Should product designers learn pure math?

If truth, taste, and aesthetic harmony in concordance with the rhythms and patterns of nature are part of your design toolkit then I think you could gain a lot from it.

I took a proof-based higher math class for the first time in my life at Northwestern while working full-time as a product designer. Given the intensity of the subject, it was a nerve-wracking choice for me.

I wanted to delve into pure math because I was doing a lot of programming both at and outside of work and sometimes I’d try to read a research paper or dig a little deeper into a topic only to find myself stymied by a wall of obtuse glyphs.

Little did I know that this intellectual excursion would leave me with some profound shifts in perspective.


The mathematical standard for truth is razor sharp. Axioms and propositions must be carefully vetted and joined together in unbreakable strings of logic in order to pass as mathematical truth.

Once you experience the strength of this type of truth, it makes you question things you thought were true in other fields or in your daily life. Could the logic of your life be predicated on falsehoods or uncertainties? Certainly, if you look deeper and begin to hold a higher standard of what is true.

Challenge and Resilience

Math is difficult subject. It requires a lot of practice, diligence, and humility to succeed in. The skills it takes to master math are transferable, and you’ll bring the same persistence and rigor to other aspects of your work.

Beauty and Transcendence

The world is full of strange harmonies that can only be grasped through the language of mathematics. Learning this language helps you hear the song of the world with new color.

A relatable example is the observation of fractals in nature. A cantor dust is a visualization of a cantor set: essentially you take a line, remove the middle third, then remove the middle third of each child, and onward ad infinitum.

When you take a cantor dust and apply the principle in two dimensions, you get Sierspinski carpets, triangles, and Koch curves: Shapes with infinite perimeters and a finite areas. In three dimensions, you get objects that have infinite surface area and essentially zero volume.

Now here’s where things get peculiar. I’ll quote James Gleick from his phenomenal book Chaos:

“As a matter of physiological necessity, blood vessels must perform a bit of dimensional magic. Just as the Koch curve squeezes an infinite length into a small area, the circulatory system must squeeze a huge surface area into a limited volume. The fractal structure nature has devised works so efficiently that no cell is ever more than three or four cells away from a blood vessel. Yet vessels and blood take up little space, no more than five percent of the body.”

These same principles help to explain noise patterns in electrical signals, the structure and function of the human lung, branching patterns in trees, and the electrical network of the heart.

This is one of an infinite number of powerful ideas from mathematics that could transform the way you see the world.

Here are some books I recommend:

Journey through Genius: The Great Theorems of Mathematics

How to Prove It

Chaos: Making a New Science

Get more book recommendations