I have intuitions about things, even though I can’t make precise what I’m thinking. A student today, was saying they were stuck on a problem in algebraic geometry. And I said, “just pullback, pullback, pullback” and he said quickly, “there’s nothing to pullback here.” Then another student said, with more precision, “oh just pullback this map blah blah specifics” and he agrees that’s the right solution. I say, “I just told you to pullback!” And that sort of thing happens frequently when I speak to people. I’ll have the right idea, and I know I’m on the right track, but I can’t make precise what I’m saying, so people think I’m wrong.

I’m an intuitionist to a fault and I liken myself more to a physicist because of the way I generalize material. But this won’t get me better at research mathematics. No, this is going to hold me back if I’m not able to zoom in and speak like everyone else. I feel degenerate in that way, because I know I’m insufficiently communicating. Joon said, “you’re not a bad analyst, you just need practice.” What I need is precision. Some of this is actually a manifestation of my inability to fully pay attention to things. If I am intaking the information and it’s fuzzy, the output will also be fuzzy. I’m working on clearing my mind.

Today is Friday, which means everyone is going to go somewhere for happy hour. But I’d rather we just all hang around and do math for fun. Of course that won’t happen.

I discovered the most beautiful book in the library today, written by a professor and graduate student at MIT. It’s an undergraduate introduction to differential forms, but on the front of the book was a Jordan curve. It’s a beautiful text. Unassuming and not filled with fluff. It’s visually beautiful, as well. I’m going to read it to prepare for manifolds, as I think this exposition and treatment of the subject is very intuitive. I mean they explain how differential forms are analogous to vector fields when speaking about curl. Such a simple sentence but powerful in illumination. I’m pretty Stoked.

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