# History of Algebra Brief Overview Essay

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Updated: Mar 22nd, 2022

Algebra is a mathematical concept that basically involves the applications of operations and relations, and the concepts that are as a result of the combination of the two. The history of algebra can be traced back to ancient Egypt and ancient Mesopotamia in Babylon. The early basic algebra involved finding solutions to linear equations which were of the form ax = b and quadratic equations which were of the form ax2 + bx = c. In most of the algebraic equations, there was more than one unknown (Snell 5). The procedures that were used to find the solutions to the algebraic equations use basically the same approach that is used today.

The mathematics of algebra was continued by Diophantus, who originated from Alexandria during 250 AD. Diophantus is always viewed as the father of algebra. His major contribution towards algebra was his compilation of books that were called Arithmetica (Snell 7). With his Diophantine equations, he contributed majorly to the number theory and the mathematics of algebra. The Diophantine equations were complex and were on a much higher level whose solutions were not easy to arrive at. The knowledge of the algebraic solutions then landed in the Arab World around the 9th century, it was then referred to as the” Science of restoration and balancing” (Rashed 45) which is an Arabic translation for al-jabru. Algebra is always thought to be of Arabian origin possibly due to the fact that the first algebraic work was found in the work of Mahommed ben Musa al-Khwarizimi (Rashed 48), who was famous during the 9th century (Rashed 50). His works basically involved the comparison and resolution of the various basic al-jabru equations that were later to be renamed algebra. It can be inferred that Mahommed ben Musa al-Khwarizimi exposed the basic theory of algebraic equations; he used both examples and proofs to confirm his assertions (Rashed 50).

Towards the end of the 9th century, an Egyptian mathematician called Abu Kamil affirmed and provided evidence on the basic algebraic laws and algebraic identities which were used to provide solutions to complicated problems such as solving for x, y, and z in quadratic equations such as x + y + z = 85, x2 +y2 +z2 = 0 and x z= y2 (Boyer 26). Ancient civilization denoted algebraic expressions using through the use of occasional abbreviations, contrary to the medieval Arabian mathematicians who used higher-order representations that involved the use of the x raised to given powers. This resulted in the development of polynomials and the operations that are related to manipulation of polynomials such as multiplication, division, and evaluating the square roots of the given polynomials (Boyer 30).

Omar Khayam, a Persian mathematician established how to evaluate cubic expressions through the use of the line segments which was as a result of the intersection of the conic sections. His limitation however was that he could not find formulae for finding the roots of the cubic expressions. During the 13th century, Leonardo Fibonacci, a mathematician from Italy, found an approximate solution to the cubic expression of the form x3 +2x2 +cx = d. It is however assumed that he used the Islamic mathematicians’ approach of Successive approximations to find the solution since he traveled across the Islamic lands (Boyer 32).

During the 16th century, a group of Italian mathematicians: Gerolamo Cardano, Nicolo Tartaglia, and Scipione Del Ferro found the exact solution to the cubic expression using the method of using constants. Developments on their methods were made to find solutions to higher-order expressions. However, during the 19th century, the Italian approach to the solution of higher-order expressions was disputed by Niels Abel from Norway and Evariste Galois from France. Important contributions to 16th-century algebra mathematics were the introduction of symbols to represent the elements being solved in terms of algebraic powers and operations (Boyer 35). These contributions were made by Rene Descartes, a French mathematician. He laid a framework for modern algebra through analytical geometry which expresses geometric problems in terms of algebraic problems, the theory of equations, and the number sign rule which are used to express numbers as either positive or negative, and as a result, the existence of negative roots. Recent developments are being made in modern algebra to aid in the solution of mathematical problems (Boyer 40).

## References

Boyer, Carl ,B. A History of Mathematics, Second Edition. New York: Wiley, 1991.

Rashed, Roshdi. Al Khwarizmi: The Beginnings of Algebra. Beirut: Saqi Books, 2009.

Snell, Melissa. About.com Medieval history. 2010. Web.

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