Mathematical Thinking

 When I was in 7th grade, I started playing chess. Winning was difficult. Often times, while solving tactics which is in my knowledge the most effective way to get better at chess, the focus is not to remember the rules or certain opening strategy. Every game of chess is different. The tactic you are solving will never be encountered in your games. Yet, it is very effective as it allows us to think in many different ways. Sometimes we think a certain set of moves is the most logical, but you never know which sacrifice can lead you to get a higher advantage on the board.

By now you might be wondering that I wanted to write this blog on chess but by mistake wrote the topic as Mathematical thinking. Well...no.

Here chess is just an example to explain the notion of "The way of Thinking".
Simultaneously, our mind rings two modes of thinking: The time when you are focused or rather threatened for the Math Exam that will be held tomorrow and you are giving your full to study whatever you can in the last night 😂 or the diffused mode, when you are stuck at a coding problem for an hour which makes you sleep, and when you wake up, you wake up with having a solution.

This post is basically going to be a fictional story about a Math Research, and what lessons it taught me.

 

All of this began with my masters thesis. It was the fall of 2017, I had it due in a week. At that time, all I thought of, was to complete the thesis asap and get done with it. My mentor, was very supportive. We had worked day and night, for this. This is was going to be revolutionary in the world of Indian Mathematics, unless this step was over.
A month later, an email had arrived, and it said: "Congratulations to every selected researcher! Here is the list of everyone selected and if you are one of them, then we'll contact you soon for the presentation and publication of your paper.".

I checked the list, and I found myself in it after a few glances!
This was a life-changing moment for me. I was officially going to publish a paper for the future of Indian Mathematics.
The presentation was very good. I did not win the conference, but my paper got published anyway, and that was the thing I was most happy about. An year later, I re-read the old paper, as I wanted to continue my work on it, but it seemed like nature of math didn't suit me. There was a way factor that was missing in the path of my proof. At the time of publishing, that it was logical, and it was a logical fact, but that didn't actually conclude or lead to my result naturally. It was as if the result never came, and it was just an idea, that I thought would be true because it would be very ugly to not be true.
And having a gut feeling about an idea, isn't wrong, infact that is the way how mathematicians get their way to a breakthrough. I call it the cool theorum, wherein, the idea that you are thinking or you are stumbled upon is cool or not, literally, checking if it is is so cool that it just has to be true.

Thanks Mithuna for the drawings in this post

 So I found there was a mistake in my paper, and I had to republish it quickly. But now I think I wasn't wrong with the math, but the idea.
Most of the research-work that I do today, isn't on paper or computer. It's rather on my way to and back from the department, because there I can experience the loose ideas rather than dealing with the equations(Diffused mode, you know). And when I finally get to the equations, I can imagine them more clearly. Although that usually isn't crystal clear, it always seems that it will get. And when things do get crystal clear, we usually realize the reason why my paper was wrong. Usually because, the thing I was trying to proof, didn't really exist. You might try to patch up the original path multiple times but to no way. And eventually you have to leave your project, having nothing to show the world, what you did in that 1.5 years.

Failure is hard. Often because, we had no other paths to go.

But, even though you have nothing to show anyone else, this journey definitely changes you! Through the ups-downs and multiple failures of this project, I'd learnt to be way more careful.

 Doing maths, is like being on a roller coaster, because finding a true mathematical fact is a heady rush and then realizing, you made an error, is like the flaw just fell on you.

I ♡ mathematics regardless.

Featured: Mithuna Yoganathan, Toby Hendy

Author: Suryaansh Chawla