History of Algebra

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Algebra is defined by Webster's New Collegiate Dictionary

as a generalization of arithmetic in which letters

representing numbers are combined according to the rules of

arithmetic. This is not a good definition of algebra. It

would take a thick book to really explain it. In fact, to

this day it is still being added to. There are always new

things to be discovered about it. It has been added to by

many different people over the centuries. Algebra has a

long interesting history.

The first work describing algebra was called

Arithmetica, a treatise by Diophantus of Alexandria. It

was a collection of 130 problem and numerical solutions.

Only 6 of the 13 books have been found, the others were

believed to have been destroyed soon after their creation.

Diophantus was known as the father of algebra. The way he

solved problems algebraically was know as Diophantine

analysis. He lived from about 200 AD to about 284 AD He

was the first to use an algebraic symbolism, in which

symbols and letters represented the unknown.

He refused to

believe that there was any such thing as a negative number.

He reasoned this by saying it is impossible to have

negative four objects. He did much work with quadratic

equations and even equations with variables to the sixth

power. Diophantus also seemed to know that any whole

number could be written as the sum of four squares. Pierre

de Fermat did some work with this but it was not proved

until later when Joseph Louis Lagrange worked with it.

Despite all of Diophantus's work algebra had a long way to

go before general problems could be written down and


There were many other influential people in the

history of mathematics. One such man was named Theon of

Alexandria. He wrote...