The artistic nature of math
Mathematics is a highly reproducible form of art.
I think art is about expressing the abstract human thought and emotions into a tangible form. And I think humans are wired to swim through this abstraction everyday. A lot of moving parts have lead me to pursue math and physics. Mathematics is that part of human endaevors which tries to formalise and develop an abstraction behind so much of the reality.
I had a very artistic experience in studying basic math very liberally over the past few months. For example, the process of solving a math problem is a very interesting one. Sometimes we have an unsettling feeling for something to be true, an abstract intuition of how things should move. But formally writing it down becomes a very non-trivial exercise. And this is where the process feels like an artistic expression. But the remarkable thing is, mathematics gives us the tools, the platform to explore that space of abstract thought very formally!
I think this also fits into a more general feeling that I have a critical creativity. I like programmable and abstract expression over more physical expressions like drawing. I like how they approximate my feelings.
\[\huge \sum_{n=-\infty}^{\infty} \hat{f}(n)e_n\]The process of doing mathematics hits home because it resonates with my creativity (which is perhaps critical), and there is a tangible reward waiting on the other side of that creative process. Learning to build those blocks/paths to reach the end point is such a rewarding process! And as I mentioned navigating the paths towards an uncertain result or an abstractly intuitive end point feels like art. There is so much freedom to explore in that space of thought, but there’s also a lot of formal guidance, so it feels home. One might argue these experiences are merely limited to education. How much do things change when one starts doing research? Is it really that disconnected?
So, I have some apprehensions about these.
$\sum_{n=-\infty}^{\infty} \hat{f}(n)e_n$ converges to $f$ in $L^2$ yes, but does it converge in $L^\infty$, or perhaps atleast pointwise?
Is it productive to have such strong personal feelings centered around the research process? Is it only selfish? Or does it atleast thrive more naturally in some specific research directions? It’s not like I am going away from the formal train of thought, it’s just there’s a richer feeling behind everything. I always thought it’s going to only guide me during the research process. And most importantly that, it’s also going to enable me to teach and communicate ideas better! But somewhere, I doubt myself, because I find the process slower than typical. During the last many months of study, I paused at so many instances to unpack a lot of artistic details (if I may put it that way) in a given problem/concept. That is inherently a slow process, but a highly rewarding one. I have a strong feeling that such a process can guide good research in its own way. I just hope someday I do really get to research math like that. I want to bet on slow, reflective and even perceptive ways of doing science, something that we might find more commonly in previous couple centuries.
It’s hard to find the presence of these ideas in the current world. But there’s a tangential hope in knowing that, there are movements wich are aiming towards bringing some change! Almost as a way to undo the consequences of the absence of above ideas, and to propagate a wave of more human approaches to science! For example, see Scholar Square and Science Gallery Bengaluru.
PS: I have an urge to gather people and conversations around these topics since a long time now - exploring non-linear narratives and careers in science. I want to call it InSciNiyat. Perhaps I can think about it after sumemr.
