For the longest of times I used to look at people with such disbelief when they used to say things like, “oh, maths is so beautiful!” or something along those lines, but that changed about four months back when I had a course in group theory. Our professor wasn’t all that supportive, but I found an amazing channel on YouTube to learn from; and there was always the textbook to refer to. Learning about isomorphisms is when shifted camps, because I realised that the numbers that we are so familiar with are just symbols that represent something that has a deeper meaning behind. Making that connection for myself is what revealed the beauty of mathematics to me. Also, the proofs. Oh god, the proofs were so beautifully logistic. The logic they followed simply flowed with such elegance from one step to another. It was as if this abstraction of mathematics was actually manifesting itself physically in front of my eyes.
Group theory was, therefore, the point where I understood the meaning behind people calling mathematics beautiful.
But as much as I like going through proofs, and as much as I love the feeling of utter joy and triumph at actually coming up with correct proofs, I really fucking hate coming up with them while I’m taking exams. I loathe it from the bottom of my heart. Because you never really have enough time to go over it again and again, you’re never too sure if you need to prove the theorem you just used to prove another theorem, and that’s why I have never been able to score in the questions which required me to write formal proofs. I have no problem writing them down when I’m studying by myself, because at that time, I have all the time in the world to go over it checking for consistency as many times as I’d like, but doing it while taking exams makes me cringe. I have a course in Analysis in One Variable and Theory of Calculus this semester and I just hope that I am able to overcome this hurdle. Would love to know if there are others out there that share my point of view!