History of Algebra
History of AlgebraAlgebra 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
solved.
There were many other influential people in the
history of mathematics. One such man was named Theon of
Alexandria. He wrote commentaries on many other works of
mathematics in his time. In many cases he added extra
steps into others proofs. He never really did anything
original but he added much to other mathematicians works.
His daughter Hypatia grew up around mathematics. As she
grew she picked up on it and eventually she even helped her
father on several works. She became the head of a
Plotinost school in Alexandria. There she lectured on
subjects such as mathematics and philosophy. Platonusts
believed that there was an ultimate reality in which humans
could never fully understand. Hypatia only lived to be
about forty five because she was brutally murdered by
Christians who felt threatened by her scholarship. One of
the works that she helped her father critique was that
called Almagest by Ptolemy. This was a thirteen page
treatise. This is the earliest of all of Ptolmey’s works.
It describes the mathematical theory of the motions of the
Sun, Moon, and the planets. Ptolmey was an interesting
man. He believed in the geocentric theory, that is the Sun
and other planets revolve around the Earth. It was
proposed by Aristotle. Another belief at the time was the
heliocentric theory in which the Earth and all of the other
planets revolve around the Sun....
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