I have a take home math exam and I'm kind of freaking out because I can't get any of the questions even though I've been working on it for hours for several days. It's open notes and no collab. Any tips on what to do??

Response from Marty:

That’s a tough position. I know it’s really stressful but I promise you that you’ll be more creative if you’re relaxed. Do whatever you need to do to calm down. Maybe take a few hours off to watch tv or meditate or exercise. I find that it’s helpful to try to put things in perspective - maybe talking to a friend of yours about their life will be good. Once you have internalized that everything is fine and that you just need to do your best, get back to work. I assume by now you’ve tried a few things for each problem. That’s great because it means you have a sense of the heart of each problem. My next move would be to skim through all the notes you have access to. Go through the chapters in the textbook or whatever and read each theorem. For each theorem, look at all the  problems and ask yourself ‘could this possibly be useful’? This is quicker than it sounds because a lot of theorems can be dismissed immediately. However, I suspect that at least once you’ll read something and be like, ‘wait a minute, the conditions of this theorem sort of match the conditions in this problem.’ At that point, you start thinking about how you could solve that problem under the assumption that this theorem is relevant. What do you need to do to apply the theorem? What does it give you? How could that possibly be helpful? This might put you down a path towards making progress.

This is usually sufficient for solving a few problems. I’ve yet to see a take home exam where there isn’t one problem that can’t be solved without much creativity. Just being super familiar with all the relevant theorems should get  you somewhere. Indeed some of the problems will require that you have a great idea, but you’ll be in a better mental space once you have some problems done. For those, I would say working on and off is important. Spend a few hours thinking about it, and then set it aside for a little bit. Relax and try to enjoy yourself without thinking about math and then come back a little later. The name of the game is just trying random shit til something works out, so taking time off lets you come up with more and more wacky ideas.