No, the common assumption is that we attempt to describe the universe with precise tools like mathematics, but the map isn’t the territory and all models are incomplete, some are just less incomplete. The universe being mathematical is a form of Platonism, which is the belief that mathematical and abstract objects are real.
It might be a distinction without a difference, but I always understood the idea to be that objects we believe to be real are actually mathematical structures.
I see it as sharing some ideas from the we-are-living-in-a-simulation idea. If we were in a simulation, you wouldn’t say data structures and objects are real but would say the table in front of you is actually just data.
You would say the table in front of me is data inside a physical computer, whatever the physics of the real world were, assuming they aren't the same as our simulated world (perhaps they are an approximation of the real all depending on the purpose of the simulation).
That's different from the world being mathematical or informational, which raises the question of what makes it real to us. What breathes life into the equations? Consciousness? Where does consciousness come into the picture?
