Fragments of Infinity: A Kaleidoscope of Math and Art

by Ivars Peterson

A visual journey to the intersection of math and imagination, guided by an award-winning author
Mathematics is right brain work, art left brain, right? Not so. This intriguing book shows how intertwined the disciplines are. Portraying the work of many contemporary artists in media from metals to glass to snow, Fragments of Infinity draws us into the mysteries of one-sided surfaces, four-dimensional spaces, self-similar structures, and other bizarre or seemingly impossible features of modern mathematics as they are given visible expression. Featuring more than 250 beautiful illustrations and photographs of artworks ranging from sculptures both massive and minute to elaborate geometric tapestries and mosaics of startling complexity, this is an enthralling exploration of abstract shapes, space, and time made tangible.
Ivars Peterson (Washington, DC) is the mathematics writer and online editor of Science News and the author of The Jungles of Randomness ( 0-471-16449-6), as well as four previous trade books.

Genres: Mathematics, Art

240 pages, Paperback

First published September 14, 2001

Reviews

[Jeff · Rating 3 out of 5]

Fragments of Infinity is a good introduction to visual mathematics on the edge of current mathematical research. Each of the ten chapters profiles artists working in specific medium and on the particular mathematics that they explore through their art. Peterson has written it to be completely accessible to the general public that knows just a little math (i.e. I don't think there is a single equation in the whole book). Consequently each chapter reads a little like a magazine article. In addition, there is a bit of repetition from chapter to chapter, as if each chapter was intended originally to stand alone, and then was woven together in this book. I found this to be a bit annoying, because once he has described an idea like minimal surfaces in one chapter, I don't need a rehash in the next chapter.

With that said, there are a number of bits to recommend this book. Specifically, the art that he highlights is fascinating but has generally not been very compelling to me. Reading about the math behind it, has spurred me to look closer and have a greater appreciation for abstract works of art and specifically sculpture. In addition, I read Sasho Kalajdzievski's textbook, Math and Art: An Introdcution to Visual Mathematics, simultaneously and got a more nuanced understanding of the mathematics that Peterson highlights. However it is Peterson's photographs of art work and descriptions that make the mathematics far more concrete and real.

However the best thing by far that I got out of the book were some of the quotes from mathematicians and artists. My favorite is at the end of the book quoted from a 1994 article in Leonardo by mathematician Howard Levine. He writes, "Mathematicians and artists are engaged in the ultimate creative activity - creating something out of nothing. We need to do more than simply understand the affinity these two disciplines share for each other. We need to incorporate their modus vivendi into our lives. For how else are we to define the good life and live it with grace if we leave the creative act and appreciation of beauty to specialists?"

[Mikkel Hansen · Rating 5 out of 5]

I really enjoyed this book. I recently became fascinated by generative art but had mostly seen examples related to chaos theory and fractals. This book widened my perspective on how much mathematics has to offer when it comes to creating art.