There are lots of things that wouldn’t exist if humans didn’t exist. The question is whether or not math is one of these things. No one is doubting the existence of mathematics. What is doubted by a great many people is whether or not math exists independent of human existence. If math is an intrinsic part of the universe then is logic also an intrinsic part of the universe? If so is it the standard logic used in mathematics? Does it include the Law of the Excluded Middle?
In other words, we're still taking sides. The existence of asymmetry in the universe, isomers, strongly suggests foundational elements of mathematical logic are inherently part of things, and that we can construct all the usual inductive layers up from and/or/not in some form mechanistically, purely from things as they are, reason absent. Beyond inductive, philosophical questions and completeness and p/np are perhaps innately artefacts of conciousness. Most of the maths of things as they are lies outside these problems. It's a very big universe to argue humans define all states of being... but I grant that the idea of a number which is one more than the value you count to, before entropy prevents all counting is "out there" as a value beyond existence as we understand it, and doubtless countless other numbers and values and expressions. I live in hope some shrimp like thing, or a gas giant conscious cloud is working on that problem.
The logic used by most mathematicians is uses exclusive or, law of the excluded middle, and is first order logic. There are some mathematicians that don’t use all of these and there are branches of math that don’t use all of them. So when someone claims math is an intrinsic part of the universe without addressing these nuance it gives the impression of an opinion without a good foundation. Assuming a finite universe (and the observable universe is finite) then math is much bigger. At most, one should say a subset of math is intrinsic to the universe.
Fair. I like Polyani so I shall put a Polyani quote here which I feel goes to your point: Mathematics as a purely formal system of symbols without a human being possessing the know-how for dealing with the symbols is impossible (1969) the wiki page I found it on is the Brouwer-Hilbert controversy (constructivism vs formalism, which seems a reasonable laymans take on a component of your point) and says: Despite the last-half-twentieth century's continued abstraction of mathematics, the issue has not entirely gone away. which is I feel, what I first said. It's a continuing difference, and as a non mathematician I take heart in that. All of these observations stem from looking at the law of the excluded Middle btw. There was a causal chain of weblinks to get there, I didn't just grab at random.
Math is fundamentally a description of the physical world. Mathematicians don’t like to hear this because they have their own ideas about the platonic realm of math, but it is true. We can debate which logical rules or axioms to include, but fundamentally any math has to have some sort of rules for deductive reasoning, which carry over from observation about the physical world: effects have antecedents, with a causal link between the two.
Now we have gone from that to the present day when we have maths which aren’t yet found to align with physical reality. So I can see why people want to say that it is a mental construction. But still, even these abstract maths operate according to rules we derived from the physical universe.
You sidestepped the question about what rules of logic are intrinsic to the universe. There are different versions of logic. Is Law of the Excluded Middle intrinsic or not? A great many physicists, philosophers, and mathematicians don’t believe logic is intrinsic to the universe. Is ZFC intrinsic to the universe? Do large exist as a deduction from the math that is intrinsic to the universe?
The law of the excluded middle is also known as the “sandwich theorem” because it drives directly from a physical observation. I happen to agree with the constructionists that mathematics is better formulated without it, but it is most definitely a rule derived from analogy to the physical world.
As a physicist myself, I’ll tell you that there isn’t a single one which believes that the universe doesn’t operate according to knowable rules. That’s kinda the definition of what it means to be a physicist.
Statisticians have a saying, “all models are wrong, some are useful”. What we have is that math is useful for modeling physics. But it is just that, a model in so far as we know. Believing that math or logic is intrinsic to the universe is not all necessary to using math and logic for modeling physical phenomena. There are quite a few physicists and mathematicians who don’t believe math is an intrinsic part of the universe.
It’s not at all clear that the Law of the Excluded Middle is an intrinsic part of the universe.
