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Illustrating Mathematics

Diana Davis, ed.
Publication Date: 
Number of Pages: 
[Reviewed by
Joel Haack
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Editor Diana Davis's book Illustrating Mathematics is a collection of approximately 70 two-page combinations of colored photographs of art pieces along with essays mentioning the mathematics and artistic techniques that helped create them. Most (all?) of the mathematicians/artists were participants in a fall 2019 Illustrating Mathematics program offered at the Institute for Computational and Experimental Research Mathematics at Brown University.
Not surprisingly, most of the works depict objects and ideas from geometry, topology, and analysis, although there are also representations of groups and prime ideals as well as prime numbers. Techniques include drawings, laser cuttings, computer graphics, video and virtual reality, 3D printing, paper and fiber arts, and mechanical constructions. 
I found most of the descriptions to be teasers, offering a suggestion as to the mathematics involved and the techniques that produced the works. A full explanation of either would require more space than the page allotted to each mathematician/artist. I am happy to say that the works shown here are fascinating and inspiring.
The interface between mathematics and art has been an exciting arena for some time now. If you are interested in exploring more, I recommend the SIGMAA on Mathematics and the Arts (ARTS SIGMAA). Other possibilities for further exploration include the proceedings of the Bridges Conferences (beginning in 1998), the ISAMA (International Society of the Arts, Mathematics, and Architecture) Conferences (beginning in 1999), the catalogs of the art exhibits at the Joint Mathematics Meetings, and other books on the topic. 
It is instructive to see now how the interest in mathematics and the arts has continued and in fact grown over the decades. One of my favorite mathematics/art exhibits was in fact held 25 years ago at the International Conference of Mathematics Education 8 in Seville in 1996. A book that was sold in conjunction with this exhibit was the catalog of a 1987 exhibition held at the Wilhelm-Hack Museum in Ludwigshafen, Germany. The title of this book, Mathematik in der Kunst der letzten dreissig Jahre (Mathematics in the Art of the Recent Thirty Years) by Dietmar Guderian, makes it clear that artists and mathematicians have explored the interface for quite some time. Of course, in the past there were not available such techniques as are represented in Illustrating Mathematics. Perhaps because there are such powerful techniques available now and more doctoral level mathematicians are involved, there are proportionately fewer works included in Illustrating Mathematics that explore number theory and elementary geometry than was the case in the past.
Anyone interested in seeing examples of the art that can be created from and which illustrates mathematics using current techniques will benefit from Illustrating Mathematics.


(Joel Haack is Emeritus Professor of Mathematics at the University of Northern Iowa. He can be reached at