All knowledge is conjectural.

It's always being guessed.

It's our best understanding at any given time.

You're right to say that the axioms might be incorrect.

How do we know that an axiom is incorrect?

Traditionally, the answer has been

because it's clearly and obviously the case.

How can you prove that x plus zero must equal x?

Well, you just have to accept that it's true.

But if we consider something like Euclid's elements,

for example, draw two points on a piece of paper.

Now, through those two points,

a unique straight line can be drawn.

This was accepted as true for centuries.

When anyone listing might want to try

the experiment for themselves,

take a piece of paper, take a pen,

draw two dots on the piece of paper.

Now, how many unique straight lines

can you draw through those two dots?

It should be fairly obvious to you

that only one in such line can be drawn.

...