I'm not exactly a math whiz. I can still remember the day in grade school when I looked up at the long division examples strung out in a display above the blackboard, and I realized this was a language that was rapidly getting beyond me. So that's my disclaimer, and take the rest of this for what it's worth.
Math likely began as a way to describe and use elements of the real world. This remains its justification to most people. But mathematics is at bottom a closed world. It deals mostly with its own assumptions, its axioms, and with its own procedures. (I wish I could remember how I did it, but in high school I proved, by using mathematical logic, that mathematical logic is illogical. Or at least absurdly circular.)
We see the perils of too much faith in math as description of the real world in today's economic meltdown. The economic theories emerging from the University of Chicago and likeminded academies were politically potent, but they became dominant at least within the field through irrefutable mathematical formulas and proofs.
Even before the real world proved them wrong, economics was slowly being influenced by psychology--slowly, painfully and awkwardly, since these gently suggested insights are elementary and simplistic compared to common knowledge and especially to what advertising and marketing has been doing for decades to functionally if somewhat accidentally support these economic theories in the real world.
These theories were deified partly because they advantaged the already advantaged, possessed by greed for wealth and power. They became the handy instrument of the Shock Doctrine. But they attained academic preeminence through math proofs. Math proved they were right. The real world--as well as common sense--proved they are wrong. And now, tragically wrong.
There are some--including author Sheilla Jones in the opening chapter of her book, The Quantum Ten (Oxford)--who fear that physics is also falling into the trap of relying too much on formal, abstract mathematics, and not enough on real world proofs.
In any case, it's a caution, and maybe something useful to throw back in the face of those who believe that literature, philosophy etc. are self-referential unrealistic dreaming, and only math and science tell us about the real world.