My head hurts.

Hello again, fellow humans. And non-humans, too, if you are indeed reading this.

Recently I came across an old Calvin and Hobbes strip (For those of you who don't know, Calvin and Hobbes is one of my favorite comics, by Bill Watterson.). It was from March 6th, 1991. Here's what the dialogue is about (no pictures, though).

(Calvin is doing his math homework, and....)

Calvin: "You know, I don't think math is a science. I think it's a religion."
Hobbes: "A religion?"

Calvin: "Yeah. All these equations are like miracles. You take two numbers and when you add them, they magically become one NEW number! No one can say how it happens. You either believe it or you don't. This whole book is full of things that have to be accepted on faith! It's a religion!"

Hobbes: "And in the public schools, no less. Call a lawyer."
Calvin: "As a math atheist, I should be excused from this."

I laughed when I first read this. It was hilarious. Well, maybe you need to know what are Calvin and Hobbes like to fully appreciate it, so I strongly recommend you to look it up.

But let's take a closer look.

I mean, I suppose now we do take 1+1=2 for granted. Thus, perhaps it is a religion, according to Calvin's definition. Our teachers at elementary school told us so, and we believe them until now.

But how did the first mathematicians manage?

Imagine. Imagine that you don't know about mathematics. Suddenly you found a pebble. You pick it up. You walk some distance. Then you find another pebble. You pick it up again. Now, you may not know that you picked up one pebble, then one other pebble, and now you have two pebbles, but I think you'd know that if you picked up the second pebble, you'd have more than before. So, is it a matter of nomenclature? Did we just give it a name? Did the concept of addition exist before we found out about it? If so, doesn't it fall under the category of science? We simply 'discovered' that 1+1=2, in the same way that Newton discovered that things maintain their speeds without outside forces. Or maybe we just named it as '1' and '2', just like we call this animal a 'dog' and that other animal a 'horse'. So I guess, for the first mathematicians, math was a science, an empirical art.

But then it evolved. People remember that 1+1=2, and they come up with concepts such as subtraction, multiplication and division, which are simply the modified and repeated forms of addition. It is taught in schools, children are told to memorize tables, and they became a form of tenets and commandments. For instance, if I were to say 1+2=4, I would be violating some kind of 'law', wouldn't I? Mathematics now has rules. It is a system. The tenets are accepted without need for proof. It became, more or less, a religion.

So, which is right? Is mathematics a thing of nature, a science which is subject to change, depending on experimental and empirical findings? Or is it a creation of man, a religion which is set in stone?

Or maybe we simply know too little.