Well, believe is a misused word.

You believe the universe is real, and so therefor, to you, it is.

This statement is a fact, and I suggest you never ever ask for me to prove it. Because you think the above is a pandora's box, well its nothing in comparison.

But, lets continue your discussion about mathematics.
Space and time are constructs. Rulers if you will.
Mathematics is similarly a ruler.
Measuring an object has no real meaning to the object, it is just for our edification and provides us "numbers" to compare one object to another.

Now, our current mathematics is based on straight lines.
The universe has no straight lines. So, we will find that our ruler is not very good at measuring universal things. We will come up with "circular geometry" soon. It is necessary for actually flying in space and describing the shape of the earth.

There you go, one way that mathematics is going to change in the future.