Indeholder "Preface", "Preface to the second edition", "Hints to the reader", "Chapter XII. Some Conspicuous Patterns", " 1. Verification of a consequence", " 2. Successive verification of several consequences", " 3. Verification of an improbable consequence", " 4. Inference from analogy", " 5. Deepening the analogy", " 6. Shaded analogical inference", " Examples and Comments on Chapter XII, 1-14", " 14. Inductive conclusion from fruitless efforts", "Chapter XIII. Further Patterns and First Links", " 1. Examining a consequence", " 2. Examining a possible ground", " 3. Examining a conflicting conjecture", " 4. Logical terms", " 5. Logical links between patterns of plausible inference", " 6. Shaded inference", " 7. A table", " 8. Combination of simple patterns", " 9. On inference from analogy", " 10. Qualified inference", " 11. On successive verifications", " 12. The influence of rival conjectures", " 13. On judicial proof", " Examples and Comments on Chapter XIII, 1-20", " First Part 1-10. Second Part 11-20", " 9. On inductive research in mathematics and in the physical sciences", " 10. Tentative general formulations", " 11. More personal, more complex", " 12. There is a straight line that joins two given points", " 13. There is a straight line with a given direction through a given point. Drawing a parallel", " 14. The most obvious case may be the only possible case", " 15. Setting the fashion. The power of words", " 16. This is too improbable to be a mere coincidence", " 17. Perfecting the analogy", " 18. A new conjecture", " 19. Another new conjecture", " 20. What is typical?", "Chapter XIV. Chance, the Ever-present Rival Conjecture", " 1. Random mass phenomena", " 2. The concept of probability", " 3. Using the bag and the balls", " 4. The calculus of probability. Statistical hypotheses", " 5. Straightforward prediction of frequencies", " 6. Explanation of phenomena", " 7. Judging statistical hypotheses", " 8. Choosing between statistical hypotheses", " 9. Judging non-statistical conjectures", " Examples and Comments on Chapter XIV, 1-33", " First Part 1-18. Second Part 19-33", " 19. On the concept of probability", " 20. How not to interpret the frequency concept of probability", " 24. Probability and the solution of problems", " 25. Regular and Irregular", " 26. The fundamental rules of the Calculus of Probability", " 27. Independence", " 30. Permutations from probability", " 31. Combinations from probability", " 32. The choice of a rival statistical conjecture: an example", " 33. The choice of a rival statistical conjecture: general remarks", "Chapter XV. The Calculus of Probability and the Logic of Plausible Reasoning", " 1. Rules of plausible reasoning?", " 2. An aspect of demonstrative reasoning", " 3. A corresponding aspect of plausible reasoning", " 4. An aspect of the calculus of probability. Difficulties", " 5. An aspect of the calculus of probability. An attempt", " 6. Examining a consequence", " 7. Examining a possible ground", " 8. Examining a conflicting conjecture", " 9. Examining several consequences in succession", " 10. On circumstantial evidence", " Examples and Comments on Chapter XV, 1-9", " 4. Probability and credibility", " 5. Likelihood and credibility", " 6. Laplace's attempt to link induction with probability", " 7. Why not quantitative?", " 8. Infinitesimal credibilities?", " 9. Rules of admissibility", "Chapter XVI. Plausible Reasoning in Invention and Instruction", " 1. Object of the present chapter", " 2. The story of a little discovery", " 3. The process of solution", " 4. Deus ex machina", " 5. Heuristic justification", " 6. The story of another discovery", " 7. Some typical indications", " 8. Induction in invention", " 9. A few words to the teacher", " Examples and Comments on Chapter XVI. 1-13", " 1. To the teacher: some types of problems", " 7. qui nimium probat nihil probat", " 8. Proximity and credibility", " 9. Numerical computation and plausible reasoning", " 13. Formal demonstration and plausible reasoning", "Solutions to problems", "Bibliography", "Appendix", " I. Heuristic Reasoning in the Theory of Numbers", " II. Additional Comments, Problems, and Solutions".

George Polya tænkte meget over det at tænke og hvordan man får ideer, når man ikke er Gearløs og har en tænkehat. Han nævner en conjecture af Euler om at tal af formen 8n+3 kan skrives som et kvadrattal + det dobbelte af et primtal. Barry Mazur skrev i 2012 at det stadig hverken er bevist eller modbevist. Euler var interesseret i at vise det, for så kunne han skrive alle tal som summen af tre trekanttal. Det har Gauss senere bevist i 1796 i Disquisitiones Arithmeticae. ( )