George Pólya's 1945 book How to Solve It (ISBN 0-691-08097-6) is a small volume describing methods of problem solving. It suggests the following steps when solving a mathematical problem: George Pólya (December 13, 1887 – September 7, 1985, in Hungarian Pólya György) was a Hungarian mathematician. ... Year 1945 (MCMXLV) was a common year starting on Monday (link will display the full calendar). ... A book is a set or collection of written, printed, illustrated, or blank sheets, made of paper, parchment, or other material, usually fastened together to hinge at one side. ... Problem solving forms part of thinking. ... A mathematical problem is a problem that can be solved with the help of mathematics. ...

1. First, you have to understand the problem.
2. After understanding, then make a plan.
3. Carry out the plan.
4. Look back on your work. How could it be better?

If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?" Look up understanding in Wiktionary, the free dictionary. ... Look up Problem in Wiktionary, the free dictionary. ... A plan is a proposed or intended method of getting from one set of circumstances to another. ... Look up Review in Wiktionary, the free dictionary. ... Scientific method is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. ...

His book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example: For heuristics in computer science, see heuristic (computer science) Heuristic is the art and science of discovery and invention. ...

The technique "have I used everything" is perhaps most applicable to formal educational examinations (e.g., n men digging m ditches) problems. Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ... In mathematics and related technical fields, the term map or mapping is often a synonym for function. ... Concept A is a (strict) generalization of concept B if and only if: every instance of concept B is also an instance of concept A; and there are instances of concept A which are not instances of concept B. Equivalently, A is a generalization of B if B is a... Concept A is a (strict) generalization of concept B if and only if: every instance of concept B is also an instance of concept A; and there are instances of concept A which are not instances of concept B. Equivalently, A is a generalization of B if B is a... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument support the conclusion, but do not ensure it. ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument support the conclusion, but do not ensure it. ... In computer science, a search algorithm, broadly speaking, is an algorithm that takes a problem as input and returns a solution to the problem, usually after evaluating a number of possible solutions. ... Pattern recognition is a field within the area of machine learning. ... In computer science, pattern matching is the act of checking for the presence of the constituents of a given pattern. ... In computability theory and computational complexity theory, a reduction is a transformation of one problem into another problem. ... Specialization is an important way to generate propositional knowledge, by applying general knowledge, such as the theory of gravity, to specific instances, such as when I release this apple, it will fall to the floor. Specialization is the opposite of generalization. ... Specialization is an important way to generate propositional knowledge, by applying general knowledge, such as the theory of gravity, to specific instances, such as when I release this apple, it will fall to the floor. Specialization is the opposite of generalization. ... In computer science, decomposition, also known as factoring, refers to the process by which a complex problem or system is broken down into parts that are easier to conceive, understand, program, and maintain. ... In computer science, divide and conquer (D&C) is an important algorithm design paradigm. ... Working backward from the goal is an application of the backward chaining strategy in artificial intelligence. ... Backward chaining is one of the two main methods of reasoning when using inference rules. ... Diagrammatic reasoning is reasoning by means of visual representations. ... In metaphysics, extension is the property of taking up space; see Extension (metaphysics). ...

The book has achieved "classic" status because of its considerable influence (see the next section).

Other books on problem solving are often related to more creative and less concrete techniques. See lateral thinking, mind mapping and brainstorming. This article or section does not cite any references or sources. ... A mind map or mindmap is a multicoloured and image centered radial diagram that represents semantic or other connections between portions of learned material. ... Look up brainstorming in Wiktionary, the free dictionary. ...

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 influential paper Steps Toward Artificial Intelligence that "everyone should know the work of George Pólya [87] on how to solve problems." [2]
• Pólya's book has had a large influence on mathematics textbooks. "Most formulations of a problem solving framework in U. S. textbooks attribute some relationship to Pólya's problem solving stages (1945)." [3] Although How to Solve It is still referred to as a primary source in mathematical education, it is now poorly received in general education; it is possible that many education scholars themselves may find the book opaque from lack of the necessary skill with mathematics.
• Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book.

Marvin Lee Minsky (born August 9, 1927), sometimes affectionately known as Old Man Minsky, is an American cognitive scientist in the field of artificial intelligence (AI), co-founder of MITs AI laboratory, and author of several texts on AI and philosophy. ... Mathematics education is the study of the practices and methods of teaching mathematics. ... Not to be confused with physician, a person who practices medicine. ... Zhores Ivanovich Alferov Zhores Ivanovich Alferov (also Alfyorov) (Russian: Жоре́с Ива́нович Алфёров) (born March 15, 1930) is a Russian physicist who contributed significantly to the creation of modern heterostructure physics and electronics. ... Hannes Alfvén (1908–1995) accepting the Nobel Prize for his work on magnetohydrodynamics [1]. List of Nobel Prize laureates in Physics from 1901 to the present day. ... 2000 (MM) was a leap year starting on Saturday of the Gregorian calendar. ...

See also

• Heuristic
• A* search algorithm
• How to Solve It By Computer

Look up Heuristic in Wiktionary, the free dictionary. ... In computer science, A* (pronounced A star) is a graph/tree search algorithm that finds a path from a given initial node to a given goal node (or one passing a given goal test). ... How to Solve It By Computer is a 1982 book by R. G. Dromey (Prentice Hall, ISBN 0-13-434001-9). ...

External links

• More information can be found at: [4]
• An uneven summary of the whole book: [5]