Does mathematics exist independently of intellects, or is mathematics an invention of the intellect?

Does mathematics exist independently of intellects, or is mathematics an invention of the intellect?
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answer:What a layman calls “math” is a combination of both. The words “multiplication” and “exponent” are human constructs, along with the symbols 0123456789 and !^*-+=<> etc. If an alien civilization existed, it would not use those words, will not use those symbols, and would represent math in a completely different notation. While the notation is a human construct, I believe that the underlying concepts are not. While other civilizations might not share the same notation, they almost certainly have something that means “first number added with second number.” If math were purely a description of the known universe, then I don’t think that it could be as powerful of a prediction tool as it is. Take the Higgs Boson for example. Nobody had ever observed it before, but the math demanded that it exist. And it does. The same thing happened with black holes. And even the atomic bomb.
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