Radical Impressionist: A Mathematician Paints

It's time to resume working on an article I've promised myself for years. Perhaps it could become a book. I've been too busy painting though. But also, the one gallery representing me (Marigold Gallery on Canyon Road in Santa Fe) closed in January so I've been thinking about next steps.  But the main reason I am thinking about this now is that I see some excitement generated in the community to revisit the design techniques that I see as mathematical, involving dynamic symmetry concepts. I could even touch on the deeper mathematics behind the techniques in an appendix. This will fulfill my need to marry my two passions: painting and mathematics. In any case, two years ago I took a zoom workshop with Michele Byrne (now of Santa Fe) well-known artist specializing in using a palette knife, my favorite painting tool. An added benefit of the workshop was to see how she employs dynamic symmetry in her work: https://www.oilpaintersofamerica.com/2022/03/dynamic-symmetry-and-ho...

(Originally published Jan, 2019)  Everyone refers to Betty Edwards' book,  Drawing on the Right side of the Brain .  And I have to admit that it was an important book for me when I began to draw and paint seriously, in fact, so much so that it contributed to my efforts NOT to use the left side of my brain. But I was a Mathematician first and throughout my painting career I kept being bombarded with left-side ideas or logic. I couldn't escape it even if I tried. But I kept pursuing my need Not to allow logic to affect my painting. Finally this year I came to grips with the fact that I am driven by logic; I am an analyst first. And in fact I realized that for me, it's important to accept the logical part in order to grow as a painter.  So I determined that I would not discourage any left-brain ideas popping up while I paint.  And I would marry both sides of my brain perhaps to establish my brand as a painter-mathematician (or mathematician-painter). We all know th...

Image from the article on iso-perimetry given at the end*   Worth posting again.  In 2019, a mathematician, painter and long-time friend, Joel Spruck, from my Courant Institute days, proved a historic conjecture that is a generalization of the Dido's conjecture: find the shape enclosed by a given 'string' with the largest area. I just reread the article and wanted to highlight the last part on painting and doing math:  For Spruck, doing math is similar to painting—he experiences both as a form of meditation. Two of his own canvases adorn his office. "You get in a certain space," he says. "When you're really thinking about things, it's like being in a meditative state. Hours and hours go by and you don't even realize it. "You take a blank canvas, you have certain fundamental rules, but it's all open. And the other thing that's like with painting, or anything else, is to love the challenges. It's not whether you succeed in the momen...

Notes I am beginning a series of shorter posts. Each post will concentrate on one topic and in an order such that they will build on each other. The series is open-ended but they will begin with topics on composition.  The underlying mathematics will be explained where ever possible or at various points. Introduction  I want to preface this post with my usual 'disclaimer'. When I first began to paint I wanted to make sure that the left-side of my brain didn't take over, which -as a Mathematician- it's prone to do; I wanted to be expressive !  However, as the years went by I couldn't avoid seeing how often mathematics entered into discussions of composition, for example. So I decided to spend time investigating for my own self the symbiotic relationship of math and art. My usual approach to a painting now is to start off analytically, with measurements and thoughts about proportions and unequal measures, and perspective in the landscape and the direction of light and...