Why Is Algebra Important In Life

There are many reasons why Algebra matters in life. One reason that comes to mind is from an early age, your understanding and success in algebra can help build math confidence, notable achievements in high school coursework and college readiness, and more importantly help predict one’s salary earnings on so many levels. As one would know that nearly all sports statistics are produced using algebraic equations. Average points per game are used to determine the Most Valuable Player. Winning percentages are used to determine top rankings. These are calculated with concepts learned in Algebra. Formulas are a part of our lives, whether we drive a car and need to calculate the distance, or need to work out our food volume intake for dieting; algebraic formulas are used every day without us even realizing it.

The history of Algebra began in ancient Egypt and Babylon, where people learned to solve linear and quadratic equations which the equations had many unknown variables, (Khan, 2015). In exploring the origin of Algebra, we first look at the word which is a Latin modified word from the Arabic word al-jabr. This came from the title of the book, Hidab al-jabr wal-muqubala, written in Baghdad

about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi, (Khan, 2015). In Khan’s YouTube video, he points out that the words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to represent two basic operations in solving equations. Jabr moved subtracted terms to the other side of the equation. For example Jabr used where x - 5 = 13 becomes x = 19. On the left-side of the equation, x is subtracted by 5, is “restored” or “completed” back to x in the second equation. Whereas Muqubalah used canceled like terms on opposite sides of the equation. Muqabalah offered x + y = y + 4 to x = 4 by “cancelling” or “balancing” the two sides of the equation (Khan, 2015). In Kvasz’s work (Kvasz, 2006), the author documents that the Alexandrian mathematicians Hero of Alexandria and Diophantus continued the traditions of Egypt and Babylon, but Diophantus’s book Arithmetica presented a much higher level of mathematics and offered several solutions to difficult indeterminate equations. Khan explained that this ancient knowledge of solutions of equations in turn found a home early in the Islamic world. According to the work (Khan, 2015), Diophantus is sometimes called “the father of Algebra” but Khan believes that this title more appropriately belongs to al-Khwarizmi. While, the research shows that ancient civilizations wrote out algebraic expressions using abbreviations, Islamic mathematicians were able to talk about high powers of the unknown x and worked out the basic algebra of polynomials, (Kvasz, 2006). Kvasz also showed that this included the ability to multiply, divide, and find square roots of polynomials as well as provide the knowledge of the binomial theorem. Kvasz’s work also added that the Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations by line segments obtained by intersecting conic sections, but he could not find a formula for the roots (Kvasz, 2006). The author Boyer offered that the Algebra historical writings which title was translated into Latin by Robert of Chester in the mid-12th century to mean “science of restoration (or reunion) and opposition” or “science of transposition and cancellation” hence the book written in 830 B.C. title “The Book of Restoration and Balancing” or “The Book of Completion and Cancellation”. Eventually the muqabalah was omitted and this type of math became known as algebra in many languages (Boyer, 228).
In reviewing similarities and differences of the earliest forms of Algebra among the people in different parts of the world, many of the mathematicians work evolved over centuries.
According to Kvasz, the great Italian mathematician Leonardo Fibonacci accomplished a similar work for the solution of the cubic equation x3 + 2x2 + cx = d in the early 13 century, (Kvasz, 2006). Kvasz suggested that because Fibonacci had traveled in Islamic lands, he probably used an Arabic method of successive approximations. Kvasz further offered that the Italian mathematicians Scipione del Ferro, Niccolo Tartaglia, and Gerolamo Cardano solved the general cubic equation in terms of the constants appearing in the equation early in the 16th century. As a branch of mathematics, algebra emerged at the end of 16th century in Europe, with the work of François Viète, (Kvasz, 2006). Kvasz also advised that one of Cardano’s follower, Ludovico Ferrari, found an exact solution to equations of the fourth degree, and as a result, mathematicians for the next several centuries tried to find a formula for the roots of equations of degree five, or higher, (Kvasz, 2006). However, Kvasz’s work showed Norwegian mathematician, Niels Abel and the French mathematician Evariste Galois verified that no such formula existed that in early 19th century, (Kvasz, 2006). Kvasz believes in the 16th century that one of the most important developments in algebra was the introduction of symbols for unknown variables and for algebraic powers and operations, (Kvasz, 2006). As a result of this development, Book III of La geometrie was written by the French philosopher and mathematician Rene Descartes. Nevertheless, Kvasz suggest that Descartes’ most significant contribution to mathematics was his discovery of analytic geometry, which reduces the solution of geometric problems to the solution of algebraic ones (Kvasz, 2006).

In comparing and contrasting the system of algebra that was introduced then and what is use today is not very different. According to Khan, Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arabic algebras, a systematic theorem for the basic theory of equations, with both examples and proofs. However, by the end of the 9th century, the Egyptian mathematician Abu Kamil proved the basic laws and identities of algebra such as finding x, y, and z in the equations x + y + z = 10, x2 + y2 = z2, and xz = y2. Subsequently, Kvasz points out that while Al-jabr wa'l-muqabala began with a discussion of the algebra of first and second degree equations and moved on in its final two parts to the business of practical applications which many scholars conceived his work as an elementary textbook of practical mathematics. Boyer suggested that Al-Khwarizmi's work is on a more elementary and rhetorical level than that of Diophantus. Al-jabr comes closer to elementary algebra of today than the works of either Diophantus or Brahmagupta, because the book is not concerned with difficult problems in indeterminate analysis but with a straight forward and elementary exposition of the solution of equations, especially that of second degree (Boyer, 228). The ancient Babylonians solved arbitrary quadratic equations as well as indeterminate equations by essentially the same procedures that are taught today. Lastly, it was until the 19th century that algebra consisted essentially of the theory of equations. Today, for example, the fundamental theorems of algebra belong to the theory of equations and it is said not to be considered belonging to Algebra.

In conclusion, this essay reviewed the history of algebra originating approximately 1500 - 2000 years BC to include the 16th century’s French mathematician who revolutionized algebra.

The essay further provided similarities and differences of the earliest forms of Algebra among the people in different parts of the world and how it evolved over centuries. As you can see al-Khwarizmi was a notable mathematician along with many other discoveries that including new ways of solving quadratic equations with algebra while keeping the problems simple and easy to manipulate. Khan suggested that al-Khwarizmi’s ways of working with quadratic equations were so popular that his book Al-Jabr was used as the principle mathematics book at European universities until the 16th

century.