zero

Early placeholders

The earliest known use of a placeholder in a positional number system appeared in Mesopotamia, where the Sumerians, about 5,000 years ago, used a slanted double wedge in cuneiform (system of writing in the ancient Middle East) to indicate the absence of a digit. A tablet from Kish (in present-day Iraq) from about 700 bce provides evidence of the use of three hooks to indicate missing digits within a number. Between the 6th and 3rd centuries bce, the Babylonians employed symbols—typically one or two wedges—to mark empty positions between nonzero digits in their number system.

In ancient Greek mathematics the concept of nothingness was acknowledged but not formalized as a number. Greek philosopher Aristotle rejected the notion of a void and argued that division by zero lacked meaning, reinforcing the absence of zero in the Greek numerical system, which relied on the Greek alphabet and was limited to positive integers. The ancient Romans also developed a nonpositional numeral system, using letters such as I, V, and X for recording values rather than calculation. Arithmetic was typically performed on a counting board or an abacus, and even though Latin had terms such as nulla to denote “none,” there was no symbol for zero in Roman mathematics.

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The Maya civilization in Central America independently developed a place-value number system that included a symbol for zero, likely by the 4th or 5th century ce. They used a shell-shaped sign to show zero in calendar inscriptions and records. This symbol helped mark when a number position had no value, similar to how zero is used in modern numerals. In Mayan calendars days were counted from 0 to 19 rather than 1 to 20. Evidence of this system comes from buildings and carvings, as many written records were destroyed in the 16th century.

The Indian invention

The concept of zero developed in India over several centuries. The earliest known example appears in the Bakhshali manuscript, a birch-bark text discovered in present-day Pakistan. Radiocarbon dating by the University of Oxford places parts of the manuscript as early as the 3rd or 4th century. In this text a dot was used as a placeholder to indicate the absence of a digit in a specific place value—the earliest recorded symbol for zero. This symbol later evolved into the open circle used in modern numerals.

By the 5th century mathematician Aryabhata described a positional system in his treatise Aryabhatiya. Although he did not employ a written symbol for zero, his system required a placeholder to differentiate numerical values based on position. In the 7th century astronomer Brahmagupta became the first known scholar to treat zero—referred to as shunya in Sanskrit—as a number in its own right. In his book Brahma-sphuta-siddhanta (628; “Correctly Established Doctrine of Brahma”), he defined rules for arithmetic involving zero, including operations with negative numbers.

From India to the world

Between the 8th and 9th centuries, Persian mathematician al-Khwarizmi studied Indian mathematical texts, including the works of Brahmagupta. In his treatise Algoritmi de numero Indorum (“Al-Khwarizmi Concerning the Hindu Art of Reckoning”), al-Khwarizmi described a positional system based on 10 symbols—1 to 9 and 0—and credited its origins to Indian scholars. His writings helped introduce the Hindu-Arabic numerals to the Islamic world. By the 9th century zero appeared in Arabic texts in a form derived from Indian notation, resembling the modern oval symbol. The system reached Europe by the early 13th century, after the Italian mathematician Fibonacci encountered it during his travels in North Africa. In 1202 he published Liber abaci (“Book of the Abacus”), a practical guide for merchants that introduced zero and positional notation to European readers. Despite its advantages, acceptance was gradual. Florence banned the use of Arabic numerals in 1299, for example, citing concerns about forgery. By the Renaissance the zero-based numeral system had gained popularity, becoming more widely used than Roman numerals in many everyday applications and paving the way for progress in mathematics, science, and commerce.

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Mathematics

Zero functions as the additive identity, meaning that adding zero to any number leaves the value unchanged. In multiplication any number multiplied by zero results in zero. Division by zero is undefined because no real number multiplied by zero produces a nonzero result. Zero is an even number because it is divisible by two without a remainder. It also functions as a placeholder in the positional number system, allowing us to distinguish values such as 205 from 25. In algebra it helps define the roots of equations, and in calculus it represents the points of convergence or divergence.

Science and technology

In science zero appears in several fundamental contexts. In physics, absolute zero (0 Kelvin; −273.15 °C; −459.67 °F) is the lowest possible temperature—the point at which a thermodynamic system has minimal energy and no heat energy is available for transfer. In computer science, zero is one of two binary digits used to encode digital information. In engineering and economics, zero serves as a baseline for measuring change, such as zero pressure or zero net balance.