Algebra has challenged and confused many human beings throughout the course of history, especially in the development of mathematics. However, this is no recent feat; algebra originated over 4,000 years ago! In order to best understand what algebra is at its core and how it came to be, we must sort through its slow and intricate history.
First of all, what IS algebra? Algebra is a branch of mathematics that converges arithmetic and abstract numbers rather than actual numbers. Typically, the abstract symbols are letters and there are various instances where you solve the equation to extract what the abstract symbol(s) represent (if an answer to the equation is already given). Based upon certain formulas and their functions, however, you plug in numbers in place of the abstract symbols to ascertain particular answers.
Much of algebra’s history occurs in the Classical civilizations that populated the Mediterranean and Asia. Research has shown that the first accounts of algebra dates all the way back to the time of ancient Egypt and Babylon. There were rhind papyrus scrolls utilized by the Egyptians dating back as early as 1650 BC! This is a direct indication that the Egyptians, for whatever reason, were using equations to calculate the growth and expansion of their empire.
What’s interesting is that the scrolls showed their ability to use TWO equations for two unknown quantities (i.e. the quadratic formula). This practice has been dated back to circa 300 BC, so the Egyptians were developing their own personal usage of algebra for quite a healthy amount of time when developing their civilization.
The Babylonians were well known for chronicling their lives on grand clay tablets, which is EXACTLY where the first equation was found! What’s incredibly compelling is that the Babylonians based their arithmetic on increments of 60, whereas our modern day decimal system is based on increments of 10. They also never really used zero and heavily utilized tables to construct their equations.
Since algebra has been tracked back to the core of early Mesopotamia, it can be accredited to the evolution of science, technology, and the evolution of human civilizations as a whole.
Although the first civilizations such as Egypt, Sumeria, & others began to utilize these algebraic principles to advance their lifestyles, the Greeks really formalized many algorithms we use today.
The Greeks are accredited with one of the most monumental discoveries in algebra. In circa 430 BC, while trying to find out the ratio between the side and hypotenuse of a right angle triangle, the Pythagoreans determined that not all lengths are proportional to one another. This is especially confounding, thus came the creation of the Pythagorean Theorem (a 2 + b 2 = c 2 ).
Following this theoretic discovery came an array of other mathematical contributions from the Greeks. For instance, Euclid’s Elements (300 BC) and the creation of proportions by Eudoxus of Cnidus (400-350 BC).
However, one of the first “Fathers of Algebra” didn’t come around until 250 AD). An Alexandrian mathematician named Diophantus wrote the book Arithmetica. Even though much of that book was lost, Diophantus made great efforts in solving algebraic equations as well as creating solutions we use today.
Additionally, Diophantus introduced one of the earliest systems for polynomial equations. A polynomial equation is “composed of a sum of terms, in which each term is the product of some constant and a nonnegative power of the variable or variables” (Britannica, 2021). Because polynomial equations are so general, it can be applied to many different mathematical relationships; Diophantus was just the first to organize it.
Civilizations in Asia such as India and China progressed moderately in their own exploratory measures with mathematics! Indian mathematicians such as Brahmugupta and Bhaskara II constructed very meticulous (and nonsymbolic) equations for solving equations that had more than one variable or in the first and second degree.
Still, probably the most profound contribution made by Indian mathematicians was the establishment of the decimal system! That’s right, they were right on the money when creating this numeral system to account for the infinite amount of numbers that exist in our universe. Not only that, but the Indians were much more expedient and efficient when working with positive AND negative numbers; they even accounted zero and correct rules to follow!
These principles were very existent in India around the 9th century. On the other hand, there are accounts to point to the notion that these were communicated to surrounding populations such as China and the Islamic domains! It’s crazy to think that these very important systems weren’t even practiced by the Eurpoeans until several hundred years past their initial birth!
The 13th and 14th centuries start to promise Europeans endeavors into the world of math, considering the contributions the previous civilizations were perceived as academic affairs. Nonetheless, Europeans artists and theorists go on to further excavate the usefulness of algebra in their cultural creations.
Without the Classical civilizations & their applicative approach to mathematics, much of what we incorporate into our daily functions would probably not be as evolved. The next time you pick up a fancy graphing calculator or handwrite out your formulas, reflect on those who made the most of the resources they were given.
Britannica, The Editors of Encyclopaedia. “Fundamental theorem of algebra”. Encyclopedia Britannica, 16 Jan. 2017, https://www.britannica.com/science/fundamental-theorem-of-algebra. Accessed 14 October 2021. Corry, Leo. “algebra”. Encyclopedia Britannica, 30 May. 2021, https://www.britannica.com/science/algebra. Accessed 20 October 2021.