Arka's Math World

  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 ...

  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 M...

  This is part 1 of a new series called Math : Art or Science ? People who have known me for the last few years, especially between 2015 to 2018, have heard me ranting about the purity of Math and Platonism at every given opportunity. And yeah, at times I have been like a fanatic and wanted to defend Platonism at any cost.  I think I have grown a lot in the last 1 year. My understanding of Platonism and my idea about the purity of Math has evolved and become more mature. So now would be a good time to actually address the issue - Math : Is it Science or Art? The difficulty in answering this question is the lack of a definition of Art. It is difficult to quantify art and what was not even present once can become a very mainstream form of art as we as humans grow (for  example, music enthusiasts will know of a newly emerging genre of music called Post-Rock). So we are going to take the other route. We are going to try to, if not define, then at least characterize Science an...

As you can see, this is my first ever blog post.  I have already started typing with no plans about what this post is gonna be about. I guess starting with a bit of introduction about myself is reasonable.  My name is Arkamouli Debnath. I am currently(2020) a PhD student in Mathematics at Tata Institute of Fundamental Research, Mumbai. I finished my Masters in Math from Indian Statistical Institute, Kolkata earlier this year. Previously I did my Bachelor's in Math from Ramakrishna Mission Residential College, Autonomous, Narendrapur and graduated with Honours in 2018. Like any other guy or girl who pursues higher education in Math, I was interested in Math from a very young age. Mostly because I was pretty bad at every other thing and Math was the only thing I was good at! And after a few years I started to feel like abstract thinking and reasoning is THE only thing that fascinates me. Concrete things have rarely appealed to me. This might sound like I am romanticizing my l...