[talanum1 (OP)]

The Universe is not mathematical if there is one instance that you cannot convert to numbers. There is such an instance: particle decay has formulas in terms of flavors of quarks: not convertible to numbers or functions of numbers.

[puppypower]

Math is like a faithful horse, that will go anywhere you ask it to go. A math horse can even remember where it went, and it forever duplicate that path without being micromanaged. We can choose any premises and it can be modeled with math, just as the same horse can be told to go to different markets.

For example, computer game physics engines use math. To make the games more enjoyable we can set conditions for the math horse, that defy science, and the math horse will still go there. We can program infinite lives into the game.

Another example, is we could model gravity using spherical coordinates instead of Cartesian coordinates. In this case, if we assumed this math approach was more than our faithful horse, it would lead some people to read special significance into the two angles of the spherical coordinate system. In reality, it is just a new path chosen by the rider and not the horse.

This is why conceptual foundations are important to math. They plot the course in advance and offer the best paths on the map, allowing the math horse to get where we need it to go, with less effort. Newtonian gravity and Einsteinian gravity both use math horses with each taking a different path. The Einstein horse backs himself into the stall to be unloaded. This offers an advantage for all.

[Kryptid]

particle decay has formulas in terms of flavors of quarks: not convertible to numbers or functions of numbers.

Sure it is. Strangeness, for example, takes on a value of +1 or -1 for anti-strange quarks and strange quarks, respectively.