Eye of the Tiger moment

Last Wednesday at work, my computer was running the third batch of simulations. Since it was gonna take at least two days to finish and the GPU was used full time at full capacity for the simulations, my computer became too laggy to work on. So I thought it was the best time "back to the drawing board" to work on a problem left aside for quite some time. The problem was basically like this : two different approaches, two different sets of formulas, to solve the same equation. At first glance, both were expected to give slightly different results. But surprisingly they gave the same result. And when compared to the results of experiments, they all fits perfectly. It was good news. It meant both approaches were valid. However that was still the question : how come? There must be some kind of link in between them but what was the link? 

I called on my supervisor and another researcher familiar with the domain to figure out the answer together. After listing out formulas of both approaches, we were staring at the white board, very little discussion, mostly silence. This was probably my first "Eye of the Tiger" moment. It wasn't the first time I stared at a bunch of equations for an extended period of time. But this was the first time I was in a group staring at equations on a white board together for a long time. For those who don't get what I mean by the "Eye of the Tiger" moment, it is originated from the episode 4 of season 3 of The Big Bang Theory. It was pretty cool came to think about it. I felt like a real scientist. Hahahahaha! 

mindblown !

The joy of solving maths problem is so gratifying. Although it wasn't me who made the critical step to find the link between the two approaches, I was so happy to see the answer unfolded with my own eyes. The critical step always seems so trivial once you know about it. It is like finding a bug in thousands lines of code but more. The elegance of the solution of a maths problem never ceases to amaze me. After we checked every steps, mindblown moment ensued. I so wanted to jump for joy but I told myself : act cool, just smile and act cool. I didn't want to feel like an idiot. 

the trifactor of college life

The elegance quality of maths is exactly why I love maths. I was lucky to have discovered through reading a lot more than the maths taught in primary and secondary school, to be able to see a bigger picture throughout my early school life. Maths problem solving is just like any other skill, it can be trained. The "Eye of the Tiger" moment in the lab reminds me of my time in la prépa, aka Classe Préparatoire aux Grandes Ecoles (CPGE) in France. There is a pseudo-theory about the triangle of choices (social life, good grades, and enough sleep) of life in college floating around on the internet. Well I had chosen good grades and enough sleep. Seriously, I was a freak during that time. Study, eat, and sleep, nothing else. I admit I should have gone out more and balanced the triangle better. The upside of this unhealthy lifestyle is, my maths problem solving skill was trained to its peak.

In prépa, especially prépa scientifique, I had to study unreasonable amount of maths and the maths were unlike anything I had learnt back in Malaysia. During primary and secondary school, it was all about memorizing some established formulas and applying them appropriately. But in prépa, it was all about axioms, conjectures, hypothesis, demonstrations, and theorems after theorems, basically maths in its pure form. The paradigm shift was hard. But once I got through the beginning of the learning curve and tonnes of effort afterwards, a whole new world was opened to me. I was so on point in maths, my maths sense was so sharp like a tiger. Intuition and ideas just kept flowing in like Niagara falls, abundantly and rapidly. Whenever other students in prépa started a conversation about their hate on maths, honestly I couldn't join them. I genuinely enjoy the process of maths problem solving.

Just like a knife, every skill needs training to stay sharp. Now no longer am I a study freak, so sometimes I am quite sloppy with my maths. But I still love maths. The time in prépa not only cemented my love for maths, but also let me understand the essence of maths. I saw a comment in a reddit post summing it up quite well. To quote : "Maths is invented and has nothing to do with the outside universe. It is a playground of human abstraction and critical thinking, and is at best inspired by the things we see around us." In maths, we can invent any concept as long as it stays consistent and doesn't create contradiction. Vsauce in his video : How to count past infinity, explains this process very well.

During the first class on complex numbers, I once asked the teacher what are the uses of complex numbers. He paused for a moment and then answered with his heavy French accent : "Just for fun !" The whole class burst out laughing. After that in a more serious tone, he explained a few examples of application. But now come to think about it, "just for fun" is actually the correct answer. The unreasonable effectiveness of mathematics in natural sciences may just be a coincidence, says Eugene Wigner. Maths is a playground of human mind and logic. So let's do maths just for fun !