First term of a proof based course. A single exercise ate 40 minutes last night and I still did not finish it, and there are six on the sheet. My classmates all say it took them twenty minutes so I cannot tell if I am slow or if everyone is quietly lying. How long should one of these actually take?
What worked for me: a hard 25 minute timer. When it goes off I write down, in words, what I have tried and where it broke, then I move to the next problem. Coming back the next morning, roughly half of them cracked in under ten minutes. Sleep does something to these that grinding does not.
Started doing the sheet the day it is set rather than the night before it is due purely so this trick is available. Biggest single grade change I made.
It also gets faster in a very specific way. You will not think faster, you will recognise faster. Around week seven you start reading a statement and thinking, that is an induction, or that smells like contradiction, and the 40 minutes turns into 15 because you skip the flailing stage.
Worth asking your lecturer how long they expect a sheet to take. Mine said six hours for six problems and half the room visibly relaxed.
Your classmates who finished in twenty minutes had either seen a near identical proof before or they wrote something that will not survive marking. Both are extremely common. Do not calibrate on other people's self reports.
@corwin_ashby · 2w ago · 3 replies
Forty minutes on a proof you have not seen the shape of before is completely ordinary and often on the fast side. Computation problems have a time you can estimate. Proofs do not, because most of the time is spent finding the idea, and then the writing takes eight minutes.
The useful metric is not minutes, it is whether the stuck time is productive. Circling the same dead end for 40 minutes is bad. Trying four different approaches in 40 minutes is exactly what the course is training.
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@napgapnora · 2w ago
Four approaches would be generous, I think I tried the same one three times with different handwriting.
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@corwin_ashby · 2w ago
Then that is the thing to fix, not your speed. Keep a running list of the techniques the course has given you and force yourself down the list when stuck.
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