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In the 18th BCE century people learned to solve linear and quadratic equations as well as indeterminate equations such as x2+y2=z2 whereby several unknowns re involved.
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In the 9th century, Al-Khwarizmi wrote first Arabic Algebra.
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At the end of 9th century, Abu Kamil had stated and proved the basic laws and identities of algebra.
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In 12th century, Omar Khayyam showed how to express roots of cubic equations by line segments obtained by intersecting conic sections.
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In early 13th century, Leonardo Fibonacci achieved a close approximation to the solution of the cubic equation.
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In Early 16th century, Scipione del Ferro, Niccolò Tartaglia, and Gerolamo Cardano solved the general cubic equation in terms of the constants appearing in the equation.
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In 18th century, Carl Friedrich Gauss, show that every polynomial equation has at least on root in the complex plane.
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In, early 19th century, Niels Abel and Evariste Galois proved that ”a formula for the roots of equations of degree five, or higher” doesn’t exists.
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In the 19th century, William Rowan Hamilton discovered the quaternions.
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In the 19th century, Hermann Grassmann began investing vectors.
