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Hypatia is one of the few female mathematicians we have knowledge on. She contributed greatly to the development of Algebra dn Geometry.
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Viète and Harriot introduced a system for denoting the unknown as well as given numbers by capital letters, resulting in a new number concept, the ‘algebraic number concept’.
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Rene Descartes popularized the “Cartesian” Coordinate system and, along with Fermat, used his Cartesian coordinates to convert algebra problems into geometry, and geometry problems into algebra.
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Newton invented Calculus. Leibnez has also been creditied wtih inventing Calculus, but recent invetigiations reveal that Newton had the ideas first but published late.
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Christiaan Huygens was the first to write about probability and mathematical expectation which was motivated by gambling.
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Al-Khwarizmi invented Algebra. Al-Khwarizmi had used the term al-jabr to describe the process of adding equal quantities to both sides of a mathematical equation.