Math is just (formal) creative writing

Let me start with a direct comparison: what is the job of an author of fiction? They create characters, settings, and the rules about how they interact. After these pieces have been created, an author facilitates their interaction. The author merely writes about the consequences of this fictional world that they’ve created.

I claim that the job of a mathematician is the same. They create objects and rules about how they interact. The mathematician then writes about the consequences of these definitions and axioms.

A Mathematician calls this result a theorem and the results leading up to it a lemma while an author similarly makes a distinction between a major plot point versus smaller events (with climax being the main result).

Consistency:

Mathematics is a discipline where creativity is the aspect of the study. Physics might require creativity in solving a problem, but the problem is always grounded in figuring out something about the world. Mathematics, on the other hand, is completely okay with abstract nonsense that exists only because of a mathematician’s creativity. However, there’s multiple rules that guide what good, productive, and beautiful mathematics is about. Consistency is an important example of this.

Consistent mathematical theory is a set of rules and objects that do not lead to a contradiction. To be more detailed, it’s a mathematical system where you cannot prove both a statement and its negation. I think the importance of consistency highlights an important aspect of mathematics, which is that we want to do mathematics that is interesting and does not lead to contradiction.

This is a starkly different expectation from the sciences. A scientist does not settle for a theory that is just consistent with empirical observations. Rather, they look for a theory that is directly supported by evidence, a verified result. In mathematics, the “correct” result is simply a consistent one.

Consistency is also an important criterion in writing. A big part of immersion is that the characters, the world, and their interactions don’t seem illogical and fits with things that you have set up before. Many literary critiques are ones directed towards consistency such as out of character dialogue, plot holes, incoherent messaging or theme, etc.

This reveals a structure in writing. Creativity is good, but creativity also has to make sense, which is what consistency exists for.

There’s an adage of “restriction breeds creativity,” and I believe this is an essential part of mathematics and writing, much more so than other fields of study. Once you have set a mathematical theory, the results that follow it comes from the restriction that it has to be consistent with your base theory. But this is also exactly what happens in writing. Good writing comes from making your events consistent with the ones that followed before. Without this structure that consistency provides, unbounded creativity does not generate a compelling mathematical result or piece of fiction.

Epistemology:

There’s a long debate of whether mathematics is discovered or invented. I must have spent too much time thinking about this as well. I think arguments for both sides are compelling and do a great job trying to ground what the nature of mathematics is.

My thesis might strongly suggest a brand of mathematical anti-realism, the notion that mathematical objects aren’t real and are invented. Specifically, it looks like it must go hand in hand with fictionalism, the belief that mathematics is a piece of fiction, albeit a useful one.

However, I claim that my thesis that mathematics is formal creative writing is not one that makes direct claims about the epistemology of mathematics. What it does argue about is the experience and process of what doing mathematics looks like, not what mathematical knowledge itself is.

In fact, I think there exists many versions of platonism that are harmonious with my thesis. If we go fully platonic and affirm the existence of ideas as fundamental, mathematics and fictional writing might literally be the same epistemological thing. Mathematics would discover the nature of numbers and shapes while fictional writing would discover the nature of emotions, morals, and other subjective properties that are equally as real as numbers for a platonist.

In this view, Romeo and Juliet is an exploration of love as a concept much like how Elements explore triangles. And these works allow us to access these abstract concepts and engage with them.

The difference:

What is then the difference between literary writing and mathematical writing? In the title, my answer is just the difference in “formality.” Though both fields have convention, the way mathematician do math is a lot more rigorous than a poet. There is also a distinction in the community, which is a difference in how accepted a writing is. Though there is both an aesthetic and judgment in skill, mathematicians have a much greater consensus on what is beautiful and what is correct while writers disagree more on this.

The point

I’m not sure what the point is, but I have always suspected that math is the weird one out of STEM and I believe that this is why. Math both in practice and epistemologically behaves much like a literary field and we should be more open about this.