It is said that the Greek philosopher Hippasus, while on board a ship, discovered that the square root of two cannot be expressed as a ratio of two whole numbers – in other words, it is an irrational number. The Pythagoreans on board the same ship,  who believed and preached that irrational numbers do not exist, were so irked by this discovery that they tossed him overboard, drowning him on the spot.

This tale is admittedly shrouded in ancient, vague and dubious reports. However, it shows that the question of whether numbers exist or not has been in the human mind for millennia.

Numbers are clearly abstract entities – we do not witness physical numbers roaming around our universe. Some numbers, like the ones we use for counting, can be linked to our reality in some way. But what about the irrational numbers, of which the constant pi is one such example? Do these numbers exist?

Mathematicians do not care much about the physical existence of their definitions. To them, the fact that many scientific fields happen to be modelled surprisingly accurately by mathematics is a nice bonus, but it is not the mathematician’s raison d’être. As Paul Lockhart says in his book A Mathematician’s Lament, in mathematics, “things are what you want them to be. You have endless choices; there is no reality to get in your way”.

To mathematicians, therefore, the physical existence of numbers is a moot question. So much so that, along the years, they have continued to create further number systems: the complex numbers, the quaternions, the p-adic numbers and many others.

Quite a few of these number systems end up having physical significance to our lives. But even if they didn’t, mathematicians are still fascinated by their beauty, just like a poet is fascinated by his or her poetry even if nobody ever reads it.