Who does the math?

There is a fascinating book about Fermat's Last Theorem called "Fermat's Last Theorem" (duh!). This theorem is recognized around the world as the longest math conjecture to be proved ever: it took nothing less than 400 years for someone to finally come up with a proof for it. Throughout these years, many amazing stories popped up related to the quest of tackling this problem: people died, faked identities, even an "all ready to go" suicider changed his mind at the very last minute because of this theorem. In 1995 a PhD finally came up with the final proof: an incredible 150 pages long, only understandable by two dozens human beings.
Is nature really that complicated that only 25 out of 6,000,000,000 people can understand it? I say it is not - but math is really complicated! Let me explain:
A human being is an incredible math machine. I really don't know how we developed to be such beasts, but the reality is that we're good in math. Notice that I'm referring to the species here, not to an average student on fifth grade who is struggling with math homework. And because we're good in doing calculations, we always try to map events occurring in nature to math formulas, and once this mapping is done, then everything is within our realm and we can then try to understand how nature works.
There isn't a problem with math per say - I love math, it is part of my day by day job, and everything related to it is logical and correct. But there is a problem when we try to map nature to math. There is a flaw somewhere: how would one explain for instance the existence of square root of -1? How come math can't give me a precise and definitive answer for even the simpler square root of 2? Math gives us an approximation, but nature gives us the precise length. Thus square root of 2 exists in the nature (just do Pythagoras with few sticks) but it does not exist in math.
Therefore, either we're not mapping events occurring in nature to math properly, or… there is something beyond math that can be used more simplistically (perhaps) to explain nature. And maybe using this new methodology (beyond the scope of this blog), Fermat's Last Theorem can be proved with a single phrase rather than an entire book.