# Algebra/What is maths, exactly?

Algebra
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## Understanding Our World

To give an exact definition for a subject as broad as mathematics is not easy. It is not just the study of numbers but taking what we know, realizing patterns and organizing it all into a something that we can work with and understand. Throughout the history of math there have been several ways to organize numbers, the most common way now is the decimal system but even today we still use several others. When man was just a nomad there was no need for numbers, the number of people in clan was small and all you had worry about was food and surviving day to day. As we started to settle down, make camps, towns and eventually cities and empires we needed new ways to talk about numbers. How many sheep are in the flock? How many people live in the tribe? How far is it to the next town? There were all things we needed numbers for to be able to communicate and understand what others were saying. There are countless things that we describe using numbers and quantities to understand their meaning.

## Discovery

A large part of Mathematics is discovery. After we defined the numbers and how we were going to measure lengths there was math everywhere just waiting to be unveiled. The area of a rectangle has always been the length times the width(${\displaystyle A=lw}$) but until we had numbers to define our length and width it could not be discovered. Volumes, prime numbers and multiples are all parts of mathematics that were just waiting to be discovered. The discoveries now are a lot more complicated to understand but they still exist.

## Invention

Often math research leads us to a point where we can’t go any further without a little invention. Imaginary numbers, which you will work with later in this book, are one example of where we had to create something to make the math work. Imaginary numbers in the real world do not exist but they have to exist to explain some of the things that happen in our physical world. We invented them to make math work in a manner that could explain the patterns we could observe.

## Abstract

Mathematics is where we find some our first abstract thoughts. A number is not the same as a letter, letters each make a noise and when we put them together they make a word that represents a noun or verb or some other part of speech. Every number represents a different quantity and even more confusing is that two 3s do not make 6 but 33. It is easy to see that 3 fingers on your left hand and 4 fingers on your right come together to make 7 and that is why you will often see grade school students adding in this fashion. Even as we become more accustom to adding, the simple facts, like adding the numbers between 1 and 9, are often memorized instead of picturing 5 of something and 8 more of them in our mind we memorize that 8 + 5 = 13. To convince you just little bit more that numbers are abstract define the letter B using only words in the definition. Now try to define the number 6 without using numbers.