http://io9.com/why-do-we-use-the-letter-x-to-represent-the-unknown-1588933259
now i aint muslim, but truth is truth, facts are facts. give props/credit where its due.
http://www.pbs.org/empires/islam/innoalgebra.html
Medieval Muslims made invaluable contributions to the study of mathematics, and their key role is clear from the many terms derived from Arabic. Perhaps the most famous mathematician was Muhammad ibn Musa al-Khwarizmi (ca. 800-ca. 847), author of several treatises of earth-shattering importance. His book On the Calculation with Hindu Numerals, written about 825, was principally responsible for the diffusion of the Indian system of numeration (Arabic numerals) in the Islamic lands and the West.
Traditional systems had used different letters of the alphabet to represent numbers or cumbersome Roman numerals, and the new system was far superior, for it allowed people to multiply and divide easily and check their work. The merchant Leonardo Fibonacci of Pisa, who had learned about Arabic numerals in Tunis, wrote a treatise rejecting the abacus in favor of the Arab method of reckoning, and as a result, the system of Hindu-Arabic numeration caught on quickly in Central Italy. By the fourteenth century, Italian merchants and bankers had abandoned the abacus and were doing their calculations using pen and paper, in much the same way we do today.
In addition to his treatise on numerals, al-Khwarizmi also wrote a revolutionary book on resolving quadratic equations. These were given either as geometric demonstrations or as numerical proofs in an entirely new mode of expression. The book was soon translated into Latin, and the word in its title, al-jabr, or transposition, gave the entire process its name in European languages, algebra, understood today as the generalization of arithmetic in which symbols, usually letters of the alphabet such as A, B, and C, represent numbers. Al-Khwarizmi had used the Arabic word for "thing" (shay) to refer to the quantity sought, the unknown. When al-Khwarizmi's work was translated in Spain, the Arabic word shay was transcribed as xay, since the letter x was pronounced as sh in Spain. In time this word was abbreviated as x, the universal algebraic symbol for the unknown.
Robert of Chester's translation of al-Khwarzmi's treatise on algebra opens with the words dixit Algorithmi, "Algorithmi says." In time, the mathematician's epithet of his Central Asian origin, al-Khwarizmi, came in the West to denote first the new process of reckoning with Hindu-Arabic numerals,algorithmus, and then the entire step-by-step process of solving mathematical problems, algorithm
--
might as well take it all the way back.
http://www.algebra.com/algebra/about/history/
The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitraryquadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.
The Alexandrian mathematicians Hero of Alexandria and Diophantus continued the traditions of Egypt and Babylon, but Diophantus's book Arithmetica is on a much higher level and gives many surprising solutions to difficult indeterminate equations. This ancient knowledge of solutions of equations in turn found a home early in the Islamic world, where it was known as the "science of restoration and balancing." (The Arabic word for restoration, al-jabru, is the root of the word algebra.) In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arabic algebras, a systematic exposé of the basic theory of equations, with both examples and proofs. By the end of the 9th century, the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of algebra and solved such complicated problems as finding x, y, and zsuch that x + y + z = 10, x2 + y2 = z2, and xz = y2.
Ancient civilizations wrote out algebraic expressions using only occasional abbreviations, but by medieval times Islamic mathematicians were able to talk about arbitrarily high powers of the unknown x, and work out the basic algebra of polynomials (without yet using modern symbolism). This included the ability to multiply, divide, and find square roots of polynomials as well as a knowledge of the binomial theorem. The Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations by line segments obtained by intersectingconic sections, but he could not find a formula for the roots. A Latin translation of Al-Khwarizmi's Algebra appeared in the 12th century. In the early 13th century, the great Italian mathematician Leonardo Fibonacci achieved a close approximation to the solution of the cubic equationx3 + 2x2 + cx = d. Because Fibonacci had traveled in Islamic lands, he probably used an Arabic method of successive approximations.
Early in the 16th century, the Italian mathematicians Scipione del Ferro, Niccolò Tartaglia, and Gerolamo Cardano solved the general cubic equation in terms of the constants appearing in the equation. Cardano's pupil, Ludovico Ferrari, soon found an exact solution to equations of the fourth degree (see quartic equation), and as a result, mathematicians for the next several centuries tried to find a formula for the roots of equations of degree five, or higher. Early in the 19th century, however, the Norwegian mathematician Niels Abel and the French mathematician Evariste Galois proved that no such formula exists.
An important development in algebra in the 16th century was the introduction of symbols for the unknown and for algebraic powers and operations. As a result of this development, Book III of La géometrie (1637), written by the French philosopher and mathematician René Descartes, looks much like a modern algebra text. Descartes's most significant contribution to mathematics, however, was his discovery of analytic geometry, which reduces the solution of geometric problems to the solution of algebraic ones. His geometry text also contained the essentials of a course on the theory of equations, including his so-called rule of signs for counting the number of what Descartes called the "true" (positive) and "false" (negative) roots of an equation. Work continued through the 18th century on the theory of equations, but not until 1799 was the proof published, by the German mathematician Carl Friedrich Gauss, showing that every polynomial equation has at least one root in the complex plane (see Number: Complex Numbers).
By the time of Gauss, algebra had entered its modern phase. Attention shifted from solving polynomial equations to studying the structure of abstract mathematical systems whose axioms were based on the behavior of mathematical objects, such as complex numbers, that mathematicians encountered when studying polynomial equations. Two examples of such systems are algebraic groups (see Group) and quaternions, which share some of the properties of number systems but also depart from them in important ways. Groups began as systems of permutations and combinations of roots of polynomials, but they became one of the chief unifying concepts of 19th-century mathematics. Important contributions to their study were made by the French mathematicians Galois and Augustin Cauchy, the British mathematician Arthur Cayley, and the Norwegian mathematicians Niels Abel and Sophus Lie. Quaternions were discovered by British mathematician and astronomer William Rowan Hamilton, who extended the arithmetic of complex numbers to quaternions while complex numbers are of the form a + bi, quaternions are of the form a + bi + cj + dk.
Immediately after Hamilton's discovery, the German mathematician Hermann Grassmann began investigating vectors. Despite its abstract character, American physicist J. W. Gibbs recognized in vector algebra a system of great utility for physicists, just as Hamilton had recognized the usefulness of quaternions. The widespread influence of this abstract approach led George Boole to write The Laws of Thought (1854), an algebraic treatment of basic logic. Since that time, modern algebra—also called abstract algebra—has continued to develop. Important new results have been discovered, and the subject has found applications in all branches of mathematics and in many of the sciences as well
now i aint muslim, but truth is truth, facts are facts. give props/credit where its due.
http://www.pbs.org/empires/islam/innoalgebra.html
Medieval Muslims made invaluable contributions to the study of mathematics, and their key role is clear from the many terms derived from Arabic. Perhaps the most famous mathematician was Muhammad ibn Musa al-Khwarizmi (ca. 800-ca. 847), author of several treatises of earth-shattering importance. His book On the Calculation with Hindu Numerals, written about 825, was principally responsible for the diffusion of the Indian system of numeration (Arabic numerals) in the Islamic lands and the West.
Traditional systems had used different letters of the alphabet to represent numbers or cumbersome Roman numerals, and the new system was far superior, for it allowed people to multiply and divide easily and check their work. The merchant Leonardo Fibonacci of Pisa, who had learned about Arabic numerals in Tunis, wrote a treatise rejecting the abacus in favor of the Arab method of reckoning, and as a result, the system of Hindu-Arabic numeration caught on quickly in Central Italy. By the fourteenth century, Italian merchants and bankers had abandoned the abacus and were doing their calculations using pen and paper, in much the same way we do today.
In addition to his treatise on numerals, al-Khwarizmi also wrote a revolutionary book on resolving quadratic equations. These were given either as geometric demonstrations or as numerical proofs in an entirely new mode of expression. The book was soon translated into Latin, and the word in its title, al-jabr, or transposition, gave the entire process its name in European languages, algebra, understood today as the generalization of arithmetic in which symbols, usually letters of the alphabet such as A, B, and C, represent numbers. Al-Khwarizmi had used the Arabic word for "thing" (shay) to refer to the quantity sought, the unknown. When al-Khwarizmi's work was translated in Spain, the Arabic word shay was transcribed as xay, since the letter x was pronounced as sh in Spain. In time this word was abbreviated as x, the universal algebraic symbol for the unknown.
Robert of Chester's translation of al-Khwarzmi's treatise on algebra opens with the words dixit Algorithmi, "Algorithmi says." In time, the mathematician's epithet of his Central Asian origin, al-Khwarizmi, came in the West to denote first the new process of reckoning with Hindu-Arabic numerals,algorithmus, and then the entire step-by-step process of solving mathematical problems, algorithm
--
might as well take it all the way back.
http://www.algebra.com/algebra/about/history/
The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitraryquadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations.
The Alexandrian mathematicians Hero of Alexandria and Diophantus continued the traditions of Egypt and Babylon, but Diophantus's book Arithmetica is on a much higher level and gives many surprising solutions to difficult indeterminate equations. This ancient knowledge of solutions of equations in turn found a home early in the Islamic world, where it was known as the "science of restoration and balancing." (The Arabic word for restoration, al-jabru, is the root of the word algebra.) In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arabic algebras, a systematic exposé of the basic theory of equations, with both examples and proofs. By the end of the 9th century, the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of algebra and solved such complicated problems as finding x, y, and zsuch that x + y + z = 10, x2 + y2 = z2, and xz = y2.
Ancient civilizations wrote out algebraic expressions using only occasional abbreviations, but by medieval times Islamic mathematicians were able to talk about arbitrarily high powers of the unknown x, and work out the basic algebra of polynomials (without yet using modern symbolism). This included the ability to multiply, divide, and find square roots of polynomials as well as a knowledge of the binomial theorem. The Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations by line segments obtained by intersectingconic sections, but he could not find a formula for the roots. A Latin translation of Al-Khwarizmi's Algebra appeared in the 12th century. In the early 13th century, the great Italian mathematician Leonardo Fibonacci achieved a close approximation to the solution of the cubic equationx3 + 2x2 + cx = d. Because Fibonacci had traveled in Islamic lands, he probably used an Arabic method of successive approximations.
Early in the 16th century, the Italian mathematicians Scipione del Ferro, Niccolò Tartaglia, and Gerolamo Cardano solved the general cubic equation in terms of the constants appearing in the equation. Cardano's pupil, Ludovico Ferrari, soon found an exact solution to equations of the fourth degree (see quartic equation), and as a result, mathematicians for the next several centuries tried to find a formula for the roots of equations of degree five, or higher. Early in the 19th century, however, the Norwegian mathematician Niels Abel and the French mathematician Evariste Galois proved that no such formula exists.
An important development in algebra in the 16th century was the introduction of symbols for the unknown and for algebraic powers and operations. As a result of this development, Book III of La géometrie (1637), written by the French philosopher and mathematician René Descartes, looks much like a modern algebra text. Descartes's most significant contribution to mathematics, however, was his discovery of analytic geometry, which reduces the solution of geometric problems to the solution of algebraic ones. His geometry text also contained the essentials of a course on the theory of equations, including his so-called rule of signs for counting the number of what Descartes called the "true" (positive) and "false" (negative) roots of an equation. Work continued through the 18th century on the theory of equations, but not until 1799 was the proof published, by the German mathematician Carl Friedrich Gauss, showing that every polynomial equation has at least one root in the complex plane (see Number: Complex Numbers).
By the time of Gauss, algebra had entered its modern phase. Attention shifted from solving polynomial equations to studying the structure of abstract mathematical systems whose axioms were based on the behavior of mathematical objects, such as complex numbers, that mathematicians encountered when studying polynomial equations. Two examples of such systems are algebraic groups (see Group) and quaternions, which share some of the properties of number systems but also depart from them in important ways. Groups began as systems of permutations and combinations of roots of polynomials, but they became one of the chief unifying concepts of 19th-century mathematics. Important contributions to their study were made by the French mathematicians Galois and Augustin Cauchy, the British mathematician Arthur Cayley, and the Norwegian mathematicians Niels Abel and Sophus Lie. Quaternions were discovered by British mathematician and astronomer William Rowan Hamilton, who extended the arithmetic of complex numbers to quaternions while complex numbers are of the form a + bi, quaternions are of the form a + bi + cj + dk.
Immediately after Hamilton's discovery, the German mathematician Hermann Grassmann began investigating vectors. Despite its abstract character, American physicist J. W. Gibbs recognized in vector algebra a system of great utility for physicists, just as Hamilton had recognized the usefulness of quaternions. The widespread influence of this abstract approach led George Boole to write The Laws of Thought (1854), an algebraic treatment of basic logic. Since that time, modern algebra—also called abstract algebra—has continued to develop. Important new results have been discovered, and the subject has found applications in all branches of mathematics and in many of the sciences as well
