How to Solve Hard Problem Sets Without Staying Up All Night

> your brain can only work productively on a hard problem for 1 -3 hours before needing to reboot

This is very different from my experience. For advanced math or physics problems, it general takes at least a couple of hours to assemble the relevant mathematical structure in your head. Only once you are familiar with the "setting" can you really start to work.

I've heard similar things about writing code.

If I took a break every 2 hours, I'd never get anything done.

I solved most of my graduate algorithms problems while lying in bed in the morning, lying on the couch, or in the shower. I simply do not understand how some people can concentrate on problems like that while jogging. My thoughts while jogging are primarily about how much jogging sucks and how I just gotta keep going. If I could solve a technical problem in my head while exercising then either the problem is really easy or I'm not getting very much exercise.

You should also work while standing up.

There's a reason why academics prefer whiteboards and chalkboards to pen and paper. It's because they feel genuinely more productive and creative while working on them. I personally think that it comes down to improved blood flow, and it's one of the key tricks that my friends and I used to earn physics degrees from Caltech. We'd go camp out in empty lecture halls late at night, filling chalkboard after chalkboard with scrawl, and only sit down to copy finished problems in their final form.

Meat of the article: "Repeated fresh attacks are how hard problems are solved in the real world. ... Until you’ve approached a problem fresh, 3 – 4 times, you haven’t really yet tried to solve it."

"When you’re given a reading assignment, for example, you can estimate, within 10 – 20 minutes, how long it will take you to complete."

As long as it's not a scientific paper...

> The ideal configuration for a problem set is a single partner who is at roughly your ability and is willing to meet earlier in the week.

I agree with everything he said, but in my experience, the part I've quoted is at least an order of magnitude more important than the rest. And don't forget the "roughly at your ability" part - if you work with someone much smarter, you may just get more confused and you certainly won't feel like you're contributing much; if you work with someone much less smart, it's a waste of time (which is not to say that helping people isn't a nice thing to do - it just won't help you complete the problem set).

This mostly matches up with my own experience. I always start several days early, and I always work with one or two other people if at all possible.

Starting several days early gives you a few days to think about a problem if you need it and ensures you don't have to pull any really late nights.

Working with people means that you won't get stuck on the easy problems if you didn't understand everything perfectly or forget one crucial fact/lemma exists (which I find is otherwise a real danger). It also gives you people to bounce ideas off of for the really hard problems,

The other thing I always do is to do my problem sets in two stages. In the first stage (which I do with other people), I figure out how to solve the problem and outline how I'm going to write it up. In the second stage (which I do alone and after solving everything), I write the problems up. As I do this, I walk through how we did the problems when we first solved them, and very often find mistakes we made.

There's also the http://www.c2.com/cgi/wiki?FeynmanAlgorithm (it's a pretty good C2 post).

>The ideal configuration for a problem set is a single partner who is at roughly your ability and is willing to meet earlier in the week.

There's really a lot of substance to this remark. I work with another guy in my class frequently and often come away feeling as though I've free-ridden somewhat.

But after looking more closely the results we get, it becomes apparent they are the product of our combined efforts and wouldn't have been achievable alone. The verbalisation is also highly conducive to understanding intuitively - a principle Salman Khan talks about and I can't agree with enough.

I gotta ask, is this a really dedicated & not too bright student or a crazy hard curriculum? Most educational problems are not this hard.

One tip I'd add: don't limit asking for prof/TA help to office hours. Knock and ask politely, and most (all, in my experience) will gladly answer questions on homeworks or lectures. Many seem to appreciate the chance to have a break from their work to talk with a student.

Sometimes I found solution in my dreams.