I thought readers might be interested why I actually chose to get my PhD in math. Yeah, it's a soft post, rather than hardcore mathematics. That's not because I don't have more technical stuff to talk about. I actually do, but since I am really busy trying to actually write a few papers, some of the blogging has slowed down a little bit.
So, why did I choose math? The most proximate answer is that I simply liked it much more than anything else at the time. A lot of that has to do with its artistic beauty, and that's true for both pure and applied math. When I chose to do an undergraduate in math, I was much more aligned with pure mathematics, and that is mostly what I focused on. But mainly part of that is that pure mathematicians are more focused on beauty when they teach it. I think applied mathematicians also find math beautiful, and I'd certainly consider myself at least partly applied now, but that was not really the way it was presented. Probably that's due to most students wanting to hear about applications.
Another huge part of math for me was that I could sense I could do really well in it. I am the kind of person that latches onto interests very seriously, and I try to master whatever I am strongly interested in. I mean that both in a technical and artistic sense. I am not joking when I say that I actually feel pain when I am not pushing myself to the limit when it comes to understanding something or creating something I think is worthwhile. Of course, there are many branches I come to in research or creation that I think are not worthwhile. That's just part of the artistic process. Anyway, the point I'm trying to make is that, wherever I am in life, I need to find something where I can continually push myself to create something outstanding, and if I don't do that, I'm just not happy. Math has been a huge part of that process for me.
Understanding also motivated my pursuit of math. I like to try and understand the world through science. I remember as an undergraduate I had this really strong feeling that I would be terribly disappointed if I didn't study math because then there would be many techniques in science (modeling, statistics, etc.) that I just would not understand properly. Although I never though I would necessary practice many of the areas I like to read about, I still need to understand them to my satisfaction. That understanding is a continuous process, and math is crucial for that.
Math to me feels like the default and pure state of my mind. Actually there are many of those pure states, and mathematical thinking is one of them. That's because there are many other aspects to being human. Those pure states of mind, once discovered, are important to explore. Or perhaps "important" really isn't the right word. Rather, I think it is a necessary consequence and duty of being fully human to explore and develop those states. "Duty" might also not be very accurate, because exploring those states to me seems the most natural path of least resistance. By exploring those states of mind, it is like exploring my own soul, and it is the entire core of my existence.
I would say there I had no practical motivations when studying mathematics. I believe that should be the approach of most life pursuits. That does not mean I can just ignore practical matters. Practical matters like learning how to cook need to be tended to every day. However, in every such little activity, one can discover art and eternal beauty. So, the ultimate motivation for the development of the mind should be the spontaneous joy of discovery, and I am happy I found that with mathematics.