Anna Kepes Szemerédi’s Art in the Life of Mathematicians is a collection of essays from mathematicians reflecting on the role of the arts in their lives. Short biographies of the contributors are included. The essays range from a one-page column on “Painting and Mathematics,” through a forty-page reflection on the author’s love of opera, to a ten-page photo essay entitled “Into the Woods.” Some of the authors are primarily aficionados, while others are also practicing artists. After an introduction, the essays are arranged alphabetically by the mathematician’s last name. The book itself is laid out beautifully on heavy glossy paper, which is excellent for photo reproductions.
The introductory essay by Asaf Naor and art historian AnnMarie Perl describes several similarities between mathematics and the arts that are different from what one usually finds, one example being the move toward abstraction and the avant-garde which occurs relatively late in the history of both endeavors. Michael Atiyah provides a brief essay on mathematics’ position between the arts and science and suggests that the best analogy to mathematics among the arts is architecture. Included is a paragraph entitled “Dreams,” which Atiyah claims is the only poetic passage he has written.
Béla Bollobás provides an extensive and enjoyable memoir of his personal experiences with and appreciation of opera. Enrico Bombieri and philosopher Sarah Jones Nelson include in their essay, on the fragility of beauty in art and mathematics, such topics as the golden ratio, structures in fives, the Laplace equation, the Penrose tiling, group theory (including the finite simple groups), and Cantor’s diagonal argument. There is a focus on art and art theory in the period 1435–1514 including a dense paragraph describing Dürer’s Melancholia I. They also address the questions of truth in mathematics and of beauty in mathematics, the arts, and history. Bombieri’s biography reveals that he is an amateur artist specializing in portraits and scenes from life.
Edward Frenkel is interested in confronting the stereotype of mathematicians in popular films who are often depicted as “weirdos and social misfits.” He decided to show the passion of mathematical research and demonstrate viscerally that a mathematical formula can be beautiful like a work of art through a film modeled on Mishima’s Rite of Love and Death. How his 26-minute film Rites of Love and Math came into being is the topic of his essay.
Timothy Gowers describes his varied, lengthy, and successful pursuit of music in its various forms throughout his life. One of his reflections is that “it is possible to make very rapid leaps forward” in music; he believes this is true in education more generally. (92) While the essay is entitled, “Music — a life not chosen,” at the end he remarks that there was no point at which he made a conscious decision to choose one fork in the road of life over another. “The life I have had (and am still having) as a result, the life of a mathematician with a strong side interest in music, has been ideal: to the extent that I made a choice, I made the right one.” (110)
In a series of two essays and an interview, collaborators Andrew Granville, screen writer Jennifer Granville, and theatre designer Michael Spencer describe a metaphor for the process of writing and performing mathematics via a case study of the creation and several stagings of the Granvilles’ screenplay Mathematical Science Investigation (MSI): The Anatomy of Integers and Permutations. The aim is to provide a solid exposition of mathematics as it is done while maintaining the interest of the audience in the project. The result is a blend of fact and fiction, modeled on the successful television series, Crime Scene Investigation (CSI). The interview with Spencer includes his thoughts on providing visual metaphors for mathematics.
Izabella Łaba’s essay on photography includes her reflections as a female mathematician, a comparison of mathematics with architecture, and a discussion of photography as art and how it differs from how we routinely experience the world. She shares several of her photographs with the reader and reflects on connections between her art and mathematics. “My creative process is ‘mathematical’ in the sense that my brain operates in much the same ways as it does in my research, but in the finished product, my visual language must first and foremost match my subject and my perception of it.” (161) “Mathematics occurs in my photography the way it does in life.” (161) “Between mathematics and art, I do not need one to justify or explain the other. I pursue each to its own ends and I follow where they take me.” (162)
Peter David Lax’s page explains that he sees more of a connection between painting and mathematics than between music and mathematics. He compares realistic images to applied mathematics and abstract paintings to pure mathematics.
Yuri Manin provides two articles. The first concerns the quality of being “convincing,” focusing on the persuasiveness of mathematics and art. The essay includes several topics from the history and philosophy of mathematics. Manin’s second essay concerns interhemispheric competition within the brain. He draws parallels between the origin and development of writing as logographic versus phonetic and between Euclid’s Elements with the contrasts of geometric and algebraic modes of thought. His interest was stimulated by his own experiences when recovering from arachnoiditis, an inflammatory condition of one of the membranes surround the nerves of the central nervous system
Matilde Marcolli describes how she came to mathematics influenced by her parents’ involvement in Italian contemporary art. The abstract art of her father and the conceptual art of her mother, together with atonal twentieth-century music, share with mathematics an appreciation of abstract structures. Her own art includes painting, where surrealism allows her to express contrasts inherent in the practice of mathematical research and to explore the inner world of patient, difficult, and painful hard work and also the bullying and “culture of cruelty” within the mathematics community. “In fact, what is truly heroic about science is the fact that it does uncover beautiful truths about the universe despite the ugliness and brutality of the human beings involved.”(226) Besides painting, Marcolli is also a writer in many forms, including science fiction, short stories, poetry, and a theater play.
Jaroslav Nešetřil and philosopher of art Miroslav Petříček write of the challenge and confusion in distinguishing surface and depth in the mathematical world via a discussion of the same issue in a number of disciplines. They provide an extended discussion of this dichotomy in the photography of László Moholy-Nagy, focusing on his 1928 photograph Radio Tower Berlin.
In an interview with the editor, Klaus Friedrich Roth discusses the importance of Latin dancing in his life, but he thinks that mathematics and dance have nothing in common. In contrast, Bálazs Szegedy, who is a performance-level salsa dancer as well as a mathematician, sees a parallel between the transcendent thought in mathematical research and the meditative state of non-analytical thinking required in the ideal dance. Further, “I go so far as to consider mathematics as a form of art. It is based on aesthetic considerations, it requires inspiration, imagination, subconscious thinking and it can bring similar joy as any form of art even salsa dancing.” (257)
In a second essay, Szegedy distinguishes the artistic point of view from the aesthetic point of view — art need neither entertain nor be beautiful; rather it, as mathematics, intends to reveal the hidden layers of reality. After calling to mind how mathematicians are divided into types (Platonists v. constructivists v. formalists, or problem solvers v. theory builders [Timothy Gowers’ proposal], or birds v. frogs [Freeman Dyson’s dichotomy]), he proposes a new categorization of mathematicians according to the type of pleasure they enjoy: the artistic type, which celebrates the metaphysical picture behind the details, and the engineering type, which enjoys seeing that everything in a theory fits together perfectly.
Cédric Villani first discusses the nature of mathematics, then talks of the art in mathematics. Finally, he suggests three bridges from mathematics to art: (1) one can use a mathematical recipe to help produce art; (2) art can be inspired by mathematics; and (3) art can display mathematical shapes and concepts. One of his books, Théorème vivant (published in English translation as Birth of a Theorem: A Mathematical Adventure) tells of the construction of a theorem within the world of university research.
The book concludes with a wordless essay of ten photographs by Vladimir Voevodsky entitled “Into the Woods.”
There is much in this book to ponder. It would be very effective as a set of readings for a seminar in Mathematics and the Arts. Many of the art works discussed were very intriguing — since reading the book, I have purchased several books by the authors of the essays and a recording of some of the musical works that were discussed in the book.
Joel Haack is Professor of Mathematics at the University of Northern Iowa.