Mathematics and Plausible Reasoning
E637312
Mathematics and Plausible Reasoning is a two-volume work by George Pólya that explores how mathematicians actually think, conjecture, and discover through heuristic and inductive reasoning rather than formal proof alone.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T7030851 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mathematics and Plausible Reasoning Context triple: [George Pólya, notableWork, Mathematics and Plausible Reasoning]
-
A.
Concepts of Modern Mathematics
Concepts of Modern Mathematics is a popular mathematics book by Ian Stewart that introduces key ideas of modern math—such as set theory, logic, topology, and abstract algebra—to a general audience in an accessible, non-technical way.
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B.
Die mathematische Denkweise
"Die mathematische Denkweise" is a work by mathematician Andreas Speiser that explores the nature, structure, and philosophy of mathematical thinking.
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C.
The Theory of Probability
The Theory of Probability is Hans Reichenbach’s influential philosophical and mathematical treatise that helped establish a rigorous, frequency-based interpretation of probability within the logical empiricist tradition.
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D.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
-
E.
The Foundations of Mathematics
The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mathematics and Plausible Reasoning Target entity description: Mathematics and Plausible Reasoning is a two-volume work by George Pólya that explores how mathematicians actually think, conjecture, and discover through heuristic and inductive reasoning rather than formal proof alone.
-
A.
Concepts of Modern Mathematics
Concepts of Modern Mathematics is a popular mathematics book by Ian Stewart that introduces key ideas of modern math—such as set theory, logic, topology, and abstract algebra—to a general audience in an accessible, non-technical way.
-
B.
Die mathematische Denkweise
"Die mathematische Denkweise" is a work by mathematician Andreas Speiser that explores the nature, structure, and philosophy of mathematical thinking.
-
C.
The Theory of Probability
The Theory of Probability is Hans Reichenbach’s influential philosophical and mathematical treatise that helped establish a rigorous, frequency-based interpretation of probability within the logical empiricist tradition.
-
D.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
-
E.
The Foundations of Mathematics
The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics book ⓘ |
| aimsTo |
bridge intuitive reasoning and rigorous proof
ⓘ
describe actual mathematical thinking ⓘ |
| author | George Pólya ⓘ |
| contrastsWith | formal proof ⓘ |
| emphasizes |
heuristics
ⓘ
informal reasoning ⓘ patterns of plausible inference ⓘ |
| focusesOn |
conjecture formation
ⓘ
how mathematicians actually think ⓘ methods of discovery ⓘ |
| hasKeyConcept |
analogy
ⓘ
conjecture ⓘ heuristic rules ⓘ induction ⓘ patterns of inference ⓘ probabilistic reasoning ⓘ |
| hasPart |
analysis of analogical reasoning
ⓘ
case studies of mathematical problems ⓘ classification of types of plausible reasoning ⓘ discussion of inductive generalization ⓘ |
| influenced |
mathematics education
ⓘ
philosophy of mathematical practice ⓘ research on mathematical heuristics ⓘ |
| language | English ⓘ |
| notableFor |
influence on problem-solving pedagogy
ⓘ
systematic treatment of plausible reasoning in mathematics ⓘ |
| numberOfVolumes | 2 ⓘ |
| relatedWork | How to Solve It ⓘ |
| subject |
analogy in mathematics
ⓘ
heuristic reasoning ⓘ inductive reasoning ⓘ mathematical discovery ⓘ philosophy of mathematics ⓘ plausible inference ⓘ problem solving in mathematics ⓘ |
| subtitle |
Induction and Analogy in Mathematics
ⓘ
linked to:
Mathematics and Plausible Reasoning
Patterns of Plausible Inference ⓘ |
| targetAudience |
mathematicians
ⓘ
students of mathematics ⓘ teachers of mathematics ⓘ |
| volume |
Mathematics and Plausible Reasoning, Volume I
ⓘ
linked to:
Mathematics and Plausible Reasoning
Mathematics and Plausible Reasoning, Volume II ⓘ
linked to:
Mathematics and Plausible Reasoning
|
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Mathematics and Plausible Reasoning Description of subject: Mathematics and Plausible Reasoning is a two-volume work by George Pólya that explores how mathematicians actually think, conjecture, and discover through heuristic and inductive reasoning rather than formal proof alone.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Mathematics and Plausible Reasoning
linked to: Mathematics and Plausible Reasoning
subject linked to:
Mathematics and Plausible Reasoning
linked to: Mathematics and Plausible Reasoning
linked to: Mathematics and Plausible Reasoning