WMC REU – Week 4, or, “To Prove a Lemma”


The students in my research group are superlative! They’re funny, intelligent, hard-working; basically, they kick serious ass. It’s easy to get frustrated during the research process. The project I designed is no different, and we’re facing our first hurdle.

When you read someone else’s proof, often you’ll think, “Well, yeah. Duh. That’s easy enough.” But here’s the thing: every problem is hard (until it’s easy). At least half of the work is the process of framing the problem the right way so that you can use the right tools. We have a problem that we’re trying to solve, but there are a lot of competing pieces of information.

To try to help out with the framing process, I took the various moving parts and used them one at a time in a sequence of reductions (numbered 0 through 4, ish). After the reductions, we have a lot of powerful assumptions that we can use. At the end of our working day on Tuesday, I felt confident that we had set ourselves up for a quick slam-dunk to win the game.

…Ha. When I got home, I started playing around and found that I couldn’t get very far. As of this Wednesday morning, it turns out, no one got very far. Back to the whiteboard for us.

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