[armchairhacker]

It depends on what you mean by "everything", "represented", and "mathematics"...

But no.

For example, there are theories which can't be proven (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...).

Moreover, there are a lot of things we don't know we can prove, which we may or may not be able to prove later by inventing new mathematical notations and discovering new theories. See: Collatz Conjecture (https://en.wikipedia.org/wiki/Collatz_conjecture) which is unproven; Fermat's Last Theorem (https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem) which was proven but took over 300 years and new mathematical developments; solved open problems and developments in 2022 (https://www.quantamagazine.org/the-biggest-math-breakthrough...)

There's also the philosophical question on how to fully "represent" anything in math notation. Like, I can't exactly describe my computer and include every single detail, in part because you can't observe some things without changing them (https://en.wikipedia.org/wiki/Uncertainty_principle)