Artist And The Mathematician
The Artist and the Mathematician
by Amir D. Aczel
Mathematics and Art
by Lynn Gamwell
This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration.
Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked “What is art?” in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing.
Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
Art in the Life of Mathematicians
by Anna Kepes Szemerédi
Why are mathematicians drawn to art? How do they perceive it? What motivates them to pursue excellence in music or painting? Do they view their art as a conveyance for their mathematics or an escape from it? What are the similarities between mathematical talent and creativity and their artistic equivalents? What are the differences? Can a theatrical play or a visual image capture the beauty and excitement of mathematics? Some of the world’s top mathematicians are also accomplished artists: musicians, photographers, painters, dancers, writers, filmmakers. In this volume, they share some of their work and reflect on the roles that mathematics and art have played in their lives. They write about creativity, communication, making connections, negotiating successes and failures, and navigating the vastly different professional worlds of art and mathematics.
Piero Della Francesca
by Judith Veronica Field, Piero
Visualizing Mathematics with 3D Printing
by Henry Segerman
Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer.
Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.
by Marc Frantz, Annalisa Crannell
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.
Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists–who include mathematicians and scientists–examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.
- Classroom-tested activities and problem solving
- Accessible problems that move beyond regular art school curriculum
- Multiple solutions of varying difficulty and applicability
- Appropriate for students of all mathematics and art levels
- Original and exclusive essays by contemporary artists
- Forthcoming: Instructor’s manual (available only to teachers)
Descartes’ Secret Notebook
by Amir D. Aczel
But Descartes had a mysterious and mystical side, as well. Almost certainly a member of the occult brotherhood of the Rosicrucians, he kept a secret notebook, now lost, most of which was written in code. After Descartes’s death, Gottfried Leibniz, inventor of calculus and one of the greatest mathematicians in history, moved to Paris in search of this notebook—and eventually found it in the possession of Claude Clerselier, a friend of Descartes. Leibniz called on Clerselier and was allowed to copy only a couple of pages—which, though written in code, he amazingly deciphered there on the spot. Leibniz’s hastily scribbled notes are all we have today of Descartes’s notebook, which has disappeared.
Why did Descartes keep a secret notebook, and what were its contents? The answers to these questions lead Amir Aczel and the reader on an exciting, swashbuckling journey, and offer a fascinating look at one of the great figures of Western culture.
by Mark A. Peterson
Imagine Math 3
by Michele Emmer
Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This volume in the series “Imagine Math” casts light on what is new and interesting in the relationships between mathematics, imagination and culture. The book opens by examining the connections between modern and contemporary art and mathematics, including Linda D. Henderson’s contribution. Several further papers are devoted to mathematical models and their influence on modern and contemporary art, including the work of Henry Moore and Hiroshi Sugimoto. Among the many other interesting contributions are an homage to Benoît Mandelbrot with reference to the exhibition held in New York in 2013 and the thoughts of Jean-Pierre Bourguignon on the art and math exhibition at the Fondation Cartier in Paris. An interesting part is dedicated to the connections between math, computer science and theatre with the papers by C. Bardainne and A. Mondot. The topics are treated in a way that is rigorous but captivating, detailed but very evocative. This is an all-embracing look at the world of mathematics and culture.
by Amir D. Aczel
The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel’s lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride.
The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.