Arguably, there is no objective truth

Yes there is, just look in Maths textbooks

since the symbols and rules of mathematics are assigned arbitrarily

The signs are, the rules aren't.

are basically a social contract, just like language!

Nope and nope. It's a tool for calculating things, nothing like a language at all.

no objective meaning of “objective”

There is, in a dictionary, just like the rules of Maths are in Maths textbooks