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Algebra, once only studied by advanced mathematicians and scientists, is now taught to every seventh and eighth grade child across the United States. While the basics of algebra may seem, well basic, it no doubt took a great deal of intelligence to form the foundations of algebra today. These basic building blocks of algebra are being used today by students, professors, physicists, and algebra tutors around the world.

Algebra can be sourced back to the Egyptians and Babylonians. The earliest equations were linear, quadratic, or indeterminate. The Babylonians were capable of solving quadratic equations using very similar formulas that are used today, while Egyptians solved the equations using geometric solutions. Today, zero can be used as placeholder to differentiate between numbers. For instance, zero is used in 7018 to show that it is a different number than 718. The Babylonians had a similar method, except with a base of 60. It is also interesting to note that the Chinese mathematicians had a multiplicative system with a base of 10. This system was most likely contrived from the Chinese counting board, which is a checker board consisting of rows and columns.

In 3rd century AD, Diophantus, aka “The Father of Algebra”, a Greek mathematician wrote Arithmetica, a math book that provided algebra help to other mathematicians of the time by providing many more solutions to algebraic problems, such as indeterminate equations. Brahmasphutasiddhanta, created by Brahmagupta, an Indian mathematician, was another piece of mathematical literature that supplied algebra help by completely describing the arithmetic solution to quadratic equations. By medieval times, mathematicians were able to multiply, divide, and solve for the square roots of polynomials. They also had knowledge of the binomial theorem. Additional algebra help and progress came in the 13th century when Italian mathematician Leonardo Fibonacci released an approximate solution on how to solve a cubic equation.

From that point in time, algebra began to make significant advances in Europe. By the 16th century, a few more Italian mathematicians, Scipione del Ferro, Niccolo Tartaglia, and Gerolamo Cardano, completely solved the general cubic equation. A significant progression during the 16th century was the creation of symbols representing the unknowns for algebraic operations. Consequently, René Descartes wrote La géometrie, which is written much like the texts algebra tutors or students would use today. His biggest contribution to the mathematical world was his discovery of analytic geometry. Analytic geometry is when the proofs from geometric problems can be reduced to algebraic solutions. Remember the important rule of signs? Descartes also came up with this rule, which determined the number of “true” and “false” roots of an equation.

By 1799, the German mathematician, Carl Friedrich Gauss, published the proof for the theory of equations. The solution proved that for every polynomial equation, there was at least one root in the complex plane. At this point, algebra had entered its modern phase. With algebraic foundations now in place, research topics became more abstract. These abstract ideas, such as complex numbers, are the topics most students seek algebra help for because of their theoretical nature.

Finally, more recently, the German mathematician Hermann Grassmann started researching vectors, which lead J.W. Gibbs to incorporate vector algebra and physics. The discoveries made in modern algebra since then have continued to grow. Algebra continues to be applied to various technical fields. The progression of algebra is fascinating and if our future findings are anything like the past, there is an uncountable amount of algebraic solutions waiting to be discovered.