Oh! That thing called Algebra.

Addition,Subtraction , Multiplication and Division, all these seem like so normal in life. Understanding Multiplication using Addition and Division using Subtraction. Further finding out that Division can be done using Multiplication! This is so awesome! Indeed. But a simple thought that how is all this even possible sends one to the wonderland called the Algebra. The ease of addition and multiplication is due to Algebra. Algebra is the provider of all the tools for such daily and petty routines that seem so natural but have got some really fine manoeuvres behind. And the world is wondering about those lofty equations! But that fundamental thing is often overlooked. 
Just as we keep on breathing and never spend a microsecond thinking what is the basis of life, we never pause writing those polynomials and equations to appreciate the fact that there goes the addition,  the Subtraction and so on! 
Oh!there was this consciousness that gave us the binary operation before which the numbers (the Varnatmak Roopa or descriptive forms of values) existed all by themselves as mere points.Enjoying themselves. The interaction between them created the Universe of Mathematics. And what kind of interactions....just so many of them. Sometimes I feel there must be some kind of Jnana Yoga for Mathematics. 
Imagine a space where numbers are suspended like tiny particles, the fundamental particles. Then with passage of time, they begin interacting, forming simple units like atoms or molecules. The forces of such formations are the binary operations that are possible between the two numbers. These forces are holding them together but without manipulating their existence. Wow! And the Universe of Mathematics is born!
The Group Theory, the Ring Theory and the Field Theory giving us the daily ease of calculation. 
Had it not been for the Fields, how would we be doing Division?
Had it not been for Rings, how would we be distributing multiplication over addition and had it not been for the Groups how would we be having 0 and 1 with us?
And now I am wondering....


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