## Mathematics and Art

1. Introduction

Squirrels, rabbits and birds are not artists. However, humans may admire a bird's nest as being a "work of art," and may find the patterns in the snow made by squirrel or rabbit tracks pleasing. Yet, the shape of a bird's nest may indeed be a form of communication for birds, just as "art" is a form of communication for humans. What constitutes art is a very complex and hotly debated subject. When Jackson Pollock first experimented with expressing himself by flinging paint at a canvas, many saw his activity as a form of self-indulgence rather than art. As another example, some people collect maps and some of these maps are art, but not all maps are art.

April is Mathematics Awareness Month, and this year's theme is Mathematics and Art. There are, in fact, many arts (music, dance, painting, architecture, sculpture, etc.) and there is a surprisingly rich association between mathematics and each of the arts. My goal here is to give some pointers concerning these many connections.

One mathematical connection with art is that some individuals known as artists have needed to develop or use mathematical thinking to carry out their artistic vision. Among such artists were Luca Pacioli (c. 1145-1514), Leonardo da Vinci (1452-1519), Albrecht Dürer (1471-1528), and M.C. Escher (1898-1972). Another connection is that some mathematicians have become artists, often while pursuing their mathematics.

Mathematicians commonly talk about beautiful theorems and beautiful proofs of theorems. They also often have emotional reactions to proofs or theorems. There are nifty proofs of "dull" mathematical facts and "unsatisfying" proofs of "nifty" theorems. Artists and art critics also talk about beauty. Does art have to be beautiful? Francis Bacon's paintings may or may not be beautiful to everyone, yet there are few people who have no reaction to his work. Art is concerned with communication of emotions as well as beauty. Some people may see little emotional content in many of M.C. Escher's prints but it's hard not to be "impressed" by the patterns he created. Some find Escher's prints beautiful but with a different beauty from the great works of Rembrandt. Like art itself, the issues of beauty, communication, and emotions are complex subjects, but then so is mathematics.

Joseph Malkevitch
York College (CUNY)

Email: malkevitch@york.cuny.edu

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