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Dating back to the Babylonians period, soon after the discovery of the clay tablet, they began using the artifact for mathematical interpretations. The people who are responsible for this discovery are himself and Neugebauer.
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Pythagoras, a Greek mathematician started solving equations visually and geometrically to make solving equations more efficient in the future of mathematics.
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In this time period, the Chinese began to publish readings related to algebra once they understood the concept.
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Diophantus is responsible for showing the concept of solving algebraic problems and how to find rational solutions to equations with variables/unknown.
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He took part in founding the Hindu numerals 1-9. He also helped create algebraic methods like balancing two sides of an equation so that they were equal.
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Arabic scholars are responsible for the word “Algebra” which really means the reunion of broken parts based on Arabic origins. Once they came up with this, the word was used everywhere.
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Girolamo wrote and published a book that inside of it contained solutions to cubic and quadratic equations, revealing more about how to evaluate equations that had to do with area, volume, etc.
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Francois created the addition and subtraction signs and he also started substituting letters for numbers.
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Niels is responsible for proving that there’s no true and general formula that works for all quintic equations. Quintic equations are equations for a polygon that is not a basic shape like a triangle, square, etc.
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Amalie made many discoveries and findings related to noncommutative algebras meaning she found out more ways to be able to move around terms in an equation and keep the sum the same.