Is there shame in not being able to solve a difficult problem?

[SpdOfLiteSqrd]

Whenever I come across something that takes me hours to find a solution, I feel satisfied that I figured it out myself after arduous examination. But there are some problems that I either get impatient with or find myself needing to look up a complete solution because I cannot finish it on my own. Especially problems that are abstract and more of an examination of my approach to a problem than demanding a solution. I never just jot down the answer and move on, I always fashion an understanding of the solution by repeating the problem on my own with the new knowledge and grind into myself the process needed for future problems. But I always feel at a loss because I couldn't do it myself. So is there a shame to it, or do I need to lose the ego and stop being hard on myself?

 

[Rocket50]

There is nothing wrong with that. It happens with everyone. Just solve more problems.

 

[heatengine516]

It's aggravating to me as well but I've learned not to linger on it. You win some, you lose some. These days if I hit a problem like that it feels fine to just do what I can and move on.

 

[Choppy]

One thing I've learned in my experience is that sometimes the odds are stacked against you.

I've struggled with a lot of problems only to find that there was a small error in how it was written, or that part of the problem was abiguous and I interpreted it incorrectly, or something of that nature.

Sometimes you learn by struggling with a problem, but eventually you reach a point of diminishing returns after which you're just wasting time. Good students learn to recognize this point quickly.

 

[SpdOfLiteSqrd]

One thing I've learned in my experience is that sometimes the odds are stacked against you.

I've struggled with a lot of problems only to find that there was a small error in how it was written, or that part of the problem was abiguous and I interpreted it incorrectly, or something of that nature.

Sometimes you learn by struggling with a problem, but eventually you reach a point of diminishing returns after which you're just wasting time. Good students learn to recognize this point quickly.

Is my approach what those good students generally do or is there an alternative?

 

[DEvens]

Nobody has been able to reduce problem solving to a recipe. But there are some general broad hints.

First, get an image in your head of the goal you are trying to reach by doing problems. Pay attention to whether working on a given problem is helping that goal. If you are thrashing on a problem, maybe set it aside and work on another problem. If you have time, come back to it. Everybody thrashes on problems now and then. "But this is... Then that can't be... Oh but what about..." And then around and around in a circle that gets you nothing. Notice when that happens and get out of the loop.

Practice, practice, practice, practice. Hopefully you see the trend by now.

Read more than one textbook on a given topic. A different viewpoint often helps.

Make up your own problems and solve them.

Try to get problems that are just inside your current ability range, with just a very few that are just a tiny bit beyond. You can finish most of them and get a warm fuzzy feeling. Then stretch yourself on the posers.

Look for the "box." Problems are often set with definite methods of solving them in mind. Maybe that method really is easier.

An approximate answer may help you to the real answer. So doing an integral for example. You might be able to get an answer that is within 30 percent of the real answer by doing some trapezoids under the curve and adding them up.

Do any part of the problem you do understand, then look at the problem again.

 

[mal4mac]

One of Hawking's class mates was a bit upset when him saw him solving problems in a few minutes that took him, and everyone else, hours to do. Still, the guy who said that still made it being a physics lecturer! (Not as famous as Hawking, though...)

 

[Choppy]

Is my approach what those good students generally do or is there an alternative?

I don't know any method that works better than practice... maybe practice with deadlines.

 

[462chevelle]

I have trouble solving simple problems sometimes, if that makes you feel any better.

 

[Ritzycat]

I can also attest to sometimes not being able to solve very simple problems... sometimes its due to stupid mistakes and sometimes its due to me not having it second nature, completely understood. Sometimes it's a combination of the two for me. If I have trouble solving simple problems sometimes, I'd say there's no shame in getting a few difficult ones wrong!

 

[Medicol]

Whenever I come across something that takes me hours to find a solution, I feel satisfied that I figured it out myself after arduous examination. But there are some problems that I either get impatient with or find myself needing to look up a complete solution because I cannot finish it on my own. Especially problems that are abstract and more of an examination of my approach to a problem than demanding a solution. I never just jot down the answer and move on, I always fashion an understanding of the solution by repeating the problem on my own with the new knowledge and grind into myself the process needed for future problems. But I always feel at a loss because I couldn't do it myself. So is there a shame to it, or do I need to lose the ego and stop being hard on myself?

You think too much about your capability. Independent works rarely gain a lot of fruitful results and more mutual understandings.
If you run into any hard problems again, please share them on PF, we'll take a look at them for you.
On PF, you.will.never.feel.lost.AGAIN.

 

[462chevelle]

I can also attest to sometimes not being able to solve very simple problems... sometimes its due to stupid mistakes and sometimes its due to me not having it second nature, completely understood. Sometimes it's a combination of the two for me. If I have trouble solving simple problems sometimes, I'd say there's no shame in getting a few difficult ones wrong!

Mine is mostly from overthinking things, i have a hard time making certain assumptions that seem counter intuitive.

 

[paalfis]

One of Hawking's class mates was a bit upset when him saw him solving problems in a few minutes that took him, and everyone else, hours to do. Still, the guy who said that still made it being a physics lecturer! (Not as famous as Hawking, though...)

In my personal opinion, I don't think that great problems solvers would surely be the better scientists in the future. Nobody will write you a problem in a piece of papper for you to solve (if you are not theoretical). Asking the right questions is as important as answering them, knowing how to apply what you are trying to prove is also crucial.