In my imagined math life, my research and writing would never stall. I would do other things, but take some time to keep working on my favorite problems every day. I would think about math as I walked home sometimes, and get little ideas, and then work these out after dinner. I would take vacations, but somehow not forget anything while I was gone. In this world I also do yoga every day and never waste time on the internet. I assume that some people actually live in this world, and I assume that they are super productive mathematicians and wonderful people. This is not my real world. In this world, I completely ignore my research for stretches of time and then need to start again. There are great parts to this world, too; I get totally immersed in other stuff that I enjoy, for example. The downside is that I constantly face the problem of restarting my research. And no matter why I stopped—whether because I got busy with something else or because I was totally stuck—starting again is really hard.
When I haven’t been working on a research problem for a while, it becomes a fearsome monster in my mind. I remember it as giant, surly, and toothy, and I become convinced that wrestling with it will only result in frustration and humiliating defeat. Often this is not true—I know that when I worked on it last, I made progress and maybe had lots of ideas for what to do next if only I’d had more time. When I was working on it last, I was immersed, excited, sure I would win. Now, though, I have forgotten everything. I don’t remember the definitions or the most basic results. Anything would be more pleasant than actually facing that vagueness and confusion. Writing a blog especially!
When I have finished doing some math but need to write it up, I have a different but similar problem. It seems that everything important is done, I understand it all, why do all the drudgery right now? It is nothing, it will take no time at all, so why don’t I just do this much more entertaining and interactive work? In fact, the writing is an enormous undertaking and usually the time when I find lots of mistakes and realize that I misunderstood something important. There are actually many small monsters lurking, perfectly capable of eating me alive, and in the back of my mind I know that my heart will drop in my chest over and over again as I discover these monsters in my “finished” work. Putting words on a page and, through this process realizing that I don’t really understand what I thought I did, is probably even less pleasant than picking up that pen to work on something that I know I don’t understand. Again, to be avoided–maybe I should work on that blog!
Well, I am now writing that blog, specifically so that I don’t have thinking about it as an excuse to avoid research and writing for the next few weeks. I just arrived in Cambridge MA for a four week research visit at MIT. As I’ve mentioned before, at Colorado College, where I teach, classes are organized into 3.5 week blocks (instead of semesters or quarters). This year, I will teach four out of eight blocks. During this time, I don’t think about research at all except for an hour a week during my SWARG* (and to be honest I don’t even make it to that every week). In my mind, the non-teaching blocks are spent mostly doing research. In reality, it is easy for several weeks to slip away just taking care of other important things that I didn’t do while I was teaching. These need to be done, but it is also much easier to complete these tasks than it is to finally pick up the math pen and just start working on my research. It’s also easier to have fun conversations with students who stop by my office, and so many other things. Hence the need for a research-cation away from the office.
So I am here, completely amazed by my good fortune, to get some research and writing done. My first impression of the MIT Math Department is of a sort of mathematical Disneyland, in the sense that mathematicians as famous in the math world as Mickey Mouse is in the larger world are everywhere, there is constant stimulation in the form of a huge array of seminars, and there is limitless free coffee instead of funnel cake. However, that analogy is frivolous, and all wrong in that it misses the essential fact that this wonderful place is also very serious, set up to make working on and talking about math as natural and effortless as possible. If I can’t get work done here, I’m done for. So I’d better do some math. Right after I write this blog, which is much easier than facing the unknown. But it’s time to get to the math now. Wish me luck.
PS Since this post has no special insight to offer about how to get past research and writer’s block, as a consolation, let me offer some pieces about writer’s block and starting something hard, which I read instead of starting to work on my research: