stranger in a familiar land: hard = good?

today i attended a seminar talk where simultaneously,

• i could parse the statements that the speaker was saying and writing on the blackboard, and they seemed reasonable,
• i had no idea what was going on.

in particular i could not tell what was hard and what was not; unfortunately, in my experience it's a typical sign of fundamental incomprehension.

yes, this should be a normal, even average experience for mathematicians. we are ultimately specialists, after all, and aside from our (few) topics of interest and expertise, there is little that we truly understand.

i suppose it means that, at my current university, we've been inviting speakers whose work is very common to ours. as a result i haven't really had to deal with utter confusion on a regular basis.

confusion, however, is oddly comforting [1].

it suggests that maybe we are approaching the boundaries of our understanding; perhaps doing so, we can extend them.

conversely, i get a little nervous when the proof to a theorem is a little too simple. it either means that there is an error somewhere and i missed the difficult, worthwhile part, or that the theorem wasn't "worth" proving.

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in other news, this research visit has gone very well so far. my co-author and i are making a lot of progress .. and of all things, our ideas from last time actually seem to be working! (-:

i liken it to going hiking with the right trail companion: every day there's ground to cover, so when one is going at a good, hard clip, one can't help but feel good .. from the shared experience of an honest day's toil.


[1] unless, of course, the speaker or author is doing an incredibly bad job at exposition, in which case it's just unnecessarily frustrating.