“Thank you so much for this opportunity for a non-mathematician to be part of the BIRS community”, wrote Alice Major. It doesn’t happen often that an illiterate mathematician gets an email from a Poet Laureate. Major was writing about her experience at last week’s workshop at BIRS (The Banff International Research Station). Entitled, “Mathematics: Muse, Maker, and Measure of the Arts”, the workshop was a BIRS classic. Her email made me feel even worse about not being there, and not only because I missed the likes of Ingrid Daubechies, David Mumford, and Robert Moody, who were merely the math. reps. for that event. Artists, musicians, poets, physicists and engineers were also there and they are now writing about it.

Artistic beauty and mathematical complexity have a history of interaction for as long as civilization itself: The golden ratio and the pyramids, Alhambra’s tessellations and the Penrose tiling, of course Di Vinci, Dali, Esher, and various minimalist and abstract schools of art, which had their roots in mathematics. But the workshop was about a totally different matter. It was about modern science and the future of such interactions.

Take for example, Stylometry analysis of literary style, which was initiated by the English logician, Augustus de Morgan, in the mid 1800’s as a way to settle questions of authorship by, for example, finding patterns in the length of words used by various authors.

While stylometric analysis of literature is now a well-established field, stylometric analysis to determine the authenticity of art is a nascent one as it requires much more sophisticated mathematical and statistical techniques, such as wavelet analysis, hidden Markov trees, and sparse coding. To learn about this, I strongly recommend the videotape of Shannon Hughes’ lecture on “Visual Stylometry on Impressionist Paintings for Artist Identification and Dating”, during the BIRS workshop.

Another example is the field of generative arts as well as other mathematical aided art making such as “Origami”, which have been greatly enhanced by the study of dynamical systems, and information theory. Penrose tiles and Shechtman’s discovery of “impossible quasicrystals”, have led to the study of aperiodic orders, and have inspired the Escheresque artistic aspirations of many mathematicians, artists and students. Some of these techniques have also found applications in the study of robotics.

Other instances of mathematical use are the advanced techniques in differential equations and optimization that are being used increasingly to enhance and restore old work of art. The work by the Chudnovsky brothers on the digital archiving of medieval draperies and the digital restoration and enhancement of old films are also such examples.

“The workshop will have a significant impact on my work both as a mathematical artist and as a designer of The Museum of Mathematics, which will open next year in New York City”, wrote George W. Hart.

“I’m just back from the Banff International Research Station for Innovative Mathematics and Discovery. I feel like a kid impressing her classmates with news of a trip to Disneyland,” wrote Alice Major in her must-read blogpost, “Math and Trap doors”, before adding, “I toss the name off as if I could actually tell a Gaussian distribution curve from a Faustian one.”   

The workshop organizers wrote: “Only by regularly interacting with the art community can mathematics find its vitality and become an important and lasting component of the study of arts.” 

 Amen! And BIRS will always make sure to contribute its share.