Are we just mathematics? Perhaps. But also perhaps, this apparent elegance of mathematics could be the result of us relying on deduction and logic to work out the Universe - the more we look for those patterns the more we discover, building on the blocks we have built before.  As we find more and more aspects of nature that fit in with our concurrently evolving mathematical tools, it almost seems as if we are not creating these objects, but discovering them.

But maths is inherently inconsistent - as Gödel showed, no system of logic can include the assumptions or axioms it is built on.  There always needs to be a way of understanding the system outside of it - "This sentence is false".  Foundations in mathematics could be as solid as sand.

Perhaps whatever tools are used, given enough time, we would create a Universe that makes sense - its just maths is our current most successful interpretation of the world.  It is a relatively modern one - its only really since the 1200s that maths has become centre point to much of science.  And lets not forget, although Newton was successful in applying his Laws of Motion in one of the greatest feats of mathematical genius, analysing the reality of nature to trace objects in motion in his calculus, with retrospect his curves were inaccurate - they worked only for objects that travelled an insignificant fraction of the speed of light. When those objects approached that speed (as most matter in the Universe is) those equations must be modified, as Einstein pointed out.  Our laws founded in maths are always with the caveat they will be modified when the model is proved insufficient.  Science argues that these models are to be discovered yet, but many have pointed out that we could one day reach a point our simulations aren't sufficient.  The natural conclusion if this is not true, that we can one day simulate reality perfectly with our simulations is that we ARE in a simulation.

Before maths' success, we relied on myths, stories and legends.  Whilst adequate for a caveman to survive, their subjectivity are only suited to tribes competing against one another for resources, otherwise we start killing each other over whose imaginary friend is better than another.  

But perhaps why both these two strands exist today, the logical and the faithful, are they are two dominant aspects of human nature.  And as they are human, we can only really talk of reality for us - to other creatures or worlds things are completely different, in ways outside of our experiences.

Those views could be just as real for them, and it would be, just not recognizable to us since we would try and measure it only in our systems of thought.

What other ways of looking at the world do our current systems not support? Obviously impossible to answer, a few guesses...

• Maths is mostly about the notion of movement - it has little to say about objects qualities of themselves.  Its always in relation to another.  Look at the difficulties we're having trying to find that most basic of qualities, mass.  
• We break up experiences into our five senses, and can distinguish between them.  But an animal simply experiences situations through all of the senses - it cannot separate a yellow ball is related to a yellow banana.
• Its more a two way exchange - our reality changes depending on our views.

The last viewpoint is most interesting to me, and there are lots of placebos being sold as cures that take advantage of it.  Its a known fact that our pain thresholds are affected by our viewpoint - I'm currently reading Predictable Irrationally  which describes how a 1p aspirin is less effective than a 50p aspirin purely due to the way our bodies anticipate it.

One interesting thing is that we may have found the mechanism that controls an ever changing subjective world, brought to us through maths - perhaps these systems we have used over the ages (direct experience, myths, maths) are necessary for each, and like astrological aeons represent different ways of looking at the world.  (the way myth has affected maths would be an interesting blog post - as this post says, "there is no written history of the evolution of language")

The same mathematician in the first video of this post also believes in the Many-World interpretation of quantum mechanics - that for each circumstance that demands a particle must be in two places at once (or be travel at an indeterminate speed*), it actually splits into two universes which we observe only one of.  Since there are billions of decisions made of this nature every time a particle interacts, this obviously increases the size of reality quite considerably.

If life has evolved to always take the most favourable path, it must interact with all of these universes and make choices. (and by life perhaps we could say "self organising information").  Or perhaps it is like the final scene of the "The Prestige" where we only remember those worlds we survive no ill effects - in which case could you forever be immortal?

Could it be possible our reality has evolved so that our desires and fears are represented in the world around us?  Before I'm flayed and executed as those who purport "The Secret" (whose author said those who died in the Thailand Tsunami "must have been thinking Tsunami thoughts" to have such a disaster befall them"), I would modify this that this doesn't mean we can simply "think" sex and riches to us with the power of thought, but rather our influence battles with the rest of society to arrive at an average world (which would say that if we eliminated suffering from the world, it would always be gone)

Whatever reality turns out to be, I will make a guess and say it won't be a truly objective experience - although science has historically always moved in the direction of humans not being in anyway special to this Universe, the fact we're the ones defining reality will always make us centre to its interpretation.  If that turns out to be purely maths, that will still be a miraculous wonder, similarly if it turns out that we need more than maths to fully describe it.  I only wish to be able to see how it turns out - one of my dreams would be to be able to see and know what the last conscious being will see and know.  This could obviously be a horrible scenario, but I have a feeling it'll be wondrous.