You and I know very well the potential of mathematics to pack — from most complex as well as to the most fundamental concepts of our understanding in a very tight and sharp form. Mathematics, since 6th century BC has been the ultimate nail in coffins of philosophies and theories.
Though, its seem to be that there exist a very smooth relation between maths and its corresponding concept, there is another dimension to their relation too.To put it in a sentence the relation between maths and concepts is like relation between a painting and its painter. Let me take you through this following example…
Consider a square of area 16 sq.unit having length of each side ‘x’. Now observe it using the lens mathematics -
x^2=16; or x = ±4
It's simple and clear that ‘x’ presents two values,one positive and one negative. But in reality only positive value of ‘x’ serves our concept of length. Try to imagine negative value of a side of a square, you can’t right — it is not possible. Negative value of length can only exist in relative to other value of a length. Though, there is no denial that with the help of mathematics we have achieved some of the most unexpected realms of our understanding. But this particular equation shows a stain on the beauty of mathematical painting.
Sometimes, study of a piece of an art can’t help us understand the artist. This is how it is, after all maths is human invention. And like all human inventions it has pros and cons.