I spent several hours this weekend trying to track down, learn, assimilate, and decipher more math for the paper on Laguerre planes. I was very successful at learning about the generalized quadrangle, but only partially successful learning anything that was actually relevant to my paper. (Some of it was really exciting, though.) I also spent several hours producing most of the second draft of the paper, which has a radically different (improved, I hope) structure from the first draft.
Learning math is hard. Organizing math concepts the way you want to write them is challenging and enjoyable. Actually writing math is...astonishingly easy. I can't believe how much easier it is to put words on paper for math than when I'm writing something like an English essay or history paper. I think it may be that I have so much material, and math is so straightforward, that there just aren't nearly as many issues with wording. And the issues you do have are about trying to make things as clear and understandable as possible, which is something I enjoy.
I was really apprehensive about this project at the beginning of the semester. I traditionally produce good papers, but I have a hard time making myself do so, and I don't really like papers or projects. I was also worried that I wouldn't be able to figure out enough math to produce a whole five pages. (My paper is currently six pages, not counting figures, and if I can write the final section it will probably be seven or eight total.)
Instead of it being a horrible nightmare, I've enjoyed it immensely.
But what's funny about it is, had I known how much work I would be doing, and how hard it would be, I would have been even more scared than I actually was. I've done so much hard work for this. I've pursued (sometimes successfully, sometimes not) so much crazy math. I've pursued the same crazy math over and over until I got it. And I've spent many hours (20, perhaps, so far?) just writing the paper, making the figures, and getting Latex to do what I wanted.
So it is definitely not that it's been easier than I expected. It's that it has been much more satisfying and enjoyable, and easier to get myself to work on, than I ever hoped.
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2 comments:
Do you think you would have enjoyed the process as much if you had been studying another (say, non-geometry-related) math topic? I guess I mean, do you have a sense to what extent your positive experience was about the topic (general or particular) or just about doing math? I suppose this also brings up the question: do you think you would (will) find it similarly exciting to do another math paper in the future?
There is definitely some kind of math that I like much better than other kinds, and I think this geometry falls into that basket. (I like stuff with axioms, discrete stuff, things with more letters than numbers, stuff that is not very calculation-oriented.)
But I don't see anything that special about Laguerre planes or, really, projective geoemtry. I think I could have enjoyed something in abstract algebra or discrete math, etc., just as much.
That's my guess, anyway.
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