Besides, mathematics does not claim to be "correct". In the 20th century, many smart people used mathematics to study mathematics itself. From a grammatical point of view, the best thing you can do is to agree that 1+ 1=2 conforms to the set theory of Zemelo-frenkel axiom and the usual von Neumann explanation of natural numbers.
But is 1+ 1 = 2 true? It is about the world. But in mathematics, this is only because of the definitions of symbols 1,+,= and 2. So this is a very tricky thing. From Russell to Frege, Wittgenstein, Godel, Turing and all profound thinkers have their own opinions. These people are thinking about what it means to use a series of symbols according to the rules.
But in my opinion, mathematics is meaningless without giving meaning to symbols. Indeed, mathematics is inspired by physics. But math is not physics.
Mathematics is as important to physicists as written language is to writers. But mathematics can be used as a tool for many other disciplines besides physics. Every aspect of physics relies on mathematics to solve problems-to describe and explore the nature of the universe and make important predictions, such as where a missile will land when it is launched at a specific angle.