Paola Antonelli is senior curator of Architecture and Design at The Museum of Modern Art. Benoit Mandelbrot is the father of fractal geometry. While studying architecture at the Politecnico in Milan in the 1970s, Antonelli was inspired by Mandelbrot’s geometric ideas and visualizations, and eventually wrote her thesis on “Fractal Architecture.” The two met for the first time last year when Antonelli invited Mandelbrot to a Seed/MoMA Salon, a monthly gathering of scientists, designers, and architects. Just before Antonelli’s new Design and the Elastic Mind exhibit opened at MoMA in February, they reconnected to discuss fractals, architecture, and the death of Euclid.

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "rough," he says. To study and learn from such roughness, for which he invented the term fractal, Mandelbrot devised a new kind of visual mathematics based on such irregular shapes. Fractal geometry, as he called this new math, is worlds apart from the Euclidean variety we all learn in school, and it has sparked discoveries in myriad fields, from finance to metallurgy, cosmology to medicine. In this interview, hear from the father of fractals about why he disdains rules, why he considers himself a philosopher, and why he abandons work on any given advance in fractals as soon as it becomes popular.

Steven Strogatz moves on to imaginary numbers as part of his series on teaching mathematics to adults.