Second, I promise to do mathematics for two hours a day, every day
But this is fishy, right? Because it’s easy to “do mathematics” for two hours every day without really learning anything. I’ve been thinking about the same kinds of problems (i.e. how to reliably learn mathematics) and one of my ideas is to use a formal proof checker. If you put yourself on a tough schedule that says something like “I will prove the first 10 theorems in PLoS by Wednesday”, then when Wednesday comes around you will understand those 10 theorems. The proof checker does not allow hand-waving; if it accepts your proof, you know you’ve achieved something. It also should permit moments of insight where you say “hey… this proof is clunky… what was Jaynes thinking? I can derive this result in 5 lines of HOL light!”
As long as I’m actually working through the texts, I’ll learn more than if I had not done the math at all, so it’s an improvement. Before my resolution, I had sat down to work through one of my texts exactly twice since I graduated and summer began. I’d been aware of my problem and wanted to do something about it for some time, but it seems my akrasia applies even to planning to do something about my akrasia.
This technique only works if you do what you commit to. Once you break your agreement, it stops working very well. You can work X amount, you cannot decide you will accomplish Y amount; what if it turns out one of the problems is much harder than you expected, or simply takes longer to work through, you will not get everything done, which will weaken the technique in the future.
But this is fishy, right? Because it’s easy to “do mathematics” for two hours every day without really learning anything. I’ve been thinking about the same kinds of problems (i.e. how to reliably learn mathematics) and one of my ideas is to use a formal proof checker. If you put yourself on a tough schedule that says something like “I will prove the first 10 theorems in PLoS by Wednesday”, then when Wednesday comes around you will understand those 10 theorems. The proof checker does not allow hand-waving; if it accepts your proof, you know you’ve achieved something. It also should permit moments of insight where you say “hey… this proof is clunky… what was Jaynes thinking? I can derive this result in 5 lines of HOL light!”
As long as I’m actually working through the texts, I’ll learn more than if I had not done the math at all, so it’s an improvement. Before my resolution, I had sat down to work through one of my texts exactly twice since I graduated and summer began. I’d been aware of my problem and wanted to do something about it for some time, but it seems my akrasia applies even to planning to do something about my akrasia.
This technique only works if you do what you commit to. Once you break your agreement, it stops working very well. You can work X amount, you cannot decide you will accomplish Y amount; what if it turns out one of the problems is much harder than you expected, or simply takes longer to work through, you will not get everything done, which will weaken the technique in the future.