A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem. In this best-selling classic, George Polya revealed how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft instructions on stripping away irrelevancies and going straight to the heart of a problem. How to Solve It popularized heuristics, the art and science of discovery and invention. It has been in print continuously since 1945 and has been translated into twenty-three different languages. Polya was one of the most influential mathematicians of the twentieth century. He made important contributions to a great variety of mathematical research: from complex analysis to mathematical physics, number theory, probability, geometry, astronomy, and combinatorics. He was also an extraordinary teacher--he taught until he was ninety--and maintained a strong interest in pedagogical matters throughout his long career. In addition to How to Solve It, he published a two-volume work on the topic of problem solving, Mathematics of Plausible Reasoning, also with Princeton. Polya is one of the most frequently quoted mathematicians, and the following statements from How to Solve It make clear why: "My method to overcome a difficulty is to go around it." "Geometry is the science of correct reasoning on incorrect figures." "In order to solve this differential equation you look at it till a solution occurs to you."

PART I. IN THE CLASSROOM

Purpose

1. Helping the student

2. Questions, recommendations, mental operations

3. Generality

4. Common sense

5. Teacher and student. Imitation and practice Main divisions, main questions

6. Four phases

7. Understanding the problem

8. Example

g. Devising a plan

10. Example

11. Carrying out the plan

12. Example

13. Looking back

14. Example

15. Various approaches

16. The teacher's method of questioning

17. Good questions and bad questions

More examples

18. A problem of construction

19. A problem to prove

20. A rate problem

PART II. HOW TO SOLVE IT

A dialogue

PART III. SHORT DICTIONARY

OF HEURISTIC

Analogy

Auxiliary elements

Auxiliary problem

Bolzano

Bright idea

Can you check the result?

Can you derive the result differently?

Can you use the result?

Carrying out

Condition

Contradictory

Corollary 73

Could you derive something useful from the data?

Could you restate the problem?

Decomposing and recombining

Definition

Descartes

Determination, hope, success

Diagnosis

Did you use all the data?

Do you know a related problem?

Draw a figure

Examine your guess

Figures

Generalization

Have you seen it before?

Here is a problem related to yours

and solved before

Heuristic

Heuristic reasoning

If you cannot solve the proposed problem

Induction and mathematical induction

Inventor's paradox

Is it possible to satisfy the condition?

Leibnitz

Lemma

Look at the unknown

Modern heuristic

Notation

Pappus

Pedantry and mastery

Practical pro bl ems

Problems to find, problems to prove

Progress and achievement

Puzzles

Reductio ad absurdum and indirect proof

Redundantt

Routine problem

Rules of discovery

Rules of style

Rules of teaching

Separate the various parts of the condition

Setting up equations

Signs of progress

Specialization

Subconscious work

Symmetry

Terms, old and new

Test by dimension

The future mathematician

The intelligent problem-solver

The intelligent reader

The traditional mathematics professor

Variation of the problem

What is the unknown?

Why proofs?

Wisdom of proverbs

Working backwards

PART IV. PROBLEMS, HINTS, SOLUTIONS

Problems

Hints

Solutions