It wasn't until the 1930s that people realised second order logic with arithmetic will always lead to contradictions without guardrails. Before then all mathematics was done in the object language of whatever the field in question was and only translated to the meta language for succinctness after the fact.

The magic of modern maths is that we can now work only with the meta language and get results free from contradiction. For this we absolutely need a modern notation to do the new type of maths since we are no longer grounded by the reality of the object language.