What is Algebra? I asked my friend what she thinks, and she said “It’s an area of math, and it deals with numbers.” Not wrong!
As I would try and explain it to someone (say, anyone under the age of 10), I’d say “Algebra is a way of thinking!” Another name for this “way of thinking” is Abstract thinking.
What the hell do I mean? Do I even know?
Yes, or so I think so.
In algebra, we first seek to be more general, by saying “this (referring to a variable) represents any number” (barring certain other restrictions, like type of number)) This is perhaps the first step to thinking abstractly.
Once we become more general in our conversation, we are less restrained in how we can talk. No longer do we have to talk about certain numbers, now we can talk about classes of numbers, including the class containing all of the numbers.
One could also say that Algebra is a method of notation, but once we get to notation, we get to the idea that “mathematics is a language” and then that “language is thought”, leaving us with “algebra is a way of thinking” like I said before. Really tho, discuss amongst yourselves.
It’s also really useful when you want to Prove things to mathematical perfection.