Zero was excluded from Western math for over a thousand years

Seife recounts how Greek mathematics, built on Pythagorean and Euclidean geometry, had no comfortable place for zero or the void it represented. The Greek universe was one of ratios, shapes, and countable, positive quantities; a number representing nothing had no geometric analog and, worse, seemed to gesture at the philosophically taboo idea of a vacuum, which several Greek thinkers considered logically impossible.

This wasn't a minor gap. Aristotle's physics explicitly rejected the void, and that rejection rippled into mathematics, where a symbol for nothingness felt less like an oversight and more like a category error. As a result, sophisticated Greek geometry advanced without a functioning zero for centuries, limiting what kinds of equations and quantities could even be written down.

The absence persisted through Rome, whose numeral system had no zero at all, making arithmetic with large numbers cumbersome. Takeaway: a civilization's mathematics is bounded by what its worldview permits it to imagine, and zero was, for a long time, unimaginable.