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The earliest mathematics appeared in Mesopotamia some 3,500 or more years BCE with a variety of specific number systems for trading with different things like grain and cereals, milk and dairy produce, or things made out of clay or wood.
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Early methods for solving problems come from the Rhind Mathematical Papyrus, written in Egypt about 1,550 years BCE. It is a 'problem text' of exercises for training scribes, who were the administrators.
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The Vedic people entered India about 1500 BCE. The name comes from their sacred rituals called the Vedas. These date from about the 15th to the 5th century BCE and were used for sacrificial rites which took place at an altar.
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The myth that the Greeks could not deal with irrational magnitudes has no basis in fact.
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The work of Diophantus was also translated and Baghdad became a centre for learning, attracting many scholars from the known world.
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Al-Khwarizmi was probably first among a number of scholars who showed how the geometrical constructions of Euclid Book II and the arithmetical heritage from Diophantus' Arithmetica , and the ideas from the Middle East and Indian scholars could be shown to be equivalent.
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Mediaeval Algebra in Western Europe was first learnt from the works of Al-Khwarizmi, Abu Kamil and Fibonacci.
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Nicolas Chuquet was described as an 'algoriste' and his manuscript on Le Triparty en la Science des Nombres (1484) was known only to a few of his contemporaries.
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Cardano earned his living as a doctor and by casting horoscopes; he wrote on probability and published other books but his importance for us rests on his Artis Magnae sive de Regulis Algebraicas Liber Unus(1545)
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By the middle of the 17th Century the representation of elementary algebraic problems and relations looked much as it is today. The major factors influencing change were the printing press that provided wider communication of ideas.
