History of Classical Algebra
History of Classical Algebra
Around grades 8 through 10, most students are learning the basics of Algebra 1 and 2. Where did this subject evolve from and who were the mathematicians who patented it? Was it just one civilization that came up with the concept or many that built on each other? These are all great questions to look at when looking at the evolution of Algebra. The ideas of Algebra were very slow developing, until a few great philosophers made some big discoveries. In order to go back to the first signs of Algebra, we have to go back over 3700 years, to the Babylonian civilization. Babylonians were particularly proficient algebraists and in the ancient civilizations they could solve quadratic problems (Kleiner, 2007). Records show that in 1600 B.C equations and symbols were not used in these problems, rather they were written out and solved verbally (Corry, 2005). Corry’s (2005) study found that a typical example of a problem made by the Babylonians was,
Method of calculating a quantity, multiplied by 1 1/2 added 4 it has come to 10.
What is the quantity that says it?
Then you calculate the difference of this 10 to this 4.
Then 6 results. Then you divide 1 by 1 1/2.
Then 2/3 result. Then you calculate 2/3 of this 6.
Then 4 results. Behold, it is 4, the quantity that said it.
What has been found by you is correct.
Most examples or evidence we have of these types of problems were used in their own real world, concrete problems such as, the weight of a stone or how to break up a piece of land among 3 pairs of brothers (Corry, 2005). Although, the Babylonians could find a solution to a general quadratic or linear equation, the solution to a simple cubic equation or even square root equation was not in their realm (Jordman, 2009). In fact, the computations of many problems included some unknown number because the number zero, negative numbers and irrational numbers were not a part of their number system (Kleiner, 2007).
Around grades 8 through 10, most students are learning the basics of Algebra 1 and 2. Where did this subject evolve from and who were the mathematicians who patented it? Was it just one civilization that came up with the concept or many that built on each other? These are all great questions to look at when looking at the evolution of Algebra. The ideas of Algebra were very slow developing, until a few great philosophers made some big discoveries. In order to go back to the first signs of Algebra, we have to go back over 3700 years, to the Babylonian civilization. Babylonians were particularly proficient algebraists and in the ancient civilizations they could solve quadratic problems (Kleiner, 2007). Records show that in 1600 B.C equations and symbols were not used in these problems, rather they were written out and solved verbally (Corry, 2005). Corry’s (2005) study found that a typical example of a problem made by the Babylonians was,
Method of calculating a quantity, multiplied by 1 1/2 added 4 it has come to 10.
What is the quantity that says it?
Then you calculate the difference of this 10 to this 4.
Then 6 results. Then you divide 1 by 1 1/2.
Then 2/3 result. Then you calculate 2/3 of this 6.
Then 4 results. Behold, it is 4, the quantity that said it.
What has been found by you is correct.
Most examples or evidence we have of these types of problems were used in their own real world, concrete problems such as, the weight of a stone or how to break up a piece of land among 3 pairs of brothers (Corry, 2005). Although, the Babylonians could find a solution to a general quadratic or linear equation, the solution to a simple cubic equation or even square root equation was not in their realm (Jordman, 2009). In fact, the computations of many problems included some unknown number because the number zero, negative numbers and irrational numbers were not a part of their number system (Kleiner, 2007).
References: Kleiner, I. (2007). A history of abstract algebra. (pp. 1-15). Boston: Birkhauser Boston. Corry, L. (2005). History of Algebra. In Encyclopedia Britannica. Chicago, IL: Encyclopedia Britannica. Jordman, F. (2009). A History of Algebra. The Brussels Journal. http://www.brusselsjournal.com/node/4131