This is part 3 of the series called Math : Art or Science? Read part 2 here So in my last post I talked about Platonism. For people seeing this concept for the first time, it was perhaps a little too extreme. I said mathematical objects reside in a realm of its own which is not affected by the physical universe. But where is this realm? It seems like the ideas of an overimaginative person. And you would not be the first person thinking that way. Platonism is not universally accepted as the philosophy of Mathematics. It is just one of many. Possibly the toughest opposing philosophy would be that of Formalism. What is Formalism? In the (late)19th and 20th centuries, Mathematicians, or rather a particular group of them, started to feel that Math is just a game. Just like chess, it has some players (mathematicians), it has some pieces with which the game is played (numbers, equations, geometric objects etc.) and most importantly it has some fixed predetermined rules of the game (
This is part 2 of the series called Math : Art or Science ? Read Part 1 As promised, I will contradict what I said in my last post. Let us finally begin talking about Platonism. What exactly is Platonism? To answer this, let us see something interesting about mathematical objects. We have been dealing with numbers like 0,1,2,69,420,-5 (and numbers like √2 and π) since our school days. Keeping the more complicated kinds of numbers aside let us concentrate only on positive integers. We all understand the idea of two-ness. We understand we have two eyes, we understand we do not have two heads, we understand that Wednesday is two days away from Monday and we understand that two books are just as many as two cups. But what is two? So far we have just shown physical examples of the idea of two-ness, i.e. the property of being two. But what or who or where is two? This is the question that immediately makes Math stand out from the rest of the sciences. We cannot dig the ground