George Pólya

George Pólya (1887–1985) was a Hungarian-American mathematician whose work spanned probability, combinatorics, and analysis. His book How to Solve It made strategies for mathematical problem-solving widely known.

How to Solve It: A 1945 book by George Pólya presenting a four-stage framework for solving mathematical problems. This book is Pólya’s best-known account of how to approach unfamiliar problems.
Stanford University: A private research university in Stanford, California, founded in 1885. Pólya spent the later part of his academic career teaching mathematics at Stanford.
Pólya enumeration theorem: A theorem that counts distinct objects formed under symmetry by using group actions and cycle indices. This theorem applies Pólya’s methods to counting arrangements that are equivalent under symmetry.
Mathematical discovery: The process of finding mathematical patterns, conjectures, methods, and results. Pólya’s writing treats discovery as a process supported by deliberate strategies.
Heuristic: A practical strategy for finding solutions that does not guarantee success or correctness. Pólya organized problem-solving advice around heuristics rather than fixed algorithms.
ETH Zurich: A Swiss public research university in Zurich, established in 1855. Pólya held a professorship at ETH Zurich before emigrating to the United States.
Pólya's theorem on random walks: A result describing whether simple random walks return to their starting point in different dimensions. Pólya used probabilistic reasoning to establish recurrence in one and two dimensions, but not higher dimensions.
Mathematics education: The study and practice of teaching and learning mathematics. His problem-solving framework influenced how mathematics is taught beyond routine exercises.
Mathematical proof: A deductive argument establishing that a mathematical statement follows from accepted assumptions. Pólya distinguished finding a plausible result from proving that it must be true.
Gábor Szegő: A Hungarian-American mathematician known for work in analysis and for textbooks written with George Pólya. Szegő collaborated with Pólya on influential texts in analysis and mathematical problem-solving.

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