Mathematics ... Myth or reality?

Galileo remarked - "Philosophy is written in this grand book - I mean the universe - which stands continuously open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics... without which it is humanly impossible to understand a single word of it. Without these one is wandering about in a dark labyrinth."

Think about it for a second. Is nature really written in the "language of mathematics"? A deeper question is whether mathematics is real or a figment of our imagination? I must confess that this line of thought is inspired by Robert Pirsig's famous book The zen and art of motorcycle maintenance (ZMM). Pirsig questions the very foundations of modern thought. I do not want to go as far as that. I am content meddling with something less deep (for now at least!).

To probe the reality (or the lack of it) of mathematics, let us take the simple mathematical concept : equality. Can two physical things (or quantities) ever be exactly equal? Note that the mathematical notion of equality is strict; there is no room for tolerance. If we do not allow for tolerance, (i.e., a little variation that we are willing to overlook) then no two things (or quantities) can be equal.

Did I make an audacious statement? Think about it. To say two things are equal, we should first have an accurate (no tolerance again) measure of the quantities in question. All current measurements are subject to error, it does not matter how small, but the error is always present. This violates our mathematical notion of equality. I can continue giving examples, however I think the point is made.

Now, please note that I am not trying to discredit mathematics. I like mathematics and love its beauty . In fact, I am trying to credit mathematicians for coming up (read imagine) with such a wonderful tool. The surprising (and beautiful) part is that the imagination works like a charm. It is so easy to describe nature in terms of mathematics. This ease has indeed made it the chosen language of scientists for generations and hence it seems natural to us. I do beleive that mathematics has evolved because people wanted to describe natural phenomena and Galelio's language (or rather the translation) seems to suggest that mathematics is eternal. How can it be eternal if it is a figment of our imagination?