Where Did Algebra Come From?

Where did algebra come from?  The origins of algebra came from ancient Babylonians over 4000 years ago.  Some people believe that the early work in algebra was done by priests to go along with religious rituals.  Other civilizations also had mathematicians that developed a form of algebra.  Let’s look at these and we’ll have a good idea where algebra came from when we are finished.

Since most historians agree that algebra came from the ancient Babylonians, we’ll start with them when considering where algebra came from.

Babylonia

Although many ancient people developed algebra, the Babylonians were more advanced that the others.   From 1800 - 1600 B.C. the Babylonians had an excellent numeration system that led to the development of algebra.  They were more advanced than the Egyptians and had the quadratic formula.  They could also deal with systems of equations.  They didn’t make use of a lot of symbols and only recognized positive rational numbers.  If a problem had no rational number solution, they just estimated.  In summary, they could deal with more than one equation and two unknowns.  

Egypt

Egyptian mathematics can be seen in the Rhind Mathematical Papyrus from 1650 B. C. which was discovered in 1858.  The Egyptians could solve an equation with one unknown, and their method was rhetorical, meaning it used no symbols.  Mathematical problems were solved verbally.  By 300 B. C. they could solve two second degree equations with two unknowns.  Their system of mathematics was not as sophisticated as the Babylonians because they did not have a good way to deal with fractions.

Other Forms of Algebra 

Hindu mathematics was strongly influenced by astronomy and astrology, so these disciplines make up part of where algebra came from.  There was a base ten positional system, which included zero as a number, in place before 600 A. D.  They introduced negative numbers because of debts, and dealt with irrational numbers.  They used symbols in algebra and knew that quadratic equations have two roots.  These roots included negative and irrational roots.  The Hindu way of solving equations in the form of ax ± by = c is the method used today. 

The Greeks did not recognize rational numbers but represented quantities as geometrical magnitudes.  They solved quadratic equations in geometric form.  This method retarded their development of algebra for several centuries.  They were highly skilled at deductive reasoning.  Around 250 A. D. the mathematician Diophantus wrote a text called Arithmetica, which had 130 algebra problems.  He is famous for his treatment of indeterminate equations which is most often two or more equations with several variables.  These types of equations are called "Diophantine equations."

Through the 14th century, the Arabs made many advances in the arts and sciences.  The Arabs preserved Greek learning through the middle ages.  Much of our knowledge today comes from their translations of Greek learning and from their own contributions.  They improved the Hindu numeration system and that system is used today.  They contributed to algebra by giving it the name “al-jabr.”  Their algebra was rhetorical and they solved quadratic equations, recognized two solutions, but rejected negative solutions.  They also solved indeterminate equations like the Hindus and Diophantus.    

Abstract Algebra 

Classical algebra is the process of solving equations.  The last 200 years or so, abstract algebra has been developed and is the study of rings, groups, and fields.  This took the study of algebra into vectors, matrices, and other mathematical objects.  Some important people in this new field were:

• Peacock - founder of axiomatic thinking
• DeMorgan - furthered Peacock’s work and operations were defined on abstract symbols
• Hamilton - showed complex numbers could be expressed as a formal algebra defining operations with ordered pairs of real numbers
• Gibbs - developed the algebra of vectors in three dimensional space
• Cayley - developed the algebra of matrices

The field of abstract algebra has grown rapidly in the 20th century and continues to do so.