Division of Zero by Ted Chiang

1+1 = 2. Or does it?

What if mathematics turned out to be nothing more than a meaningless "mnemonic trick" (a phrase spoken by the protagonist)? That’s the unsettling premise in Division by Zero, another sophisticated short story by the amazingly talented Ted Chiang. Renee, a renowned mathematician, stumbles upon a proof that undermines the entire basis of arithmetic. As she explains to her husband:

"One and one will always get you two on your fingers, but on paper I can give you an infinite number of answers, and they're all equally valid, which means they're equally invalid."

That’s pretty wild—even if I don’t fully understand the formulas behind it. (I barely survived high school calculus, so my ability to grasp advanced mathematical paradoxes is about as solid as my ability to do long division without a calculator.) But while the complex math might have gone over my head, the emotional weight of the story resonated with me the most.

Renee’s discovery doesn’t just challenge mathematical truth—it shatters her entire worldview. For her, math has always been the one unwavering constant, the key to understanding the universe. Now, faced with the realization that it’s all built on contradictions, she spirals into depression. Her husband, deeply devoted but struggling to reach her, watches helplessly as she unravels. Their crumbling marriage and personal tragedy coincides with the author's historical reflections on the nature of mathematics, grounding the abstract theory in something profoundly human.

One particularly relevant quote from Einstein sums up the paradox at the heart of the story:

"Insofar as the propositions of mathematics give an account of reality they are not certain; and insofar as they are certain they do not describe reality."

Chiang's deeply intellectual premise never overshadows the story's emotional core. Even if the mathematical proofs went over my head, the philosophical depth and the deeply empathetic characters stand out.

"She, like many, had always thought that mathematics did not derive its meaning from the universe, but rather imposed some meaning onto the universe. Physical entities were not greater or less than one another, not similar or dissimilar; they simply were, they existed.