Is mathematics a science, after all? Those university friends of mine who took mathematics majors did end up with bachelors of science degrees, just as surely as my physics kin. In Tobias Dantzig’s beautiful 1930 history of the field (titled, simply, *Number*), he refers to mathematics as a science quite unapologetically. Friedrich Gauss called it the Queen of Sciences.

Sure, mathematics is abstract, seemingly existing in some magic realm outside of the physical world. I remember Plato. But the edges of math and physics constantly bleed into each other (consider the non-Euclidean spacetime we’re swimming in). And with Kurt Godel’s Incompleteness Theorem, Karl Popper, philosopher of science *par excellence*, suggested that even pure mathematics might be as falsifiable, and thus as scientific, as molecular biology.

So if math is a science, with number, logic, and formulae apparently writ into the fabric of the universe, take it one step further. We should also concede that just as one can write cyberpunk, biopunk, or good old space opera, there must be a speculative sub-genre for mathematical fiction.

And there is! In most science fiction, equations on a blackboard sometimes serve the purpose of incantations in fantasy: as a device to move the plot forwards and nothing more. But there are stories where the math is simultaneously central to the story, while also speculative enough to count as genre.

In the chronology of my own reading, the first story I discovered to fit these criteria was Ted Chiang’s “Division by Zero.” It’s of the “imaginary technology/science which changes everything” school of speculative fiction. Unlike, say, any of a plethora of time travel stories, the discovery here seems downright mundane. A mathematician proves that, well, you can’t prove anything. Not even that 1 + 1 = 2. Not logically.

The only outcome of this is a loss of certainty in the world. And at that, only a loss of certainty for the select few whose mathematical genius allows them to actually understand the proof. Yet it *is* world-shattering, and what’s more, the reader believes it.

After showing this story to everyone I could think of, including the math class I was teaching at the time, I started looking for more examples of this genre.

I grabbed a copy of Edwin A. Abbot’s very short book, *Flatland*, which imagines life in two dimensions, or even one, and then goes on, by a simple extension of logic, to mathematically deduce a fourth dimension, a fifth, ad infinitum. This is, admittedly, borderline fiction literature, almost fitting better in a popular science or even social commentary category, like *Gulliver’s Travels*. Still, it was something.

Soon after I read a vintage Isaac Asimov tale, “The Feeling of Power.” This was of the “extrapolate an emerging technology to its logical conclusion” school of SF, and imagined that hand-held calculators would change society in far more sweeping ways than they actually have (Isaac perhaps failed to take into account that electronic calculators were merely replacing slide rules, an only slightly less effective technology).

Then there’s Robert Heinlein’s “—And He Built a Crooked House,” where a design based on a 3D projection of a four-dimensional shape actually shifts to an upper dimension during a minor earthquake. Rounding off our Big Three, Arthur C. Clarke wrote “The Nine Billion Names of God,” wherein a brute-force approach solves an ancient religio-combinatorial problem and heralds doomsday.

Speaking of combinatorics, I’ve read not one, but two different stories featuring typing monkeys. The earlier, by publication date, is Russell Maloney’s “Inflexible Logic” (1940), in which a gentleman of leisure acquires six monkeys and typewriters hoping to see a great work of literature randomly punched out. In defiance of common sense, the monkeys type *nothing but* famous works of literature for weeks on end, without ever making a mistake. In Mur Lafferty’s “Been a Long, Long Time” (1970), a bumbling angel should be so lucky. He waits eons hoping for such a result.

Eventually, one of these stories (I can’t recall which one) led me to a 1958 anthology from Clifton Fadiman, called *Fantasia Mathematica*. I discovered many old favourites and several new ones. In “The Captured Cross-Section” by Miles Breuer, some mathematical work on four-dimensional coordinates leads to a higher-dimensional being rotating into 3D space, but only one impossible-to-interpret cross-section at a time. In “The Devil and Simon Flagg” by Arthur Porges, the devil gambles for someone’s soul, but meets his match when he’s challenged to prove Fermat’s Last Theorem (proved in real life by Andrew Wiles in 1995).

Fadiman put together a second collection, *The Mathematical Magpie*, and were he alive today, he could certainly do a third, a fourth, who knows how many volumes, really (though Jorge Luis Borges’s “Library of Babel” might suggest a place to start calculating). From Lewis Carroll to Douglas Hofstadter, there’s plenty of mathemagical gold out there, though I wager this set is a subset of all such excellent math-based science fiction with the potential to be written.

**J.J.S. Boyce** is a writer, educator, and semi-pro omelette chef. He can frequently be found writing at the Green Man Review, Library Journal, and Care2. He also maintains a meta-narrative at his blog, The Back of the Envelope.