Is there a connection between artistic beauty and mathematical beauty?

This question led me from the arts to mathematics. Before starting, note that emotions and beauty are distinct issues. It’s not common among mathematicians to break into tears when they encounter mathematical beauty, nor is it common to cry when viewing Niagara Falls. The latter provokes a sense of awe very similar to the former.

It has been known since ancient times that mathematics and music are connected. Proportions of dividing a string produce pleasing (consonant) and unpleasant (dissonant) tones. But this is a difficult pathway to appreciate the beauty of mathematics when you start with music. I personally started with music but didn’t discover (note the choice of word) mathematics until I started doing algorithmic arts and design. In fact, proportionality of architecture is much closer to the idea of cohesion in a mathematical construction.

So it’s important where one starts his/her journey. The beauty of mathematics is not something that is accessible at first glance (unlike Niagara Falls, for instance). And so it should be discovered. Some people confuse the beauty of mathematics with a mere eureka moment of discovering something. That’s fun, but discovering a sense of cohesion in a mathematical structure is beyond that.

As a personal experience, the first ever truly algorithmic design I made was a hypocycloid.

A hypocycloid is the curve traced by a fixed point on a small circle as it rolls without slipping inside a larger circle.

It was fun to code that. And the result, the curve, was in some ways beautiful. But what truly struck me was the connection between the smaller circle and the bigger one, their radii, and the way the simple trajectory of a point on a small circle turns into something way more complicated when it is combined with the rotation of a bigger circle. For me, the beauty of the hypocycloid, regardless of its potential applications in engineering, etc., lay in the connections between components involved in the design.

Equipped with these insights, I can now connect mathematical beauty to musical beauty, for instance, where interactions of different instruments and sounds form the music. But the other way around is more complicated. The abstract beauty of mathematical constructions should be discovered.