Zero
The number for 'nothing' — and one of the most consequential conceptual inventions in human history.
Origin
A symbol for nothing as a placeholder appears in Babylonian and Mayan systems, but zero as a number you can compute with — add, subtract, multiply — was developed in India around the 5th century CE, formalized by Brahmagupta in 628. Arab mathematicians carried it west; it reached Europe in the 12th century through translations, where it was initially regarded with suspicion (some Italian cities banned it as suspicious for bookkeeping). Without zero, there is no place-value notation, no algebra, no calculus, and no computers.
Modern usage
'Starting from zero,' 'zero-sum,' 'zero tolerance,' 'sub-zero,' 'patient zero' — the number is conceptual furniture. Programmers argue endlessly about whether arrays should start at zero or one. The history of zero is a regular pop-math topic; the canonical popular book is Charles Seife's Zero (2000).
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