114:. The first problem in the first chapter is to guess the rule according to which the successive terms of the following sequence are chosen: 11, 31, 41, 61, 71, 101, 131, . . . In the next chapter the techniques of generalization, specialization and analogy are presented as possible strategies for plausible reasoning. In the remaining chapters, these ideas are illustrated by discussing the discovery of several results in various fields of mathematics like number theory, geometry, etc. and also in physical sciences.
35:
106:, but as a way of guessing new results. He shows how the chance observations of a few results of the form 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc., may prompt a sharp mind to formulate the conjecture that every even number greater than 4 can be represented as the sum of two odd
126:. The relation of these patterns with the calculus of probability are also investigated. Their relation to mathematical invention and instruction are also discussed. The following are some of the patterns of plausible inference discussed by Polya.
80:
describing various methods for being a good guesser of new mathematical results. In the
Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing."
849:
Alexanderson, G. L. (1979-01-01). "Review of
Mathematics and Plausible Reasoning: Vol. I: Induction and Analogy in Mathematics; Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference, George Polya".
757:
Meserve, Bruce E. (1955-01-01). "Review of
Induction and Analogy in Mathematics, Vol. I, and Patterns of Plausible Inference, Vol. II, of Mathematics and Plausible Reasoning".
778:
Savage, Leonard J. (1955-01-01). "Review of
Mathematics and Plausible Reasoning. Volume I, Induction and Analogy in Mathematics. Volume II, Patterns of Plausible Inference".
807:פ., א. י. י. (1957-01-01). "Review of Mathematics and Plausible Reasoning. Volume I: Induction and Analogy in Mathematics; Volume II: Patterns of Plausible Reasoning".
736:
Prager, W. (1955-01-01). "Review of
Mathematics and plausible reasoning. Volume I: Induction and analogy. Volume II: Patterns of plausible inference".
828:
Stein, Robert G. (1991-01-01). "Review of
Patterns of Plausible Inference. Vol. 2 of Mathematics and Plausible Reasoning (R), George Pólya".
85:
reviewing the book summarised the central thesis of the book thus: ". . . a good guess is as important as a good proof."
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Van
Dantzig, D. (1959-01-01). "Review of Mathematics and Plausible Reasoning, G. Pólya".
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Johansson, I. (1955-01-01). "Review of
Mathematics and plausible reasoning, I and II".
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Broadbent, T. A. A. (1956-01-01). "Review of
Mathematics and Plausible Reasoning".
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895:
Mathematics and
Plausible Reasoning Volume I: Induction and Analogy in Mathematics
524:
Bernhart, Arthur (1958-01-01). "Review of Mathematics and Plausible Reasoning".
676:
Bush, Robert R. (1956-01-01). "Review of Mathematics and Plausible Reasoning".
910:
Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Inference
571:
Rado, Tibor (1956-01-01). "Review of Mathematics and Plausible Reasoning".
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Iyyun: The Jerusalem Philosophical Quarterly / עיון: רבעון פילוסופי
584:
925:"Review: G. Pólya, Mathematics and plausible reasoning"
122:
This volume attempts to formulate certain patterns of
59:
51:
41:
780:Journal of the American Statistical Association
94:Volume I: Induction and analogy in mathematics
929:Bulletin of the American Mathematical Society
8:
27:
98:Polya begins Volume I with a discussion on
118:Volume II: Patterns of Plausible Inference
76:is a two-volume book by the mathematician
33:
26:
697:
658:
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852:The Two-Year College Mathematics Journal
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885:
7:
28:Mathematics and Plausible Reasoning
73:Mathematics and Plausible Reasoning
18:Mathematics and plausible reasoning
678:The American Journal of Psychology
25:
526:The American Mathematical Monthly
738:Quarterly of Applied Mathematics
941:10.1090/s0002-9904-1955-09904-x
395:is just a little more credible
286:formerly verified consequences
207:formerly verified consequences
1:
912:. Princeton University Press.
897:. Princeton University Press.
717:Nordisk Matematisk Tidskrift
351:is very improbable in itself
331:just a little more credible
383:is quite probable in itself
994:
453:is somewhat more credible
205:is very different from the
110:. This is the well known
32:
923:Halmos, Paul R. (1955).
639:The Mathematical Gazette
363:very much more credible
830:The Mathematics Teacher
759:The Mathematics Teacher
699:2027/mdp.39015008206248
660:2027/mdp.39015008206248
547:2027/mdp.39015008206248
908:Polya, George (1954).
893:Polya, George (1954).
284:is very similar to the
104:mathematical induction
935:(3 Part 1): 243–245.
573:Philosophy of Science
493:is incompatible with
144:plausible conclusion
112:Goldbach's conjecture
252:much more credible
124:plausible reasoning
29:
786:(272): 1352–1354.
614:10.1007/bf00486196
173:is more credible.
968:Mathematics books
515:
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511:is more credible
482:is less credible
424:is more credible
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16:(Redirected from
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83:P. R. Halmos
78:George Pólya
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46:George Pólya
946:16 February
55:Mathematics
962:Categories
880:References
836:(7): 574.
765:(4): 272.
579:(2): 167.
301:, . . . ,
222:, . . . ,
978:Inference
973:Reasoning
564:121427033
141:Premise 3
138:Premise 2
135:Premise 1
100:induction
842:27967294
821:23301574
771:27954884
750:43634251
729:24524537
630:46957889
622:20114312
602:Synthese
502:is false
473:is false
374:implies
342:implies
263:implies
184:implies
155:implies
872:3027025
800:2281238
708:1418146
669:3608848
556:2310741
518:Reviews
415:is true
389:is true
357:is true
164:is true
132:Sl. No.
89:Outline
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593:185607
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102:, not
42:Author
868:JSTOR
838:JSTOR
817:JSTOR
796:JSTOR
767:JSTOR
746:JSTOR
725:JSTOR
704:JSTOR
665:JSTOR
626:S2CID
618:JSTOR
589:JSTOR
560:S2CID
552:JSTOR
52:Genre
948:2015
325:true
246:true
65:1954
937:doi
860:doi
788:doi
694:hdl
686:doi
655:hdl
647:doi
610:doi
581:doi
542:hdl
534:doi
310:of
231:of
964::
933:61
931:.
927:.
866:.
856:10
854:.
834:84
832:.
813:ח'
811:.
794:.
784:50
782:.
763:48
761:.
742:13
740:.
719:.
702:.
692:.
682:69
680:.
663:.
653:.
643:40
641:.
624:.
616:.
606:11
604:.
587:.
577:23
575:.
558:.
550:.
540:.
530:65
528:.
323:+1
294:,
282:+1
271:+1
244:+1
215:,
203:+1
192:+1
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939::
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862::
844:.
823:.
802:.
790::
773:.
752:.
731:.
721:3
710:.
696::
688::
671:.
657::
649::
632:.
612::
595:.
583::
566:.
544::
536::
509:A
505:–
500:B
495:B
491:A
487:9
480:A
476:–
471:B
466:B
462:A
458:8
451:A
447:–
442:B
437:B
433:A
429:7
422:A
418:–
413:B
408:B
404:A
400:6
393:A
387:B
381:B
376:B
372:A
368:5
361:A
355:B
349:B
344:B
340:A
336:4
329:A
321:n
317:B
312:A
307:n
303:B
299:2
296:B
292:1
289:B
280:n
276:B
269:n
265:B
261:A
257:3
250:A
242:n
238:B
233:A
228:n
224:B
220:2
217:B
213:1
210:B
201:n
197:B
190:n
186:B
182:A
178:2
171:A
167:–
162:B
157:B
153:A
149:1
20:)
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