grey and black. During these years, he also reconsidered Cauchy's work on equations and this time developed a broader palette. A geometric perspective to this theory, coupled with the complexity of the visual evidence, made the use of colour desirable, and he spoke of red and blue curves, and regions tinted in sable, gules, argent and azure. For Cayley, colour was much more than a cosmetic device, for it could be used for achieving clarity, making new discoveries and suggesting valuable ideas.

JOC/EFR November 2014