Index Theory and Life(except from a letter)

It is not clear to me what is the purpose of my graduate school studies. When I was an undergraduate, I chose a huge topic as the goal of my college studies, and my advisor was able to guide me in every crucial turning point because he worked over the same topic 20 years ago when he is an undergraduate in Princeton, and had a better understanding it during his graduate studies in Cambridge and Harvard. I felt fortunate that I had such a great advisor. But I found I am at lost at graduate school, because essentially I do not know what topics I am interested that might coincide with others’ interest, and what might be a good research problem to work on in future.

You have asked me earlier while I was in Bard what my dream is, and I told you the stock response that I wanted to understand the nature of the universe. This is certainly true, only that I did not spend much energy and time to realize it. To me the understanding of nature is something physical; one usually has to propose a theory based on observations and check if the theory matches its predictions. I was rather diffident with my experimental skills and such “checking experimental data” work did really cater to my interest. I was also diffident by the sheer complexity of the physical theory being established. For quite a few subjects, I only know that the laws are true but it is unclear to why they are reasonable in the first place. Further I noticed I could not really getting along in a highly competitive environment where one’s talent relative to others is more important than his or her’s original opinion. I know that nowadays high energy physics is extremely competitive and totally detached from real life. So as a career choice I found studying physics to be incompatible with my personal characteristics. I took a few physics classes at Bard (Modern Physics and Quantum Mechanics), and I found myself feeling quite awkward in these classes. The sheer amount of computation bore me down before revealing me anything interesting, and my lack of patience/diligence did not help either. I do not really know how to tell you about this in the dinning table, because even then it was not entirely clear to me. I still have personal interest in physics, however because my lack of training it is becoming more of a hobby than an integral part of my life.

I found an asylum in mathematics, where I may pursue my interest of understanding the universe abstractly and be detached from people. This is not a progressive choice that one seek deeper understanding in a subject because that fits his/her career goals or personal ambitions. I chose to do mathematics mostly because it is enjoyable, interesting and in my imagination a field required high originality. Also studying mathematics enable me to understand other branches of science rather easily, and I like to associate an abstract theory with something seemingly distant away. For example you know I am interested in mathematical biology, even though I understand little of the subject I found it intellectually appealing that I may understand biological processes via mathematics. The same principle extended over mathematics itself, for which I mean I wish to understand the subject as a whole and not constituted by separated parts.

However, it is not clear to me how to balance the holistic ideals with real life. I am rather busy this semester with all kinds of assignments, and it is becoming increasingly difficult to focus on every field in the same time. Maybe I did not push myself hard enough and wasted too much time. But even if I tried to study very hard, it is clear to me even in fields I have a rather deep understanding, my knowledge is rather superficial due to the level of training I had at Bard. Therefore the only way to solve the problem is to understand deeper rather than expanding wider. But I am in a poor position this semester to study them all deeply enough. While the superficial understanding I achieved at this point is satisfactory to me, they are of little use in practical research and I may forgotten them in a few months without reviewing the material.

The situation is exacerbated because I am running of classes at here, which would not happen in a different university with a larger math department. So while this semester I took 3 classes, next semester I will only have 2 classes available, because 2 of them is in conflict and I can only take one. While I am not really worrying about classes, I am wondering with such a passive choice of learning (taking the highest level classes offering at here) is really optimistic for my future studies. It seems to me the only way to get out of this is to focus on a topic I really wanted to know, and work with an advisor who has more experience in that subject than I do to produce good research. My experience in Bard made me understand the fact that often one does not know what are all the necessary material one need to know until the later stage of research. Then one can naturally expand from his/her research results to other subjects related, and together he/she will have an overall better understanding of the subject.

There are several factors hindering this approach. One is despite of the level of classes I am taking, I am still mathematically immature and need time to decide what my future mathematical interest will be. I emailed Jim Belk (whom you must remember) last semester asking for his advice as I do not have a potential advisor matching my interest at here, and he suggested me to wait one year and expand my interest first. Therefore it seems unrealistic that I should make such decision right now or in next semester.

The other one is more essential. I am interested in the crossroad of three different mathematical subjects, each has a lot of interplay with the other ones. So to do good research on this topic, one need to have a rather deep understanding of almost all related subjects. While a detailed working knowledge of every subject may not be needed, a deep understanding of how them being put up together is almost required. I was fortunate enough to be guided by my advisor and went through some of the associations when I was at Bard. But there are still too much I do not know. This constitute the basic barrier when I want to choose a topic for future studies or consider transferring, because I do not know what I am really interested except some rough idea in the overarching topic. It is possible for me to go to any field of research except really applied ones, for which I have little preparation or knowledge. So I do not really know what to choose for future.

I am planning to make the decision based on my summer school experience. I have applied 3 program and had been accepted by 2 so far (the other one has not send me any decision letter yet). There are in 3 different subjects, and I feel I may have a better understanding of my natural interest if I went through them one by one. But essentially I do not know if this is the right approach. It is clear to me that sometimes one is unhappy with a subject not because the subject is unappealing, but because one formed a rather superficial understanding of it based on limited exposure and little patience. I do not really know if I will like a subject, or a topic if I found some subtopic may be productive for future research.

I am interested in working with Professor P if I chose to stay and need to decide advisor right now. His topic is the very type I mentioned in last paragraph. It is surprisingly deep and very technical. I do not think about these things every day because I am busy with other things, and I could not really talk to anyone about this at here. I really hope I can come up with an interesting topic myself rather than solving someone else’s problems. And it would matter a lot more to me than to get a PhD degree in a higher ranked university but with little creativity output. However, I am unhappy with the low level understanding/training I had in his field of mathematics so far, and it is immature to dream of such things. So I am progressing really slowly this semester, just want to keep a stable pace and not to get lost myself. But maybe I am progressing too slow, for reason I wrote below.

Here is something I could not tell you when you ask me “how are you” every time. I found I cannot focus my attention in work or reading very intensely. This has seldom occured to me and I suspect if I were having obsessive compulsive disorder as my therapist at Bard suggest. For example during the Boston tragedy, which you must have heard and has killed one of Sining’s high school classmates, I could not focus on my studies. I feel anxious as much as everybody else, not that I am particularly worried that my friends may be attacked there, but the suspension of uncertainty made me wondering why this kind of bad thing would happen and how it will end up eventually. And I cannot do work this way as I check CNN periodically. Almost everyday I found a topic “worth” paying attention this way. I found it to be rather damaging my life and my studies, as I often stay up rather late reading meaningless material. I need to find ways to exercise self control and stop this. I do not want to see a therapist again to solve this medically, because I do not want to be addicted. I do not know if this is because of Aspergers, but the syndrome itself does not mean anything and I have to come up with something myself.



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