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mathematics and plausible reasoning wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 outline toggle outline subsection 1 1 volume i induction and analogy in mathematics 1 2 volume ii patterns of plausible inference 2 reviews 3 references toggle the table of contents mathematics and plausible reasoning add languages add links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia mathematics and plausible reasoning author george pólya genre mathematics publication date 1954 mathematics and plausible reasoning is a two volume book by the mathematician george pólya describing various methods for being a good guesser of new mathematical results 1 2 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 p r halmos reviewing the book summarised the central thesis of the book thus a good guess is as important as a good proof 3 outline edit volume i induction and analogy in mathematics edit polya begins volume i with a discussion on induction not mathematical induction 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 prime numbers this is the well known goldbach s conjecture 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 volume ii patterns of plausible inference edit this volume attempts to formulate certain patterns of plausible reasoning 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 sl no premise 1 premise 2 premise 3 plausible conclusion 1 a implies b b is true a is more credible 2 a implies b n 1 b n 1 is very different from the formerly verified consequences b 1 b 2 b n of a b n 1 true a much more credible 3 a implies b n 1 b n 1 is very similar to the formerly verified consequences b 1 b 2 b n of a b n 1 true a just a little more credible 4 a implies b b is very improbable in itself b is true a very much more credible 5 a implies b b is quite probable in itself b is true a is just a little more credible 6 a analogous to b b is true a is more credible 7 a analogous to b b is more credible a is somewhat more credible 8 a is implied by b b is false a is less credible 9 a is incompatible with b b is false a is more credible reviews edit bernhart arthur 1958 01 01 review of mathematics and plausible reasoning the american mathematical monthly 65 6 456 457 doi 10 2307 2310741 hdl 2027 mdp 39015008206248 jstor 2310741 s2cid 121427033 rado tibor 1956 01 01 review of mathematics and plausible reasoning philosophy of science 23 2 167 doi 10 1086 287478 jstor 185607 van dantzig d 1959 01 01 review of mathematics and plausible reasoning g pólya synthese 11 4 353 358 doi 10 1007 bf00486196 jstor 20114312 s2cid 46957889 broadbent t a a 1956 01 01 review of mathematics and plausible reasoning the mathematical gazette 40 333 233 234 doi 10 2307 3608848 hdl 2027 mdp 39015008206248 jstor 3608848 bush robert r 1956 01 01 review of mathematics and plausible reasoning the american journal of psychology 69 1 166 167 doi 10 2307 1418146 hdl 2027 mdp 39015008206248 jstor 1418146 johansson i 1955 01 01 review of mathematics and plausible reasoning i and ii nordisk matematisk tidskrift 3 1 64 65 jstor 24524537 prager w 1955 01 01 review of mathematics and plausible reasoning volume i induction and analogy volume ii patterns of plausible inference quarterly of applied mathematics 13 3 344 345 jstor 43634251 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 the mathematics teacher 48 4 272 jstor 27954884 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 journal of the american statistical association 50 272 1352 1354 doi 10 2307 2281238 jstor 2281238 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 iyyun the jerusalem philosophical quarterly עיון רבעון פילוסופי ח א 48 49 jstor 23301574 stein robert g 1991 01 01 review of patterns of plausible inference vol 2 of mathematics and plausible reasoning r george pólya the mathematics teacher 84 7 574 jstor 27967294 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 the two year college mathematics journal 10 2 119 122 doi 10 2307 3027025 jstor 3027025 references edit polya george 1954 mathematics and plausible reasoning volume i induction and analogy in mathematics princeton university press polya george 1954 mathematics and plausible reasoning volume ii patterns of plausible inference princeton university press halmos paul r 1955 review g pólya mathematics and plausible reasoning bulletin of the american mathematical society 61 3 part 1 243 245 doi 10 1090 s0002 9904 1955 09904 x retrieved 16 february 2015 retrieved from https en wikipedia org w index php title mathematics_and_plausible_reasoning oldid 1369811595 categories mathematics books reasoning inference this page was last edited on 17 august 2026 at 09 04 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia 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