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negative numbers
Long denied legitimacy in mathematics, negative numbers are nowhere to be found in the writings of the Babylonians, Greeks, or other ancient cultures. On the contrary, because Greek mathematics was grounded in geometry, and the concept of a negative distance is meaningless, negative numbers seemed to make no sense. They surface for the first time in in bookkeeping records seventh-century India and in a chapter of a work by the Hindu astronomer Brahmagupta. Their earliest documented use in Europe is in 1545 in the Ars magna of Girolamo Cardano. By the early seventeenth century, Renaissance mathematicians were explicitly using negative numbers but also meeting with heavy opposition. René Descartes called negative roots "false roots", and Blaise Pascal was convinced that numbers "less than zero" couldn't exist. Gottfried Leibniz admitted that they could lead to some absurd conclusions, but defended then as useful aids in calculation. By the eighteenth century, negative numbers had become an indispensable part of algebra.
Related categories
• TYPES OF NUMBERS
• MATHEMATICS
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