You're wrong about animals not having a concept of "2+2 = 4". Since 2009, it has been known that even young chicks can not only count but also add and subtract small numbers (1, 2, 3). This should not be surprising; humans are just animals with a larger mental capacity after all.
And if you know a bit of mathematical logic, you would also know that there is no such thing as a single "mathematics". "Mathematical platonism" is often brought up, but it is in fact an ill-defined concept, and you'll only understand this if you know basic FOL (first-order logic) and know various foundational systems for mathematics (with all the technical details), such as PA, ACA0, ATR0, Z2, ZFC, ... (See here for where to start learning all this, and here for a brief sketch of the hierarchy of common foundational systems.)
The correct answer to your question is that only a miniscule fragment of mathematics, somewhere between ACA and Z2, is relevant to the real-world. PA− axiomatizes basic counting, and PA (which is PA− plus induction) extends that to support reasoning about basic counting, and so far we have good empirical evidence that theorems of PA are true when translated into real-world statements. This empirical evidence extends to ACA via a syntactic interpretation of the 'sets' in ACA (see here for more details), but fails to extend much further. I think on conceptual grounds one can justify up to ATR0, but beyond that it is unclear what 'sets' would mean in the real-world. Logicians generally do not believe that there is a real-world interpretation for anything from Z2 onwards.
So one can expect that ACA has platonic meaning, but higher mathematical reasoning that is not support by weaker subsystems of Z2 cannot be justified (as of now) to have platonic meaning, so we are left with ascribing them with more formalist meaning.
"2+2 = 4" is easily observed in the real world, so you should expect any conscious being with a small amount of mental capacity for forming and acting upon empirical hypotheses to realize this fact. There is no reason to think there is any "coercion" in this realization. Also, mathematics is a socio-historical construct, so mathematical concepts beyond PA− cannot be blindly considered on par with "2+2 = 4". In fact, numerous people who followed their mathematical desires ended up proving nonsense.
Maybe you need to reconsider what "2+2 = 4" really means in the real-world. It implies statements like "If you (using a 2 L jug) pour 2 L of water into a pail, and then pour another 2 L of water into the same pail, you will get the same result as if you (using a 4 L jug) pour 4 L of water at one go into the pail.". The reproducibility of verification of this statement is what makes it an empirically verified instance of the abstract statement "2+2 = 4". If this instance is not objective, then almost nothing else is, and all science is indistinguishable from magic.
But your question title has the nebulous term "mathematics". As I said above, what mathematicians count as "mathematics" goes far beyond "2+2 = 4", so your title's question cannot be answered if you don't even specify which foundational system for mathematics you are considering. One can defensibly argue that all mathematics supported by ACA are discovered in the sense of translating to a discovery about the real world, but general theorems of ZFC are merely discovered as symbolic features of ZFC that may not have real-world relevance (and hence cannot be experienced).
Note that even for PA, you cannot really experience certain theorems, such as a suitable translation of the following:
For every program P and input X, either P halts on X or P does not halt on X.
The problem is that you cannot experience "non-halting" in any meaningful way unless someone can concretely justify it to you (say via game semantics). And by the incompleteness theorems one cannot always determing halting behaviour, not to say justify non-halting even when it holds.
However, we can experience every instance of "halting" (by following the program execution until it finishes), and in some sense that is really the limit of what part of mathematics we can experience fully. After all, every theorem that is proven in a foundational system is witnessed by the fact that the proof verifier for that system halts on the purported proof of that theorem. But this is only an experience of the formal system, and not of any 'truth' stated by the theorem. Even a simple claim like "∀k∈ℕ ∃m∈ℕ ( k = 2·m ∨ k = 2·m+1 )" cannot be experienced fully; via game semantics you can experience "∃m∈ℕ ( k = 2·m ∨ k = 2·m+1 )" for more and more instances of k∈ℕ, but only finitely many of them.
