The History of Abstract Algebra
The language of geometry was transmuted into algebra, which led to the formation of Geometric Algebra.
The beauty of mathematics is well established throughout the world. Centuries passed but the growth and achievement are still a continuous process which flows like a river through time. Eventually mathematics became a language surpassing every other science subject. Like the present day, the history is also breathtaking. Each theorem portrayed like this is it, but mathematicians always craved for something more. Above all, today’s discovery became tomorrow’s history.
The Babylonians: Root concept
Ancient Babylon and its civilization were clever and observant enough to create a concept like mathematics. Even they felt the need for their children to learn the basic concepts of it. Root concept of a Polynomial equation or Quadratic equation was well known among them. Although one important drawback was that the concept behind using a root or solving an equation using root was undefined and unclear.
The Greeks: The Algebra
From many sources it has been proven that Greeks were inclined towards mathematics in every possible way. Legends were born with the capability of creating magic using numbers and structures. Geometry was the root behind the formation of algebra in Greek. The language of geometry was transmuted into algebra, which led to the formation of Geometric Algebra. These new concepts created a path to justify laws of algebra and to find the solutions of Quadratic equations. Proper formation of algebraic equations was done within 300 B.C.
Algorithms: Algebra in India
The word Algorithm was derived from the name of a great mathematician, Al-Khwarizmi, who presented a new era of algebra around the fifteenth century AD. Using Polynomial equations, he was able to classify the quadratic equations into five different parts. But till now none of the propositions were given by taking negative or zero value in account. Everyone admitted, the solutions must be positive.
Cardano: The order of three
Before Cardano nobody thought about solving the quadratic equations as cubic roots. The order till 1545 was two for the polynomials but he was brave enough to introduce the order of three, which led to cubic roots and three solutions of an equation.
Complexity: Numbers are Complex too
The conception of cubic roots was strong enough to give birth to the complex numbers. After a long hustle of acceptance, the mathematicians were able to figure out the concept behind this new addition of the number system. Not only in the system denoting numbers but also in their brains they had to make a large enough space to fit that.
This is an endless path which leads us towards infinity, with a lot of boundary values and exceptions.