Art of Problem Solving

[rktpro]

I am not particularly weak when it comes to solving problems in Math,Physics and Chemistry. Instead, I enjoy doing problems. I particularly like difficult problems. Even in tests, I am pleased if the questions asked are unseen and all students stand a fair chance to score. That aside, I wish to know if problem solvers, like those who can solve complex problems of rigid body dynamics, integral calculas etc, really contribute to mainstream? Are all physicist know to be extraordinary problem solvers? Also, how much practice did you do with problens? Thanks.

Edited May 7, 2014 by rktpro

[ajb]

In mathematics* there are roughly two kinds of people;

 

i) The problem solvers

ii) The theory builders

 

Loosely, the problem solvers look for unanswered questions in existing established theories. To be successful they are often able to see how different branches of mathematics intertwine and apply techniques from one branch in another.

 

Then there is the theory builders who look at the general structure of existing theories and generalise them. They are looking for new and novel ways of viewing existing theories as well as opening up new directions.

 

There is of course some overlap and this distinction is not always clear. For example one may need a new theory to solve an existing problem and once a new topic is uncovered there will be hard questions that follow.

 

 

 

* I guess this is also true in theoretical physics.

[Unity+]

In mathematics* there are roughly two kinds of people;

 

i) The problem solvers

ii) The theory builders

 

Loosely, the problem solvers look for unanswered questions in existing established theories. To be successful they are often able to see how different branches of mathematics intertwine and apply techniques from one branch in another.

 

Then there is the theory builders who look at the general structure of existing theories and generalise them. They are looking for new and novel ways of viewing existing theories as well as opening up new directions.

 

There is of course some overlap and this distinction is not always clear. For example one may need a new theory to solve an existing problem and once a new topic is uncovered there will be hard questions that follow.

 

 

 

* I guess this is also true in theoretical physics.

And then there are the theory builders that also do problem solving.

[rktpro]

In mathematics* there are roughly two kinds of people;

 

i) The problem solvers

ii) The theory builders

 

Loosely, the problem solvers look for unanswered questions in existing established theories. To be successful they are often able to see how different branches of mathematics intertwine and apply techniques from one branch in another.

 

Then there is the theory builders who look at the general structure of existing theories and generalise them. They are looking for new and novel ways of viewing existing theories as well as opening up new directions.

 

There is of course some overlap and this distinction is not always clear. For example one may need a new theory to solve an existing problem and once a new topic is uncovered there will be hard questions that follow.

 

 

 

* I guess this is also true in theoretical physics.

Initially, in their young age, theory builders used to be good problem solvers?

[ajb]

Initially, in their young age, theory builders used to be good problem solvers?

I don't know. You can look up some big names and see what you can find out.

[rktpro]

I know about a few physicist and mathematicians like Fermi, Feynman, Hardy, Gauss being extraordinary problem solvers from their biographies, anecdotes etc.