We invented mathematics to help describe the world around us. First we wanted to count things, so we invented simple number systems. Then we could say, “Hey, I saw three sheep in that field over there?”
But in case the person you were talking to didn’t know which field you were talking about, we needed ways to describe distances. So measurements were invented. Now you could say, “That field over yonder, three rods and a chain from here.”
But your pal might not know how long it would take to get there, so we needed a method for counting time. Then we needed a way to express velocity, so we had to invent division and figure out distance / time.
Now that we had a way to measure time, people started realizing they had far too much of it to spare. So they started observing how the world works. They noticed the sun running in circles around the earth, and so they invented geometry and trigonometry to track its motion, and one smart dude used it to figure out how big the world is, despite the fact that he hadn’t been all around it.
Also around this time people started buying things with money, instead of other things, and so accountants were invented. This is the time when old people started complaining that the young people were making everything go to hell, and the old people haven’t stopped, since every generation breeds more and more accountants. Accountants are very good at counting stuff in really complicated ways, which is why “count” is in their name.
In order to kill the accountants, people needed to invents swords and other metal items, which rely on creating sophisticated alloys. In order for the alloy to form properly you have to mix molten metals at the right ratios and tempuratures, so fractions were invented.
Speaking of tempuratures, did you know that Mr. Fahrenheit, the guy who invented the Fahrenheit scale, used two reference points to calibrate his thermometers? The first was the melting point of water, which he marked as 32, and the second was the tempurature of his dog’s ass, which he marked as 96. Having 64 degrees between the two reference point made it easy to create the rest of the marks by simply dividing the distance in half several times. That dog is a hero.
Later on, Isaac Newton and Capernicus and Galileo and a bunch of other guys came around and invented math for describing gravity and motion. That dude Isaac decided he would like a way to quantify the rates at which other rates changed, and so he decided to invent Calculus. Sir Isaac was later lynched by a mob of pissed off college students. Fortunately, they were able to calculate the exact force which the noose would extert on poor Sir Isaac’s neck, and decided to name the Newton (the amount of force necessary to accelerate a one kilogram mass 1 m/s[sup]2[/sup]) in his honor.
Another useful trick with math is that it can be used to predict what we think will happen, even if we haven’t seen it yet, and then look at nature to see if it’s true. Some dudes did this and tried to prove that light waved traveled in a mysterios medium called The Ether. They failed, though, and so this dude called Einstein invented Special Relativity to explain it. And wouldn’t you know it, with some modern technology, we can prove that Special Relativity accurately describes the motion of light.
Speaking of the Ether, they also needed math to invent Ethernet, without which we could not have had this enlightening conversation.
I hope that helps.