How to Solve It¶
Pólya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. Princeton University Press.
Cited by¶
8 citations across 8 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Analogy
- Mathematics uses analogy to transfer proof techniques across structurally similar problem classes, and category theory formalizes structural correspondence as a universal construct.
This sourceFoundational pedagogical pattern catalog: codifies recurring problem-solving heuristics (understand the problem, devise a plan, carry out the plan, look back) into teachable vocabulary; prototype of pattern-language thinking in pedagogy.
Supported in partVerified against the publisher's abstract
Publisher blurb says Polya's heuristic dictionary covers analogy as a way to attack problems, but not proof-technique transfer or category theory.
“includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction”
- Mathematics uses analogy to transfer proof techniques across structurally similar problem classes, and category theory formalizes structural correspondence as a universal construct.
- Decomposition
- Each piece becomes a bounded focus of attention; patterns within pieces become visible; relationships between pieces can be designed deliberately—a heuristic Pólya (1945) codified as "if you cannot solve the proposed problem, try to solve first some related problem" via sub-problem reduction.
This sourceCodifies problem-solving heuristics including 'if you cannot solve the proposed problem, try to solve first some related problem' (sub-problem reduction).
- Each piece becomes a bounded focus of attention; patterns within pieces become visible; relationships between pieces can be designed deliberately—a heuristic Pólya (1945) codified as "if you cannot solve the proposed problem, try to solve first some related problem" via sub-problem reduction.
- Design Patterns
- Polya's (1945) How to Solve It established the prototype of pedagogical pattern thinking by codifying recurring problem-solving heuristics into a teachable vocabulary.
This sourceCodifies recurring problem-solving heuristics (understand the problem, devise a plan, carry it out, look back) into a teachable vocabulary, including 'look at the unknown… think of a familiar problem with the same/similar unknown.'
Supported in partVerified against the work's full text
The publisher's description confirms Polya codified problem-solving heuristics into a teachable dictionary, but nowhere says the book founded pedagogical pattern thinking.
“How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know.”
- Polya's (1945) How to Solve It established the prototype of pedagogical pattern thinking by codifying recurring problem-solving heuristics into a teachable vocabulary.
- Heuristic
This sourceFoundational pedagogical pattern catalog: codifies recurring problem-solving heuristics (understand the problem, devise a plan, carry out the plan, look back) into teachable vocabulary; prototype of pattern-language thinking in pedagogy.
- Inversion
- Mathematics and formal systems: Inverse functions (f and f^(-1)), matrix inversion and linear algebra, group inverses and multiplicative structure, duality in category theory and functional analysis, inversion in permutation theory (cycle structure and sign).
This sourceFoundational pedagogical pattern catalog: codifies recurring problem-solving heuristics (understand the problem, devise a plan, carry out the plan, look back) into teachable vocabulary; prototype of pattern-language thinking in pedagogy.
- Mathematics and formal systems: Inverse functions (f and f^(-1)), matrix inversion and linear algebra, group inverses and multiplicative structure, duality in category theory and functional analysis, inversion in permutation theory (cycle structure and sign).
- Problem Representation
- Mathematicians solve problems by changing representation: polar to Cartesian, time to frequency, primal to dual.
This sourceReformulation heuristics, including "consider a related problem you can solve," as moves that change the representation to make a problem tractable.
- Mathematicians solve problems by changing representation: polar to Cartesian, time to frequency, primal to dual.
- Problem Space
- Problem space trains reasoners to ask a core set of diagnostic questions, paralleling the heuristic decomposition Pólya (1945) sets out in How to Solve It (understand the problem, devise a plan, carry out the plan, look back).
This sourceFoundational pedagogical pattern catalog: codifies recurring problem-solving heuristics (understand the problem, devise a plan, carry out the plan, look back) into teachable vocabulary; prototype of pattern-language thinking in pedagogy.
Supported in partVerified against the work's full text
The publisher's description confirms Pólya codified problem-solving heuristics into teachable vocabulary, but never names the four phases the claim attributes to him.
“How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know.”
- Problem space trains reasoners to ask a core set of diagnostic questions, paralleling the heuristic decomposition Pólya (1945) sets out in How to Solve It (understand the problem, devise a plan, carry out the plan, look back).
- Progressive Refinement from Core Model
- The emergent-prime signature: across physics (perturbation series), applied math (asymptotic expansions), economics (comparative statics around equilibrium), engineering (linearization around operating points), ecology (perturbing steady-state population models), climate modeling (perturbations around baseline GCM runs), organizational theory (changes modeled as small deviations from current operating mode), and machine learning (fine-tuning, LoRA), the same recipe appears: (a) select a tractable baseline f_0, (b) parameterize the deviation by ε, © compute f = f_0 + εf_1 + ε²f_2 + ..., (d) estimate where the series loses predictive validity.
This sourceFoundational pedagogical pattern catalog: codifies recurring problem-solving heuristics (understand the problem, devise a plan, carry out the plan, look back) into teachable vocabulary; prototype of pattern-language thinking in pedagogy.
- The emergent-prime signature: across physics (perturbation series), applied math (asymptotic expansions), economics (comparative statics around equilibrium), engineering (linearization around operating points), ecology (perturbing steady-state population models), climate modeling (perturbations around baseline GCM runs), organizational theory (changes modeled as small deviations from current operating mode), and machine learning (fine-tuning, LoRA), the same recipe appears: (a) select a tractable baseline f_0, (b) parameterize the deviation by ε, © compute f = f_0 + εf_1 + ε²f_2 + ..., (d) estimate where the series loses predictive validity.
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Read against the text for 3 of 8 citations: 3 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:120db10a759b · see in the full table