For over a thousand years, merchants and scholars in ancient India kept two kinds of accounts. Positive numbers recorded what a person owned. But they needed a way to record what a person owed — a quantity that was real, but less than nothing.

Brahmagupta (bra-mah-GOOP-tah), a mathematician working in Rajasthan, India in 628 CE, was the first to write formal rules for calculating with these quantities. He called them "debts" and defined how they behaved when combined: a debt plus a debt produces a larger debt. A debt added to a fortune produces a smaller fortune. A debt subtracted from a fortune produces a larger fortune. His rules, written in the Brahmasphutasiddhanta, are recognizable as the rules for negative numbers students use today.

European mathematicians, working independently centuries later, resisted this idea. Many called negative numbers "absurd" or "fictitious." As late as the 1600s, scholars argued that a quantity less than nothing could not exist. The concept requires a kind of abstraction — treating a debt as a number, not just a situation — that takes time to develop in any mathematical tradition. The negative sign you write today came directly from the accounting systems Brahmagupta formalized more than 1,400 years ago.