The Music of Mathematics: Primes, Fractals and Cube Symmetries in Art and Science

Overview

In this talk, the speaker argues for bridging science and the arts through mathematics. He introduces three core mathematical blueprints that permeate both nature and culture: primes, fractals, and cube symmetries. Through vivid stories about Messiaen and Shakespeare, Pollock and Pixar, Xenakis and live performance, he demonstrates how mathematics unlocks creativity and how creative practice reveals hidden mathematical structures.

The talk concludes by urging researchers and artists not to separate their domains, echoing Stravinsky’s idea that structure can fuel creativity across disciplines.

Introduction: A Bridge Between Art and Science

The speaker recalls a common educational pressure to choose between Shakespeare and physics, Debussy and DNA, art and science. He describes his own path of integrating mathematics with the arts, inspired by a teacher who reframed mathematics as a creative language. The talk sets up a model of mathematics as a study of structure and a set of nine blueprints that recur in art, science, and nature.

The Triangle of Structure: Math, Art, Nature

A central idea is a triangle with corners for mathematics, the creative arts, and nature. Structures found in the natural world underlie both mathematical thinking and artistic practice, suggesting a shared language across disciplines.

Blueprint 1: Prime Numbers in Music and Literature

The prime numbers blueprint begins with Olivier Messiaen, whose 17 and 29 note/chord schemes create rhythms that stay out of sync, yielding unsettling yet beautiful musical textures. The speaker explains how 17 and 29 are primes and how their interaction with a 17‑note rhythm and a 29‑chord harmony prevents exact repetition. He recounts Shakespeare’s use of prime-length lines, such as 11 syllables in certain famous lines, to signal magic or significance, and notes how primes appear in art as a code, guiding rhythm, meter, and emphasis. The cicadas’ 17‑year life cycle and predator cycles are used as a natural example of how primes can stabilize life cycles by maintaining out-of-sync timing with predators, illustrating an evolutionary use of prime-based timing. The connection to Radiohead’s irregular beats is offered as a pop example of primes in rhythm, reinforcing the idea that mathematics quietly guides artistic creativity across media.

Blueprint 2: Fractals in Pollock and Pixar

Turning to fractals, the speaker discusses Jackson Pollock, whose drip paintings reveal fractal geometry when viewed at different scales. He demonstrates that Pollock’s method is not merely random but can be described by chaotic dynamics, specifically a double pendulum, whose chaotic motion creates fractal structures on the canvas. The talk argues that fractals arise naturally in nature, from trees to broccoli, and that artists exploit simple iterative rules to yield complex, scalable patterns. The animation and film industry use fractals to create realistic natural environments, with Pixar employing fractal mathematics in generating lifelike jungles and other 3D scenes. The Mandelbulb and higher-dimensional fractals extend these ideas into three dimensions, appearing in contemporary visual effects and in Marvel’s Living Planet concepts as well as in modern computer graphics.

Blueprint 3: The Cube and Xenakis Nomi Alpha

In the third blueprint, a Platonic solid, the cube, structures a musical work by the Greek composer Iannis Xenakis. The solo cello piece Nomi Alpha is built around the 24 symmetries of the cube, with textures mapped to the cube’s corners and a path traced through them that corresponds to two interwoven tetrahedra. The composer’s symmetries are explored through a Kaley graph, showing how different rotations and reflections generate a sequence of movements that never quite repeat, due to the interplay of cube symmetries. The talk highlights how Xenakis used group theory and a geometric framework to inform musical form, and how a live performance can incorporate visualizations that map the cube’s symmetries to musical textures and time. The closing idea is that the dialogue between mathematics and art is bi-directional: artists discover structures that mathematicians formalize, while mathematical frameworks stimulate new artistic directions and questions about symmetry, paths, and structure.

Conclusion: Mathematics as a Language of Creative Creation

The talk ends with a call to maintain dialogue between scientists and artists, echoing Stravinsky’s assertion that structure enables creativity. The speaker emphasizes that mathematics is not only a tool for describing the universe but a creative language that can enrich all forms of expression, from music to architecture to literature.