What is Expressive Mathematics?

To be absolutely clear—I made it up. Whatever follows, view with a healthy mix of skepticism and curiosity.

Expressive Math is leveraging inspiration from mathematics to express ideas.

Where does the concept come from?

Frequently people only view calculations, statistics, and geometry as math. This is a vast misrepresentation of the true contributions mathematics has made to society. Mathematicians don’t typically spend their time performing repeatative calculations. Instead, they spend their time studying the logic of formal systems and developing intuition for new abstract concepts. They then leverage concepts found in these systems to help them reason abstractly and find patterns in the work they are doing. Once the pattern is identified, they break it down into a language they can share with others. Eventually, these patterns are taught in schools. But what often gets lost in translation is how to do this process yourself.

Why isn’t this taught in school?

A big question like this requires more, but for now, hopefully this summary will suffice. Mathematics requires building intuition before you can get to the abstractions. Consider teaching someone to count who has no prior experience with the process or the language. The truth is, if they don’t take the time to develop a number sense, no matter what language is used they will remain confused. Most people only experience mathematics from the practice vantage point. They view math as memorization, or a bunch of confusing rules. Expressive math adjusts the approach to try to connect with people in places they are already building intuition. Instead of providing the abstraction and the process, we will try to build off where you already live, and practice every day.

Expressive math has existed, nameless, for a long time

Perspective is a wonderful example of leveraging mathematics to tell visually stunning stories. Rhythm without counting is random and can feel eerie. Body flow and movement are easier to measure if you have a rhythm. I think because each subject has its own theory (i.e. theory of art, theory of music, or the theory of dance) people are less likely to realize when these subjects are actually doing mathematics. Not everything is math, but regular abstract reasoning we apply, stems from basic mathematical ideas. Would we have science if we could not measure?

How to apply expressive math?

Where pure mathematics is formal and structured, expressive math is more intuitive and open-ended. It allows you to go where you want without a right or wrong way to apply it. It’s a form of building intuition for a given practice. For example, you didn’t learn to count overnight. It took practice. You gained new insights into counting every time you gave it a go. This helped you develop a language and a basic number sense. Though probably challenging at the time, you have become so accustomed to counting that you may not even remember what it was like to learn the topic. This process occurs with just about everything else in your life. Math isn’t about memorization, it’s about abstract reasoning. We use abstract reasoning to engage in storytelling, design, play, and creative expression. To do expressive mathematics is as simple as trying to express the abstract patterns that exist within the things you typically do on a regular basis.

Expressive mathematics seems easy — how can it be math?

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”

You may fall into the category of people that brushes this off as nonsense. That’s understandable; as a society, we’ve grown to think of mathematics as hard and complicated. So when math is easy, it gets written off as not truly mathematics. However, this isn’t true. You can count to 100 with total confidence. That’s still math. Though we’ve both likely mastered this ability, new math concepts follow a similar pattern. Math requires abstract reasoning and it’s not always simple. But when it is simple, it doesn’t magically change to a different topic. It is still mathematics.

Isn’t expressive mathematics just science?

I’m glad you noticed! The answer is no.

Science is formal and requires peer review. It’s not really a form of self-expression as it is a form of discovery. Expressive mathematics is a form of expression and self-discovery. To uphold the integrity of formal science and math, please don’t write scientific papers about expressive mathematics. That is not the right forum. This also means expressive math is not scientific or mathematical fact! Ever.

Summary

Much of what we do relies on abstract reasoning — playing video games, listening to music, reading, watching movies, even sharing the thrill of a story. These are all places where mathematical ideas take root. You engage with them naturally, without effort or anxiety. It’s true: you may never publish a breakthrough proof. But that was never the point. You don’t need to be a mathematician to be good at math. You just need to recognize the reasoning you already use — and let it grow.

Trust me, you are better at math than you think.

Convinced or not, I’m confident there is something here for everyone. Come along. Let’s explore this topic together.