Let me elaborate upon Jonathan's answer because I believe it is worth replying to. Suppose there is some mathematical universe of all possible mathematical structures. Already, "all" and "possible" have to be defined. Each mathematical structure is a whole in itself, but a structure also has to be made up of or at least contain parts. Otherwise, it can't be a structure. A single structure by itself is insufficient to describe our universe because our universe is not some undifferentiated formless singular entity. To say a given mathematical structure is our universe, that is to say, "is" and not "corresponds to" or "describes", is incomplete. Subentities within our universe exist. Many of them. They have "existenceness". MUH says these subentities are also mathematical structures in their own right because they exist, but they have to be a different mathematical structure from our universe as a whole. To say our universe is a solution to some laws of physics is to say the laws of physics exists as a mathematical structure, and there exists some set of multiverses containing all possible solutions to these laws of physics. Relations between structures have to exist, and by existing, these relations must also be mathematical structures in their own right. A tangled web of relations between structures, which is also a structure, has to exist. The many worlds interpretation posits that the wave function of the universe exists as a mathematical structure, but also that each branch exists as a mathematical structure, including the branch we find ourselves in. My point is, selecting a single structure and calling it our reality is insufficient to describe our reality.
"Exist" comes from a Latin root meaning "to stand out". To exist is to stand out from the other potential structures. A common analogy is the light analogy. If a beam of light shines upon a structure, it stands out and by virtue of standing out, exists. The light can be traced back to the Source from which the light of the world shines. The Source shines its light on one particular choice of laws of physics among all possible ones. Among all possible solutions to these laws, it shines upon one particular solution. Among all the branches making up the multiverse, it shines on our branch, a branch containing conscious observers. To shine is to "collapse the wave function". Within that branch, it shines on the conscious observer.
The light and the Source lies outside the mathematical universe. Anything which exists has to be more than just a mathematical structure of relations. It has "suchness" or "essence" coming from the Source. It is "like this" and not "like that".