I used to often worry about the fact that I was never really focused on a research problem. I would hear about researchers making amazing discoveries after single-mindedly pursuing their goal for months and years, and I would often think that that would never be me. Instead of focusing on one thing, I would pursue whatever struck me as interesting in the moment, and of course that wouldn’t last very long.
I have spent the last month or so, however, obsessing on a problem that my advisor gave me. I wasn’t on a deadline. I wasn’t even expected to solve the problem. We both agreed that I should focus on a simpler problem for my thesis. However, I somehow started spending all my time on it.
Over the last week, it has gotten to the point where I have trouble sleeping because of it. I go to sleep thinking about it, and wake up early in the morning still thinking about it. When I try to distract myself by reading a book or watching something on Netflix, I find myself returning to it within minutes.
It would be interesting to introspect on why I was particularly nerdswiped by this problem, and whether this insight can be harnessed to generate interest in other problems in the future. Some reasons that I could think of:
- I was making progress on the problem. When I tried this problem in the past, I was making no progress, and was not even sure that I had the right “picture” in mind as to what was happening. However, this time we had a pretty good idea of what was happening. I knew that I “had it in the bag”. Perhaps this motivated me to push harder.
- More importantly, my advisor’s insight into what the solution should “look like” considerably narrowed the solution space for me. After that, it was mostly about making sure that certain pieces fit. This transformation of a somewhat difficult task to a much simpler task was perhaps what made me much more interested in the problem.
In some sense, narrowing down the possible set of solutions was what made me very interested in the problem. This is similar to what happens in a crossword, when you have found all letter except one or two. You know that the solution can be found after a few minutes of thinking. You know that you are close. That is when you can’t stop thinking about the word.
Previously, I wasn’t as interested in the problem because the solution space was huge. I wasn’t sure that I even knew the techniques that would perhaps be required to ultimately solve the problem. The possible size of the solution space turned out to be the biggest obstruction to getting interested in the problem.
Hence, when we talk about famous scientists and mathematicians obsessively chipping away at problems, we are perhaps only observing the fact that they were “smart” enough to reduce the solution space on their own, and hence knew that they were close to a complete solution. Achievement is not a result of focus. Focus is a result of smartness and achievement.