History of Algebra

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

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. Along with this he also

figured out the seasons. He discovered that every day was

about 1/300 of a year. Later the exact number of days in a

year, 365 1/4, was determined by Hipparchus. Ptolmey also

started studying the motions of the moon. He discovered

using an inscribed 360-gon that pie was 3 17/120 which is

really close to pie's true value. Also using this 360-gon

he discovered that a 60 degree chord with the length of

radical 3 is 1.73205.

Another important figure in the history of Algebra is

Pythagoras of Samos. He is often described as the first

pure mathematician. Pythagorus founded a philosophical and

religious school. It's many members had no personal

belongings and they were vegetarians. He believes that at

it's deepest level, reality is mathematical in nature. He

believes anything about nature relates to a mathematics

law. Pythagorus had a rather odd belief that each number

had it's own individual personality and the number 10 was

the best number because it was the sum of the first 4

numbers. Pythagorus was best known for his famous geometry

theorem. It stated that the sum of the squares of the

lengths of the two sides of a right triangle is equal to

the square of the length of the hypotenuse. He also

discovered that the angles of a triangle add up to 2 right

angles. Pythagorus is also credited with the discovery of

irrational numbers. Irrational numbers are numbers that

are non-terminating non-repeating decimals. Pythagorus is

a very important figure when it come to developing algebra

and mathematics.

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