It feels good to be back "in the game." Granted, I'm still doing more reading than anything else. I was suggested a new paper to read, but on a wholly different topic this time: last week it was Hajlasz, Sobolev spaces, and approximations on manifolds and metric spaces, and this week it's Milnor, smooth functions, and manifold theory.
I've learned a few lessons already:
- Fibre bundles are pretty cool, once you hear about them from someone who understands them.
- I will never again underestimate how hard the smooth category is. Before I was mistaken: I thought once you had a smooth function, then life was relatively easy.
Suffice to say, that is far from the truth!
So long a time spent, writing something, and so equally long a time spent reading the same something! I could make an analogy to Achilles and the tortoise, but just mentioning that probably gives my meaning already.
One last thought about reading and work: the list piles up and up. Besides Milnor, there is material to read about:
- the Ahlfors Measure Conjecture, for a student talk for my Hyperbolic manifolds class;
- Gromov-Hausdorff convergence of metric spaces, for a talk I promised the folks at Student Geometry-Topology Seminar;
- and certainly not least, my prelim reading!
The books by Evans-Gariepy and by Mattila are sitting in my bookbag and if I don't start now, I won't know the results and details well enough to talk competently about them!
4 comments:
... and after?
Afterwards I went home, read a bit from Mattila's Geometry of Sets and Measures in Euclidean Spaces, and then watched a DVD.
I like Thursday nights: nice and calm. (;
I meant to ask if the line of your thoughts (or is that an unrectifiable curve?) was affected by the Brown Jug meeting.
My professor in Alg.Topology class once handed out photocopies of Milnor's paper. The prof, the class and the paper were all v.cool, but I hated them all (and still do.)
This Thursday I pulled an all-nighter grading tests. 8-/ Needless to say, Friday's lectures were not among my best.
I'm not sure which thoughts you meant. Everything has an effect, sure enough, but if you want to know whether I still think that (a) vector bundles are cool and that (b) results in the smooth category are hard, then yes.
As for my thoughts on how long it takes to read/write mathematics, when I wrote that, I don't think I meant to be pessimistic (though rereading it now, it may seem that way) and after the Brown Jug, I wasn't any less optimistic about it.
Let me add a caveat, here. I'm unsure of when it began, but I've resigned myself to the fact that I will never understand all the mathematics that I wish to understand. The interesting thing is that I find that a very relieving fact. Think of the alternative: if one day you could achieve all the maths that you ever wanted, then what would you do next?
It's kin to that legend concerning Alexander the Great: it's said that after he conquered all the lands that he could conquer, he fell to the ground and wept, for he could no longer struggle, and as a result, no longer win.
Post a Comment