A New Level

I have really found a new level of love for mathematics as of late. I think it sparked a lot last semester and really came to a head over break. You see, after I spent 29 hours of my life reading The Count of Monte Cristo, I began to read a brief history of mathematics, Infinite Ascent. Now, I learned that a lot of the mathematics that I am studying now is at most 4oo years old! And, much of what I’m studying this semester (including my research which I will talk about later) is at most 150-200 years old! That is absolutely astounding to me. The fact that so much of what I’m studying is so new and fresh excites me. I really have loved learning about so much of this history.

Now, one of my professors this semester is quite boring. He has a monotone voice and is slightly hard of hearing, I think. Many of my classmates complain he is a bad teacher (and he has his moments of being horrendous), but a lot of the things the complain about are things that simply need to be done. There are things we are asked to prove that are just obvious, yet, the proofs don’t come by easily all the time and so they complain. I feel I’m coming off as a prick sometimes, but for the first time EVER, I understand the importance of these “duh” proofs and showing work. I feel almost dirty saying it. I think a lot of it has come from the research I’ve done and the way I’ve handled past classes. I also really love what my Topology professor said last semester, “If you say ‘duh’, then it should be easy to prove. So prove it.”

Now, I mentioned my previous math experience may have something to do with my understanding. Well, freshman year of high school, I accelerated through mathematics. Specifically, Algebra II and Geometry. Now, I still had to take tests but the learning was all up to me. It was a sweet deal. I did enough to get by with Bs in both classes. There were concepts (especially in Algebra II) that I just didn’t understand. I scraped past them so I could do well enough on a test but chose not to really learn it. What would I need it for? One of those concepts was logirithms. I found out my mistake when Calculus rolled around. I did it in Modern Algebra as well with bijectivity. I scraped by with minimal understanding and had to crash course for my research last semester.

What my friends don’t understand is how important these simple concepts are. And yes, we can just state the definition and theorems, but you gain so much understanding in proving it. Yes, there are concepts that talk about the exact same thing, but in a different light. Well, one way may be more beneficial for one proof and another for a different proof. There are needs for all of these things. The moment you decide you won’t need something is the moment it will haunt you. Trust me.

Now, my research has taught me one very important thing about mathematics, especially modern mathematics: it is very field based. That is, we have certain concepts that break into all sorts of branches of mathematics, yet, each field may define it slightly differently or need to show it differently to use it. So, we may be repeating material, but it’s important until you know where you’re going to study. And even then it’s great to know so that you may be able to bridge a gap between fields on a concept or take a concept from one field and apply it to yours. It’s really a beautiful thing.

My research proposal to my adviser went better than I expected. I am hoping to plug into work that will not just be a simple one semester thing. Actually, the concept I want to study (the Riemann Hypothesis which has go 150 years without being proved true or false) will be a much longer endeavor. But, my research from last semester has ties into some of its concepts and it’s something that has interested since 5th grade when I learned what a prime number was (though, I didn’t know it then). I’m excited for my research and taking a couple classes (well, one class and a seminar) on concepts I enjoy and would probably study if I go to grad school. Needless to say, I’m excited and I’m finding this amazing new love for mathematics. I’ve jumped a step in understanding (not to say I always understand concepts easily) what mathematics really is. It’s just pure beauty. God definitely created math and is in the workings of it all.