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Is it okay to prioritize problem-solving over theory when studying physics or math? (sh.itjust.works)

submitted 1 day ago by [email protected] to c/[email protected]

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I have a unique way of studying that seems to work well for me, but I’m curious if it’s a good long-term strategy.

Whenever I start a new topic in physics or math, instead of diving into the theory or derivations, I first skim through a variety of solved problems to get a sense of the types of questions typically asked. I take notes on the key concepts and methods I encounter, focusing on recognizing patterns across different problems.

Once I’ve built a mental "map" of the topic through problem-solving, I attempt unsolved problems using my notes and keep adding new observations as I go. By the end, I feel confident about most question types and can solve them quickly. After that, I might revisit the theory with a sense of curiosity, wanting to understand the "why" behind the formulas and patterns I’ve observed.

This approach has helped me become faster at solving problems compared to my peers. However, I sometimes worry that I might miss out on deeper conceptual understanding, especially for rare, extremely challenging problems.

The reason I lean toward this method is that I tend to forget theoretical details over time, but problem-solving strategies stick with me much longer. It feels like I develop an intuitive "second brain" for tackling problems.

So, is this a valid way to study? Or should I switch to the more conventional approach of learning theory first and then solving problems?

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[–] [email protected] 2 points 1 day ago* (last edited 1 day ago)

I would say... This is exactly how you should do it, and the "conventional" way is pretty stupid.

Everything we've discovered so far in science was to "solve" some kind of "problem". I don't mean "solve problem" in the way it's usually used, like idk figure out what's the most efficient way to travel from A to B, but in the way "there's some unexplained phenomenon here and our existing models don't cover it, so we gotta figure out a solution that works (predicts it)".

For all these new problems, it doesn't help you to be able to understand a theory by reading, it helps if you know how to problem-solve, i.e. figure out ways to apply your existing knowledge in previously non-existent combinations. Of course you got to have the knowledge of the previous theories or concepts to not go down routes already traveled, so you gotta learn your theory. But the methods you're building by being problem-focused is imo exactly what you need to build to actually work in the real world and not just in an academic, "get your degree" kind of way.