Despite having an abiding interest (and a degree) in mathematics, I’ve never tried to write a science fiction story in which math plays a central role. Computers and robots, sure I’ve done that, but not hard sci-fi about hard mathematics.

Is it even possible? It seems easy to extrapolate current science into the far future, or the distant past, and write exciting stories about the consequences. Does anyone care enough about Fermat’s Last Theorem or differential equations to make up an engaging story about them?

A few weeks ago (March 2023), I read a news article about two new solutions to a centuries-old problem in plane geometry. The problem is how to tile a flat surface using tiles that fit together without overlapping and with no gaps, but do not form a repeating pattern. These are called aperiodic tilings, and for centuries mathematicians have attempted to find the smallest set of tile shapes that can do that. In 1974 the mathematician Roger Penrose found a pair of shapes that accomplish it, but until recently, nobody could find a single shape that did the trick.

Then last March, four mathematicians from the Universities of Yorkshire, Cambridge, Waterloo, and Arkansas (where I now reside), discovered the “einstein” tile — a single shape that, when rotated and mirrored, could tile the entire plane without repeating patterns. No, it’s not named after the famous physicist, but after the German phrase ein stein which means “one stone.” A few weeks later, another group of mathematicians found a way to smooth out the corners of the einstein tile to accomplish the same tiling without having to use mirror images — the so-called “vampire einstein” tile.

Interesting, but is it possible to write an engaging story about what happens with shapes on a flat, 2D surface?

Then I remembered an old sci-fi novel I read a long time ago titled Flatland: A Romance in Many Dimensions. It is a novel-length satirical story about beings who live in a 2D world and whose geometrical shapes determine their social caste. The narrator of the story is A Square (that’s his name and shape). It’s an entire book about geometry, written in 1884, and it is every bit as biting and socially relevant as 1984, Brave New World, or Animal Farm.

The einstein tile, with its 13 sides, would have been a high priest in Flatland.

As I continued thinking about sci-fi stories in which mathematics plays a major role, a couple of stories by Isaac Asimov came to mind. Of course, the Foundation stories and novels all rely on a mathematical conceit — a fictional branch of statistics called psychohistory that can reliably predict the future of societies. It still seems plausible to me that the behavior of large groups of people would be more predictable than the behavior of an individual in the group.

The Feeling of Power, a lesser-known Asimov story from 1958, seems completely prescient today. It is the story of an advanced human civilization that has grown to rely entirely on computers to do basic mathematics, including simple arithmetic.

Far-fetched, you say? How many of us, when faced with the need to divide two integers, would grab a pencil and paper rather than ask Alexa? And how many of you can still compute a square root by hand? I can’t.

In Asimov’s story, a lowly technician reinvents the “technology” of doing arithmetic with a pencil and paper, and it changes everything. There’s a great scene where the technician is initially convincing a congressman he can actually compute things without a computer.

“Now seven times three is twenty-one.”

“And how do you know that?” asked the congressman.

“I just remember it. It’s always twenty-one on the computer. I’ve checked it any number of times.”

“That doesn’t mean it always will be though, does it?” said the congressman.

Here are some links to the three stories I mentioned above. The archived link to the first-ever Foundation story is especially interesting because it consists of images from a vintage copy of the entire ASF issue in which it was published. Please wash your hands before you touch it :)

Edwin Abbot’s Flatland — 1884 Novel

Isaac Asimov’s Foundation (original short story) — May 1942 Astounding Science Fiction

Isaac Asimov’s The Feeling of Power — August 1958 Worlds of Science Fiction

So, I think I’ll try again to write a good sci-fi story focused on mathematics. If I succeed, I’ll submit it to scifishorts.co for publication, so please subscribe and watch the pub for my future story about the future of math.

It may or may not be titled:

The Happiness Equation: And its unexpected solutions

Nice blog. Does “orbital mechanics” count as hard maths SciFi, if it does then you could count Cixin Liu’s The Three Body Problem as a good example of hard maths SciFi.