How to Solve It

Reference

First published: 1945
Print length: 253 pagesDoubleday, 1957

Description

George Pólya treats problem solving as a craft that can be examined, practiced, and improved rather than as a mysterious flash of inspiration. Addressing mathematics students and teachers through elementary algebra and geometry, he organizes the work around understanding a problem, devising a plan, carrying it out, and reviewing the result. Within that framework, he demonstrates flexible heuristics: work backward, test a special case, search for an analogy, use induction, or restate the unknown in a more revealing form. His recurring demand is to strip away irrelevant detail without losing the structure that makes a problem solvable. Although grounded in mathematics, the method applies more broadly wherever careful reasoning must convert uncertainty into a sequence of useful questions.

Reading profile

About this profile

Collected’s assessment, not reader ratings. Complexity runs from 1 (least demanding) to 5 (most demanding).

Writing: How much attention the sentences and language require.
Ideas: How much interpretation or abstract reasoning the book asks of you.
Structure: How much you need to keep track of speakers, timelines and connections.
Background knowledge: Prior knowledge needed to follow the book, beyond what it explains.
Emotional intensity: Emotional pressure, from gentle (1) to intense (5). Separate from difficulty.

Writing style

Academic · Conversational · Direct · Technical

Pace

Measured

Tone

Cerebral · Earnest · Philosophical

Structure

Reference

Focus

Ideas · Information

Emotional intensity

1 / 5

Reading complexity

1–5 · higher means more demanding

Writing: 3 / 5
Ideas: 4 / 5
Structure: 3 / 5
Background knowledge: 3 / 5

Themes

Knowledge and truthTransformationWork

About George Pólya

George Pólya was a Hungarian-American mathematician whose career joined wide-ranging research with an unusually sustained interest in how mathematical ideas are found and taught. A professor at ETH Zürich and later Stanford University, he made important contributions to combinatorics, number theory, numerical analysis, and probability, while also writing influentially about heuristics and education. His books treat problem solving as a disciplined craft rather than an inexplicable gift. How to Solve It sets out a practical sequence of understanding a problem, planning an approach, carrying it through, and reviewing the result. Mathematics and Plausible Reasoning examines the exploratory work that precedes proof, showing how analogy, induction, evidence, and pattern recognition can guide conjecture without replacing rigor. In Problems and Theorems in Analysis, written with Gábor Szegő, demanding exercises develop technique across a broad mathematical range. What distinguishes Pólya’s work is its close attention to mathematical thinking in motion: not only finished arguments, but the habits and provisional judgments that make discovery possible.

Book details

For the print edition listed above.

Publisher: Doubleday
Language: English

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