Interview with Bahman Kalantari Dr. Bahman Kalantari discusses software he has developed through his research into polynomial root-finding.


The Rise of Polynomials: A polynomiograph of z3 - 1 coming to life through 3D animation (and music).

Valentine's Day Special A heart themed animated polynomiograph.


Store: Exclusive, original Polynomiography merchandise is now for sale! Visit the Polynomiography Store to get yours today!

More News: Visit Bahman Kalantari's personal home page to learn additional news and other information related to polynomiography.

New Book Announcement: "Polynomial Root-Finding and Polynomiography" by Bahman Kalantari.

Article: Polynomiography is featured in the April 2007 edition of Muy Intersante. Spain's popular science magazine.

Cover: A polynomiograph featured on the February 2007 cover of the Finnish science magazine Tiede.

Cover: Kalantari's Polynomiography on the cover of Princeton University Press Mathematics Catalog [pdf]

Cover: Kalantari's Polynomiography on the cover of Princeton University Press book Fearless Symmetry: Exposing the Hidden Patterns of Numbers.

Exhibit: Kalantari's Polynomiography artwork part of traveling art-math exhibit in France and Greece.

Quotes and Comments


A variety of artists, scientists, mathematicians, and educators have praised Bahman Kalantari and his work with polynomiography. Read a sampling of these kind comments below:

Bahman Kalantari's work on Polynomiography is visually striking and provides profound insight into root finding algorithms. In future generations, I expect that visualization of mathematical algorithms will become an expected part of mathematical research. The computer skills and artistic skills that requires will be studied by mathematics students. Bahman Kalantari's skills are here now and we can enjoy the beautiful results as he has applied them to Polynomiography.

Cliff Reiter
Professor of Mathematics
Mathematics Department, Lafayette College
Easton, PA 18042 USA

POLYNOMIOGRAPHY is a truly revolutionary theory/medium, and I am sure that it will ultimately get the full recognition that it deserves.

It is amazing how from these age-old objects, called polynomials, one can get such rich universes.

On behalf of the mathematics department and myself, I wish to thank you for the BEAUTIFUL and INSIGHTFUL Colloquium talk. It was a marvelous blend of art and math. This is indeed a "New Kind of Art", rooted in deep mathematics, and raising interesting questions. What is so fascinating and promising about it is that one does not merely "push a button", but there is still room for human creativity and imagination to make the full use of it, in other words, it is a great artistic tool.

Doron Zeilberger
Professor of Mathematics
Rutgers University

Bahman Kalantari's work is multidimensional. It is recognised for its broad diversity by artists and scientists.

Lillian Schwartz
Pioneer of New Media

Professor Kalantari's work combines in a very striking way mathematics and visual arts. His work on "polynomiography" is very original and pretty.

Cumrun Vafa
Professor of Physics
Harvard University

From a mathematical point of view, Polynomiography, that is defined to be the art and science of visualization in the approximation of zeros of complex polynomials, has an enormous and fruitful field of applications in visual arts, education and scientific research. Although the main and most well known products are beautiful two-dimensional images, polynomiography could also be used to design three-dimensional objects with many interesting purposes of different uses. And this is today still an unexplored research field!

Dr. Vera W. de Spinadel
International Mathematics & Design Association

"Yesterday, a few pupils from one highest class-room of a French Lycee came to visit the [Henri Poincare art-math] exhibit. The answer to the question : "Is the person who conceived this carpet an artist or a mathematician?" was ... : "an artist". The students were surprised to learn they were wrong. Indeed this story about Kalantari's carpet shows how much mathematics, being a source of creation of new attractive designs, enriches the artistic universe. But this is not the end of the story since these students came also to get an idea on how these works have been produced: they discovered the great diversity of the very concrete mathematical objects that were completely unknown to them; these unusal and sometimes fascinating objects they were looking at were a source of cultural enrichment and of attraction to the many aspects of mathematical world. Students were surprised that a mathematical problem, to find the roots of a polynomial equation, could lead to such new creations. We do not know what will be the influence of this visit in the long run. But from this kind of physical experience, we can assert that art is an efficient tool to stimulate the general interest in mathematics."

Claude P. Bruter
Professor of Mathematics
University of Paris 12
Organizer of art-math exhibit at IHP

"Bahman's polynomiography shows many of the possibilities of algorithmic art. His woven polynomiography carpet is truly beautiful."

Ed Pegg Jr
Wolfram Research

"I've been amazed at the beauty of Kalantari's polynomiographs. The field of polynomiography is a truly unique interdisciplinary field which will draw the interest of artists and art lovers to mathematics. I want to learn more!"

Dr. Russell E. Goodman
Assistant Professor of Mathematics
Central College, Pella, Iowa

Arts and Mathematics: a (more than) possible dialogue

The beauty of Mathematics lies beyond the operating tools which make our daily routine easier. To mention just some instances, the cinematographic animation techniques use mathematics, the artist makes use of proportions and symmetry, and in the musical harmony the mathematical logic is applied.

Taking advantage of the richness that Mathematics offers, Professor Bahman Kalatari has generated fantastic images with his polynomiography, transforming a topic which is so arid for so many in beautiful pictures, this way bringing the beauty and harmony of this school subject to the students´ universe.

Arts and Mathematics have already been related by many authors. The mathemathician and philosopher Gottfried Leibniz (1646-1716), for instance, states that "Music is a secret exercise in the arithmetic of the soul, unaware of its act of counting." Leibniz points out the numerical world in relation to the most charming harmonies and melodies.

Therefore, understanding the connection between Arts and Mathematics as a means for the man to express himself within his historical time and to respond to the real demands that the world imposes on him, presents itself as the first possibility of projecting a new way of looking at the contemporary and of observing how fragile the existing frontiers between the mathematical ideas and the production of different artistic languages are.

It is then possible to conclude that all the ones who are able to see beauty in the various forms of art expression would be enchanted with the demonstration of a theorem and would join the great philosopher, logician and social critic Bertrand Russel (1872-1970) when he declares: "Mathematics, righthy viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture."

In Brazil, this way of considering Mathematics has influenced the Ético Sistema de Ensino while devising its teaching materials. Being an enterprise in the educational segment, with head offices in the city of Ribeirão Preto, in the state of São Paulo, the Ético gives assistance to schools all over Brazil, providing an inovative method as well as a proposal for significant education. Their teaching materials are devised by an experient group of professionals, all of them committed to the students´ human formation. Aiming at making learning more and more pleasant and inter-disciplinarian, the Ético´s materials for high school and for courses preparing students for the university entrance tests present pictures created by Professor Bahman Kalantari´s polynomiography. By using those, the students can develop a new view by means of the mathematical language, demonstrating how the equations can generate such beautiful works.

Denise Favaretto
Pigmento Editorial
Ribeirão Preto - SP- Brasil