Here is one - there are finitely many mathematical symbols (or at least, all mathematical symbols can be defined in terms of a finite core of symbols).

That means the set of all mathematical definitions is countable (i.e. you could assign a whole number to each one, putting them into an infinitely long ordered list).

However, the set of real numbers is uncountable (by Cantor's argument).

Therefore the vast majority of numbers ("almost all" numbers, in a mathematical sense) cannot be defined, even in principle.

The big question is, can we ever know if the laws of the universe are governed by those undefinable ("uncomputable") numbers?

Can I move an object X meters away from me, where X is an uncomputable number?

Whether the answer is yes or no, the consequences are very interesting to me.

The vast majority of numbers also aren't useful or interesting.

Damn, I think I need chatgpt to explain me this one