Mathematics and painting

Abstract

Mathematics and painting are interrelated in many ways. At a technical level mathematics can be used to enhance our appreciation of paintings. This was recently demonstrated beautifully by Taylor, Micolich, and Jones in their analysis of Jackson Pollock's drip paintings, which led them to the conclusion that Pollock's paintings are in a way figurative pictures. Relations also exist at a more basic level. Painting and mathematics can share subject matter, as is illustrated here by a discussion of the mathematical concepts ‘open’ and ‘closed’, which are related to paintings by Pollock, Kandinsky, Turner, and van Gogh. It is suggested in conclusion that mathematics and painting are so closely related and have so many similarities that it is reasonable to consider them simply as two different but complementary ways of visualising aspects of the concrete or abstract reality in which we are embedded.

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References

Colour versions of all the paintings discussed in this paper are accessible via the Web Museum, Paris at www.ibiblio.org/wm/.

Kandinsky

: ‘Point and line to plane’; 1979, New York, NY, Dover (originally published in 1926, in a series of Bauhaus books, as ‘Punkt und Linie zu Fläche’).

Taylor

, Micolich

, and Jones

: ‘Fractal expressionism’, Physics World, 1999, 12, October, 25–28.

Itten

: ‘The art of color’; 1973, New York, NY, Van Nostrand Reinhold (originally published in 1961 as ‘Kunst der Farbe’ by Otto Maier Verlag, Ravensburg, Germany).