I’ve been reading a lot of math papers lately.

I’m a computer scientist by trade, and theoretically should be able to speak this language. In fact, we take so much math as computer science engineers that we can’t double major in applied math since that’s already built into our coursework (something that would have shaved at least half a year off my college life if I’d known it sooner).

Some of those later courses were tough, but even math students at the most basic level have encountered knowing the answer, but not knowing how to get to the answer. On a particular test problem where I ran into this situation, I wrote “Poof! And the magic occurs!” between the problem and my answer. Suffice it to say, that was insufficient explanation.

Math writing is inherently logical. You define your terms, make your propositions, prove your theorems, then move on to the next property of whatever you’re studying. The problem occurs when you forget to define your terms, or leave out a step, or assume everyone in the universe has the same base knowledge as you.

I spent at least an hour last night trying to figure out how to change Fibonacci words into generalized Fibonacci snowflakes. I was missing one crucial piece of information that I finally had to track down in one of the cited papers, that all the addition in these equations was mod 4. The moment of finally watching something work the way you expect it to can feel a lot like magic, but a lot of trouble might have been saved on my part if the author had bothered to work out the interim steps in the paper. There were many other places where they had done this, but this one lacking piece of information was right in the middle from one really cool graphic to another.

So how do we apply this more generally?

Constructing a story, particularly a mystery, is a lot like proving a math theory. You discover evidence, make some conclusions, and prove your theory. Sure, a good mystery has some misdirection. You don’t want the reader to arrive at your conclusion too quickly. But you want your solution, your ending, to be the satisfying and logical progression of what has come before. Put another way, you want your ending scene to be “earned” by what you’ve written before it.

The problem as writers is that we always know this universe of our story better than our readers, to the point that sometimes we don’t know if we’ve said all we need to make it clear to others. You may know a character’s motivation, but if you leave no sign of it in the book, then the reader doesn’t know why they should care. Bad mysteries often introduce a surprise villain at the end of the book, rather than in the first 20%, cheating the reader of the opportunity to engage with finding the solution.

I don’t think this means you need to beat your readers over the head with facts already in evidence. But if something is important to things you’re going to write later, be sure you’ve actually said it the once. Beta readers and editors are especially helpful in finding these sorts of flaws, as is having an outline where you work out all of these connections ahead of time.

And incidentally, and separately from the main point of all this, writing in a technical language is not always better than the vernacular. I understand that academic papers serve different functions and are targeted at different audiences than more general work. But math doesn’t have to be obscure. Part of the reason I’m slogging through all this work is to write something I can share with everyone. This is something to keep in mind when you’re tempted to insert a lot of techno-babble or overly sophisticated words into your stories. Sometimes telling a story clearly, plainly and succinctly is the best way to go.

Just make sure to show your work.