Axioms are beautiful. Why?

Because when you look around, everything else rests on something else. Not axioms.

They are the first ideas that need not be explained. An axiom can stand on its own and needs no proof.

They are the simplest ideas, and yet possess infinite generative potential. They give birth to new disciplines, new systems and hence new worlds. And in these worlds, everything leads back to the axiom. But what really happens when you reach the axiom? 

Axioms are dangerous. Why?

Because when you look around, everything else rests on something else. Not axioms.

They are the first ideas that need not be explained. An axiom can stand on its own and needs no proof. 

They are the simplest ideas, and yet possess infinite generative potential. They give birth to new disciplines, new systems and hence new worlds. And in these worlds, everything leads back to the axiom. But what really happens when you reach the axiom?

Do you see?

I have a vivid memory of opening my geometry textbook in class 8th and reading about them for the first time:

“Axioms are statements that are accepted as true without needing a proof….”

At that moment, it was a huge sigh of relief. Less work for exams!

But now when I look back at the same moment, I am like “WTF!”

What do you mean that some statements that are accepted as true without any proof? And you have built entire disciplines out of them? Everything inside the discipline will of course make sense, because the axiom is God.

What if the axiom itself was wrong, or harmful or flawed? Just because something is useful and consistent, is this a good enough reason to accept it?

And who decides the axioms? And why them, and not someone else?

Axioms are chosen, not discovered.

So when you finally reach the axiom, you discover beauty and the beast.

PS: This was never about geometry.