Never be afraid to get dirty, but be sufficiently sure-footed to avoid the abyss of contamination.

Change of Focus

When I was in Seattle, I asked my friend Eugene for some photography advice. Eugene has been taking photos for a while now, so it seemed natural to ask him questions. I was particularly curious about the technical aspects of photography, including aperture, ISO, etc. Eugene was receptive to my questions and even gave me a bird’s eye view of pictures he’s taken since he started getting into photography.

As we went from his initial photos to his more recent ones, there were dramatic differences not only in the quality of the pictures, but also in the choice of subject. The earliest photos were often of the same object, perhaps as mundane as a lamp, using different photographic effects. The emphasis in these photos was on the technical aspects of photography. As these skills became second nature, the photos started to reflect a more discriminating choice of subject. Technique now existed as a means to bring out qualities of the subject the photographer wanted.

If people could take snapshots of my approach to research over the past few years, they might notice a similar trend. When I started graduate school, I was happy to do whatever research projects were assigned to me. Technically difficult projects gave me a chance to practice proof techniques and similar skills. When I attended talks, the ones with the most challenging mathematics were the ones that impressed me the most. These talks inspired me to take courses to further hone and develop my skills.

As I was wrapping up my Master’s research, I had a discussion with my advisor about what research projects might be interesting to pursue next. He said that the best thing for me to do was to find a project that interested me personally and consider that. While the answer he gave was liberating at first, it was also unsatisfying. I hadn’t really thought about the subject of my research up to that point, so I didn’t have a good sense of what I wanted to do.

As I began thinking more about the subject of my research, the way I viewed the field changed. Technical talks were still interesting, but I took more notice of the questions they were trying to answer. Researchers had different sensiblities about what constituted an interesting question, and slowly, I have started to find my own.

Earlier this summer, I was invited to join a reading group on proof techniques popular among members of our field in Europe. The reading group consisted of junior as well as senior graduate students. The younger students were focussed intently on the technical aspects. I, on the other hand, just wanted to understand how the techniques might be useful to my research.

After sitting in on the first few meetings, I decided to leave. If a research question I want to answer requires those techniques, I can always learn them at that point. In the meantime, I have research problems I want to formulate.


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