What are the boundaries of the mathematical universe? How far is mathematics from describing the sub-atomic, or the pre and post Universe? And, will mathematics ever describe the essence of things, or the phenomenon knows as Immediate Experience?

Mathematics is an artifact, constructed to emulate the physical and some imaginary worlds. As a product of imagination, mathematics is unbounded. New algebras can be invented any time. Their usefulness in application or understanding is what determines which are remembered and perpetuated in text books. As a human endeavor, mathematics will never be completed, but we can always expect novelty in that arena.

But, what about the experience of the color blue, for example. How can mathematics approach this part of the conscious experience? So it can have useful purposes, like AI applications, for example.

Well you could represent the color blue as a wave length of light which in turn can be expressed as a number.

From the viewpoint of a conscious experience, you could represent the neural network of the brain as a very massive mathematical equation and the color blue would simply be expressed as a sum of a series of neurons firing in response to particular wavelength. In other words, express reality through numbers. There is of course the age old debate about determinism, but that's not what this question is about.

Basically, numbers represent things in nature - just like words or sounds do. The number 2 by itself means nothing really. Its just another mental construct. But something like 2 oranges, has a reference to reality.

Basically you are taking a visual sensory input - in this case, the English alphabet (which represents sounds) then composing a series of sounds together to create a word. This sound - the sum of other sounds known as the alphabet is a reference to an object in reality, which we call an orange. By adding the number 2 to that sentence one is simply stating that there are x number of objects in reality that are being referenced.

Thats an awful lot of explaining for something so simple but sometimes you really have to tear things apart into tiny pieces to better understand them.

So in essence, blue can be expressed as a number because both words and numbers are mental constructs used to reference to things in reality. Whether you call an apple - an apple or you call an apple - 432987 makes no real difference what it is. You can represent things from a scientific point of view in consciousness and come up with some sort of numerical representation, but when its all said and done, numbers and words are really the same thing.

Blue has a range of electromagnetic wavelengths.

Humans perceive those as reflecting that specific color.

We associate the color blue with different things because of evolutionary propensities for certain associations - for example, we associate bright colors on animals with being either poisonous or just not good to eat because some animals with bright colors are not good to eat.

I find people overthink the philosophy of consciousness WAY too much and don't rely enough on what we already know from cognitive research, psychology, and evolutionary biology.

Max, in reference to your example, yes. You could represent something, probably anything with any given number. You can mathematically reconstruct an orange all the way down to its atomic structure. And then, you could represent, this way, as many oranges as you want. But that's just my point. The real oranges are still there, in front of you. You have the orange in one hand, and the mathematical representation of an orange in the other. And then if there are two oranges, mathematics will just give me a number to represent that there are two objects with the same structure. But it tells me nothing about the fact that these two objects are completely different and sepperate from each other, occupying a different place in my concsiousness. It tells me nothing about the ESSENCE of these two seperate entities.
Same with the color blue. You can mathematically brake down the mechanics of how the color came to being in my concioussness: The energy wavelength, the firing of the optic nerves, ect. But again, mathematics tells me nothing about the unique experience of the color blue. Not to mention other immediate experience such as Inspiration or creativity, to name a few. My original question, as I re-state it here is: Will mathematics ever explain these concsiouss phenomena. And if not, how will we ever explain it?

I am reminded of the popular consciousness thought experiment of the color blind color scientist. She was born color blind (saw only shades of gray) but eventually learned everything there is to know about color: how the eyes work, how photons are generated and interact with matter, wavelengths, psychology of color, etc.

Then one day she had an operation that gave her color vision.

One philosophical camp (call them A) will say that seeing color for the first time will not add anything to her knowledge (because she already knew everything that could be learned (transmitted in the form of ideas) about color). Camp B will say that experiencing color is key to knowledge of color (and that she had not really known anything essential about it previously).

Which camp are you in, A or B?

Mathematics can't deal with experience. Mathematics is an idea. Consciousness is a substance.

The irony is hard to miss: A creation that happens to fall short of understanding her creator? As an unbounded product of the imagination, and as a product of an ever-evolving consciousness, I reason this will not always be the case?
And, to answer your question, camp B. I happen to believe that there is more to sentiency than the sum of all of its parts. What about you, and why?