This week I’ve been thinking about some problems outside my usual zone of expertise — namely, questions about the mapping class group and the Johnson kernel. This has been my week:
- Three days of trying to prove a cohomology class is nonzero;
- Then over Thanksgiving I worked out an argument that it was zero and was confused about that for a couple of days because I feel quite deeply that it shouldn’t be zero;
- This morning I was able to get myself kind of philosophical peace with the class being zero and was working out which refined version of the class might not be zero;
- This afternoon I was able to find the mistake in my argument that the class was zero so now I hope it’s not zero again.
- But I still don’t know.
There’s a certain frustration, knowing that I’ve spend a week trying to compute something which some decently large number of mathematicians could probably sit down and just do, because they know their way around this landscape. But on the other hand, I would never want to give up the part of math research that involves learning new things as if I were a grad student. It is not the most efficient way, in the short term, to figure out whether this class is zero or not, but I think it probably helps me do math better in a global sense that I spend some of my weeks stumbling around unfamiliar rooms in the dark. Of course I might just be rationalizing something I enjoy doing. Even if it’s frustrating. Man, I hope that class isn’t zero.
Surely by now you have realized that when you think “aha! experts in area X will be able to instantly answer my problem” they almost invariably cannot. Well, unless that expert is Beilinson. Come to think of it, I have a question I want to ask Beilinson; I should go do that.
Or maybe you should spend a week being a grad student about it first!
Oh I am doing that already! (three weeks so far). I believe (and you probably agree) that before asking a question, you should first do at least one relevant thing on your own first, even if it turns out to be stupid or even wrong — having thought about it yourself, you are more receptive to the wisdom of the oracle.
What’s the class?
If that question was directed towards me, I meant it (“being a graduate student”) only in the metaphorical sense — thinking about something one don’t understand and being confused.
Ah sorry, no — I meant, what’s the *cohomology* class!