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Babylonian clay tablets show problems that involved solving for a missing or unknown value.
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This ancient Egyption texts show the earliest problem solving of linear equations.
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Al Khwarizmi wrote on of the first Arab works on the basic theory of algebra and solving equations.
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Greek mathematicians Euclid and Pythagoras made vital discoveries that regarding proportional relationships.
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Diophantus of Alexandria introduced systematic solution strategies,
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Al-Samawal defines algebra as "[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.”
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François Viète introduced algebraic notation beyond the use of letters. He is considered the "Father of Algebraic Notation."
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In René Descartes' Book III of La géometrie, symbols were used to represent unknown quantities. (Variables) At this point, equations look most similar to what we see in modern algebra.