How to solve it - wikipedia How to solve it First edition ( publ. Princeton University Press ) How to Solve It ( 1945 ) is a small volume by mathematician George Pólya describing methods of problem solving. Contents 1 Four principles 1.1 First principle : Understand the problem 1.2 Second principle : Devise a plan 1.3 Third principle : Carry out the plan 1.4 Fourth principle : Review / extend 2 Heuristics 3 Influence 4 See also 5 Notes 6 References 7 External links Four principles How to Solve It suggests the following steps when solving a mathematical problem : First, you have to understand the problem. After understanding, make a plan. Carry out the plan. Look back on your work. How could it be better ? If this technique fails, Pólya advises : `` If you ca n't solve a problem, then there is an easier problem you can solve : find it. '' Or : `` If you can not solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem ? '' First principle : understand the problem `` Understand the problem '' is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they do n't understand it fully, or even in part. In order to remedy this oversight, Pólya taught teachers how to prompt each student with appropriate questions, depending on the situation, such as : What are you asked to find or show ? Can you restate the problem in your own words ? Can you think of a picture or a diagram that might help you understand the problem ? Is there enough information to enable you to find a solution ? Do you understand all the words used in stating the problem ? Do you need to ask a question to get the answer ? The teacher is to select the question with the appropriate level of difficulty for each student to ascertain if each student understands at their own level, moving up or down the list to prompt each student, until each one can respond with something constructive. Second principle : devise a plan Pólya mentions that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included : Guess and check Make an orderly list Eliminate possibilities Use symmetry Consider special cases Use direct reasoning Solve an equation Also suggested : Look for a pattern Draw a picture Solve a simpler problem Use a model Work backward Use a formula Be creative Applying these rules to devise a plan takes your own skill and judgement. Third principle : carry out the plan This step is usually easier than devising the plan. In general, all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work, discard it and choose another. Do n't be misled ; this is how mathematics is done, even by professionals. Fourth principle : review / extend Pólya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked and what did n't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem. Heuristics The book contains a dictionary - style set of heuristics, many of which have to do with generating a more accessible problem. For example : Heuristic Informal Description Formal analogue Analogy Can you find a problem analogous to your problem and solve that ? Map Generalization Can you find a problem more general than your problem ? Generalization Induction Can you solve your problem by deriving a generalization from some examples ? Induction Variation of the Problem Can you vary or change your problem to create a new problem ( or set of problems ) whose solution ( s ) will help you solve your original problem ? Search Auxiliary Problem Can you find a subproblem or side problem whose solution will help you solve your problem ? Subgoal Here is a problem related to yours and solved before Can you find a problem related to yours that has already been solved and use that to solve your problem ? Pattern recognition Pattern matching Reduction Specialization Can you find a problem more specialized ? Specialization Decomposing and Recombining Can you decompose the problem and `` recombine its elements in some new manner '' ? Divide and conquer Working backward Can you start with the goal and work backwards to something you already know ? Backward chaining Draw a Figure Can you draw a picture of the problem ? Diagrammatic Reasoning Auxiliary Elements Can you add some new element to your problem to get closer to a solution ? Extension Influence It has been translated into several languages and has sold over a million copies, and has been continuously in print since its first publication. Marvin Minsky said in his paper Steps Toward Artificial Intelligence that `` everyone should know the work of George Pólya on how to solve problems. '' Pólya 's book has had a large influence on mathematics textbooks as evidenced by the bibliographies for mathematics education. Russian physicist Zhores I. Alfyorov, ( Nobel laureate in 2000 ) praised it, saying he was very pleased with Pólya 's famous book. Russian inventor Genrich Altshuller developed an elaborate set of methods for problem solving known as TRIZ, which in many aspects reproduces or parallels Pólya 's work. How to Solve it by Computer is a computer science book by R.G. Dromey. It was inspired by Pólya 's work. See also Heuristic How to Solve It By Computer Inventor 's paradox Notes Jump up ^ Pólya, George ( 1945 ). How to Solve It. Princeton University Press. ISBN 0 - 691 - 08097 - 6. Jump up ^ Pólya 1957 pp. 6 - 8 ^ Jump up to : Pólya 1957 pp. 8 - 12 Jump up ^ Pólya 1957 pp. 12 - 14 Jump up ^ Pólya 1957 pp. 14 - 15 Jump up ^ Pólya 1957 p114 Jump up ^ Pólya 1957 p33 Jump up ^ Pólya 1957 p214 Jump up ^ Pólya 1957 p99 Jump up ^ Pólya 1957 p2 Jump up ^ Pólya 1957 p94 Jump up ^ Pólya 1957 p199 Jump up ^ Pólya 1957 p190 Jump up ^ Pólya 1957 p172 Pólya advises teachers that asking students to immerse themselves in routine operations only, instead of enhancing their imaginative / judicious side is inexcusable. Jump up ^ Pólya 1957 p108 Jump up ^ Pólya 1957 pp103 - 108 Jump up ^ Pólya 1957 p114 Pólya notes that ' human superiority consists in going around an obstacle that can not be overcome directly ' Jump up ^ Pólya 1957 p105, p29 - 32, for example, Pólya discusses the problem of water flowing into a cone as an example of what is required to visualize the problem, using a figure. Jump up ^ Pólya 1957 p105, p225 Jump up ^ Pólya 1957 pp141 - 148. Pólya describes the method of analysis Jump up ^ Pólya 1957 p172 ( Pólya advises that this requires that the student have the patience to wait until the bright idea appears ( subconsciously ). ) Jump up ^ Pólya 1957 pp148 - 149. In the dictionary entry ' Pedantry & mastery ' Pólya cautions pedants to ' always use your own brains first ' Jump up ^ Pólya 1957 p. 35 Jump up ^ Pólya 1957 p. 36 Jump up ^ Pólya 1957 pp. 14 - 19 Jump up ^ Diagrammatic Reasoning site Jump up ^ Minsky, Marvin. `` Steps Toward Artificial Intelligence ''... Jump up ^ Schoenfeld, Alan H. ( 1992 ). D. Grouws, ed. `` Learning to think mathematically : Problem solving, metacognition, and sense - making in mathematics '' ( PDF ). Handbook for Research on Mathematics Teaching and Learning. New York : MacMillan : 334 -- 370... Jump up ^ Dromey, R.G. ( 1982 ). How to Solve it by Computer. Prentice - Hall International. ISBN 978 - 0 - 13 - 434001 - 2. References Pólya, George ( 1957 ). How to Solve It. Garden City, NY : Doubleday. p. 253. External links Wikiquote has quotations related to : George Pólya More information on Pólya can be found here. Softpanorama page about the value of the book in programming Retrieved from `` https://en.wikipedia.org/w/index.php?title=How_to_Solve_It&oldid=829307326 '' Categories : 1945 books Heuristics Mathematics books Mathematics education Problem solving Princeton University Press books Self - help books Talk Search Contents About Wikipedia Español Esperanto Polski Português Suomi Українська 中文 Edit links This page was last edited on 7 March 2018, at 21 : 09 ( UTC ). About Wikipedia

Question: who wrote the book how to solve it which outlines a general approach to problem solving
Answer: mathematician George Pólya