How to attack an unknown problem.

AlbertEinstein

Suppose you were given a problem.How do you attack it, I mean to say how to proceed and what ideas to apply in solving that problem?

berkeman

Depends on the subject matter. Do you have a specific subject area in mind? I'll usually try to picture what the solution will be like, and then try to picture what approach I can use to get me there. I also like to look at the constraints on the problem, and let them "teach" me how to approach the solution. I generally need to remind myself that the problem is physical, so there should be a physical solution (or solutions). Finally, if I'm stumped temporarily, I'll look to see if I can code up a numerical solution or simulation to help give me some insight into a quantitative solution.

AlbertEinstein

However there are many problems which require the concepts of other branches, in that case how do you reconise how to apply that "outside idea".Does this depend on intution or experience or are both the equivalent?

Another thing, suppose a mathematicisn has to prove a conjecture.Then how he determines how to use an idea and prove it in a few pages to 50-75 pages or more than that(poincare conjectyre was settled in 300 pages).

matt grime

In the words of Feynmann, approximately, "you might think that this is a clever idea, so let me tell you of the hundreds of stupid ones I had before I came to the clever one."

DaveC426913

First thing is to define, clearly, what the problem is.

Second is to determine what would be considered an appropriate form of the outcome (how can you demonstrate that you've solved it?)

Edgardo

Hi,

have a look at here:
http://www.math.utah.edu/~pa/math/polya.html
http://www.math.grin.edu/~rebelsky/P...ays/polya.html

Those are summaries of the book "How to solve it" by George Polya.

berkeman

Thank you for that! I was trying to remember what the name of the book was that I read long ago that gave me so many thinking tools that I've used over the years. I couldn't figure it out with a search, but that name Polya rings the bell! I'm going to go get a copy for my kids. Thanks again!

JasonRox

I think the first and second steps are the most crucial. The other steps seem to follow from them since you are trying to solve a problem.

If you don't understand the problem fully, forget it. You'll never solve it.

If you don't have a plan, that's useless too. Where to start solving it?

Integral

To general of a question.

TRIZ is a Russian solution to systematic invention problem solving. It is a very involved procedure, but has a central core of solid problem solving.

Karlisbad

For me the "method" would be this:

a) reduce the problem to a "Math" expression (only numbers and equations) and then ask help to a mathematician.

b) Seek for a problem you can solve and consider your problem as "just" a
perturbation of your initial problem under several conditions.

c) If you are a "Computer maniac" use your Pc or Mac to find a numerical
solution and try to justify the result.

d) change the condition of the probem or approximate it.

e) take advantage of some similar result used before.

Office_Shredder

Considering this is posted in the math section, I don't think reducing the problem to numbers is very useful.

About proving the conjecture... usually you start with something you know is true, and you just start figuring out what else you know is true. Three days later, you shave, drink some coffee, and realize you solved it after about an hour of work

The second step is purely optional of course, but gives you good stories to tell fellow mathematicians