manner by which the "New Math" was introduced, then
abandoned, in primary and secondary education has led
many persons working in the arts and humanities to
reject powerful conceptual tools in logic, set theory
and abstract algebra that could be useful to them. Yet
modern artists and scholars cannot avoid having to
deal with areas of mathematics relevant to their
Artists and mathematicians have always collaborated. For example, covering a plane with congruent tiles depends upon a special algebraic group of 17 elements, familiarly known as the "wallpaper group" from its application to wallpaper design. Every one of these 17 basic congruent tiling patterns can be seen in the abstract mosaics of Arab civilization, and are all present in the stonework of the Alhambra in Granada, Spain.One sees them also in Japanese prints and in the works of the Dutch artist, M.C. Escher.
Music and mathematics would appear to be the dual faces of the same intellectual faculty; indeed in the curriculum developed by the great Roman scholar, Boethius, which dominated education in the Middle Ages, music and mathematics were treated as complementary branches of the same subject.
Knowledge of the relationship between consonant musical intervals, the lengths of strings and heights of wind columns was attributed to the Pythagoreans as early as 500 BC.
The content, if not necessarily the form, of prose and poetry often treats of current science, including mathematics. Certainly science fiction writers would greatly benefit from more direct communication with mathematicians, physicists and other scientists.
In a few words, modern artists, writers and scholars can no longer avoid having to deal with those branches of mathematics relevant to their discipline. It is therefore often advisable to consult with someone trained in mathematics who has also done a considerable amount of work in arts and letters.
I have worked with composers, musicologists, poets, economists, historians, graphic artists and others, and have been often credited with a natural ability to convey difficult subject matter.