Mathematics is something that exists in and describes the structures of reality.

There's little doubt that mathematics rules the reality roost when it comes to the laws, principles and relationships within the sciences in general and the physical sciences in particular. Further, mathematics plays a dominant role when it comes to the purely economic aspects of our lives and where would sports be without statistics? However, when it comes down to brass tacks, how much of really real reality is actually reflected in our mathematics?

The Non-Reality of Mathematics.

The following examples are some of what I term the non-realities of mathematics.

• Hyper-cubes are a nice abstract concept that mathematics / geometry can incorporate. However, while you might be able to play with real cubes, like dice, hyper-cubes will be forever beyond you.

• Stephen Hawking's concept of negative time. Since IMHO time is just change and change is just motion, then negative time would have to be negative change and negative motion. That doesn't make any sense at all. So while Hawking's negative time might be useful in a mathematical sense, it has no bearing on our reality and can safely be ignored.

• Lots of quantum mechanical equations yielded up infinities so a sleight-of-hand concept called re-normalization was invented to deal with those cases involving infinities. That strikes me as dealing cards from under the table or otherwise known as a inserting a "fudge factor". Does re-normalization represent really real reality?

• The mathematics of singularities inherent at the moment of the Big Bang or in Black Holes goes down the rabbit hole in that the laws, principles and relationships inherent in the physical sciences that are so otherwise adequately described mathematically now break down when trying to describe singularities and thus so does the accompanying mathematics that are involved as well. So what actually is the really real reality behind singularities?

• Mathematics are perfectly capable of dealing with alleged extra dimensions inherent in String Theory. However, that doesn't make String Theory a reality, not does it make a half-dozen extra and hidden dimensions a reality.

• Mathematics is perfectly capable of dealing with an inverse cube law that has no correspondence with our physics. Just because a mathematical equation works doesn't mean that there is a one-on-one correspondence to the real physical world.

• Mathematics are perfectly capable of dealing with zero, one and two dimensions yet these are just mental concepts that can't actually be constructed and thus have no really real reality.

• Space-Time: Since space is just an immaterial mental concept (that imaginary container that actual physical stuff has to reside in) and since time is also just an immaterial mental concept (our way of coming to terms with change which is just motion - which is also an immaterial mental concept since motion itself isn't composed of anything physical), then space-time has to be an immaterial mental concept. Neither space nor time nor space-time is actually composed of any material substance and the trilogy has no material 3-D structure. However, the mathematics involving the concept of space-time are a useful tool in describing reality, but not actually really real reality itself.