Mathematics and Art Let us investigate a possible analogy
between mathematics and art—art as analyzed in Collingwood‘s
Principles of Art. It may be useful to keep in mind the
disclaimer in Collingwood’s preface: Everything written in this
book has been written in the belief that it has a practical
bearing, direct or indirect, upon the condition of art in
England in 1937. For Collingwood, art should be distinguished
from what used to be called art, but is rather craft, or τέχνη
(tekhnē) in Greek. Art is an expression, an exploration of our
emotions, in order to find out what they are. Art as such does
not arouse these emotions; we already have them. There is no
technique for expressing emotions [pp. 109–111]. We do it by
creating an imaginary experience [p. 151]. The imaginary
experience is the real work of art: a painting on the wall, for
example, is the residue of this experience and is perhaps a hint
by which the viewer can recreate the experience for himself.
Ultimately, art is language [p. 273]. The strug