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writes the Al-Mu'adalat which deals with eight types of cubic equations with positive solutions and five types of cubic equations which may not have positive solutions. He uses what would later be known as the "Ruffini-Horner method" to numerically approximate the root of a cubic equation. He also develops the concepts of the maxima and minima of curves in order to solve cubic equations which may not have positive solutions.
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\ He replaces geometrical operations of algebra with modern arithmetical operations, and defines the monomials x, x2, x3, .. and 1/x, 1/x2, 1/x3, .. and gives rules for the products of any two of these.He also discovers the first numerical solution to equations of the form ax2n + bxn = c.Al-Karaji is also regarded as the first person to free algebra from geometry operations and replace them with the type of arithmetic operations which are at the core of algebra today.
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gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.
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Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation, gives integral solutions of simultaneous indeterminate linear equations, and describes a differential equation.
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writes the Brahmasphuta-siddhanta, where zero is clearly explained, and where the modern place-value Indian numeral system is fully developed. It also gives rules for manipulating both negative and positive numbers, methods for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta theorem
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begins to write Treatise on Demonstration of Problems of Algebra and classifies cubic equations.
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a Kerala school mathematician, writes the “Aryabhatiya Bhasya”, which contains work on infinite-series expansions, problems of algebra, and spherical geometry
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in a posthumous publication is the first to use symbols < and > to indicate "less than" and "greater than", respectively.
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René Descartes introduces the use of the letters z, y, and x for unknown quantities.
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Seki laid foundations for the subsequent development of Japanese mathematics known as wasan;[2] and he has been described as "Japan's Newton"
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solves systems of simultaneous linear equations using matrices and determinants.
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in his treatise Introduction to the analysis of algebraic curves, states Cramer's rule and studies algebraic curves, matrices and determinants.
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proves that the general quintic equation is insoluble by radicals.
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provides a modern definition of groups.
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solves the general quintic equation by means of elliptic and modular functions.
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Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics.274 Einstein's work is also known for its influence on the philosophy of science.Einstein is best known by the general public for his mass–energy equivalence formula E = mc2 He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photo.electric effect",
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He was one of mathematicians who supported the dawn of Japanese mathematics world. At the same time as Emmy Nater and others, he played a major role in the abstraction of algebra. A study on separability was later applied to economics by Morijima Michio.
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extends Hilbert's theorem on the finite basis problem to representations of a finite group over any field.
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develops the theory of hyperbolic groups, revolutionizing both infinite group theory and global differential geometry,
