# How to attack an unknown problem.

• AlbertEinstein
In summary, when faced with a problem, it is important to clearly define the problem and determine what would be considered a successful solution. Then, it is helpful to try and visualize the solution and consider possible approaches based on the constraints of the problem. If stuck, it may be beneficial to try a numerical solution or simulation. In cases where the problem crosses into other subject areas, intuition and experience may play a role in determining how to apply outside ideas. When proving a conjecture, it is often helpful to start with something that is known to be true and use that as a starting point to build upon. And finally, it is important to keep trying and experimenting, as sometimes the solution may come after many failed attempts.
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?

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.

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).

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."

AlbertEinstein said:
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?
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 said:
Hi,

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

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

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?

To general of a question.

http://www.triz-journal.com/" is a Russian solution to systematic invention problem solving. It is a very involved procedure, but has a central core of solid problem solving.

Last edited by a moderator:
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.

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

## 1. How do I approach an unknown problem?

The first step in attacking an unknown problem is to gather as much information about it as possible. This includes identifying the problem, understanding its scope and context, and identifying any available resources that may help in finding a solution.

## 2. What is the importance of defining the problem in attacking an unknown problem?

Defining the problem is crucial in attacking an unknown problem because it allows you to clearly understand the issue at hand. Without a clear definition, it is difficult to determine the appropriate approach and potential solutions.

## 3. How can I break down a complex unknown problem into smaller, more manageable parts?

One strategy for breaking down a complex unknown problem is to use the divide and conquer method. This involves breaking the problem into smaller sub-problems that are easier to understand and solve. Another approach is to analyze the problem using a systems thinking approach, which considers the interconnectedness of different elements in a problem.

## 4. What are some effective problem-solving techniques for tackling an unknown problem?

Some effective problem-solving techniques for tackling an unknown problem include brainstorming, which involves generating multiple ideas and solutions, and trial and error, which involves trying different approaches and learning from mistakes. Other techniques include root cause analysis, which helps identify the underlying cause of the problem, and SWOT analysis, which assesses the strengths, weaknesses, opportunities, and threats related to the problem.

## 5. How do I know when I have successfully solved an unknown problem?

Solving an unknown problem is not always a clear-cut process, and success may look different for each individual. However, some signs that a problem has been successfully tackled include a clear understanding of the problem, the implementation of a solution that addresses the root cause, and measurable improvements in the situation. It is also important to reflect on the problem-solving process and identify any areas for improvement in future problem-solving endeavors.

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