# George Pólya

> Hungarian mathematician (1887-1985)

**Wikidata**: [Q296259](https://www.wikidata.org/wiki/Q296259)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/George_Pólya)  
**Source**: https://4ort.xyz/entity/george-polya

## Summary
George Pólya was a Hungarian mathematician renowned for his extensive contributions to heuristics, probability theory, combinatorics, and mathematical education. He is best known for his influential book *How to Solve It* (1945), which established a systematic method for mathematical problem-solving and discovery. A member of the prominent group of Hungarian scientists known as "The Martians," he held academic positions at ETH Zurich, Brown University, and Stanford University.

## Biography
- **Born:** December 13, 1887, in Budapest, Hungary
- **Nationality:** Hungarian (later a citizen of the United States)
- **Education:** Doctorate from Eötvös Loránd University (1912); also studied at the University of Vienna (1910–1911) and the University of Göttingen (1912–1913)
- **Known for:** Heuristics, the Pólya enumeration theorem, the Pólya conjecture, and the Pólya urn model
- **Employer(s):** ETH Zurich (1914–1940), Brown University (1940–1942), Stanford University (1942–1953)
- **Field(s):** Mathematical analysis, combinatorics, mathematics, number theory, numerical analysis, probability theory, heuristic, education

## Contributions
George Pólya's work spanned multiple domains of mathematics and education. His most famous publication, *How to Solve It* (1945), provided a framework for mathematical heuristics and problem-solving that remains influential in pedagogy. In pure mathematics, he developed the **Pólya enumeration theorem** in combinatorics and the **Pólya urn model** in statistics and probability. He formulated the **Pólya conjecture** in number theory (later disproved) and the **Hilbert–Pólya conjecture** regarding the Riemann zeta function. Other significant contributions include the **Fueter–Pólya theorem** on quadratic pairing functions, the **Pólya–Szegő inequality**, the **Laguerre–Pólya class**, and the **beta negative binomial distribution**. His 1912 doctoral thesis, titled *On some questions of the calculus of probabilities and certain related integrals*, was completed under the advisorship of Lipót Fejér.

## FAQs
**Where did George Pólya work?**
Pólya served as a professor at ETH Zurich from 1914 to 1940, moved to Brown University from 1940 to 1942, and subsequently joined Stanford University, where he remained from 1942 until 1953.

**What are George Pólya's most significant mathematical contributions?**
He is celebrated for the Pólya enumeration theorem in combinatorics, the Pólya urn model in probability, and the Pólya conjecture in number theory. He also authored the seminal book *How to Solve It*, which focuses on mathematical heuristics.

**Who were George Pólya's notable doctoral students?**
His doctoral advisees included a wide array of mathematicians, such as Hans Albert Einstein, Imre Lakatos, Alice Roth, James J. Stoker, Albert Pfluger, and Fritz Gassmann.

**What awards and honors are named after George Pólya?**
The Mathematical Association of America established the George Pólya Award in 1976. Additionally, the London Mathematical Society (1987) and the Society for Industrial and Applied Mathematics (1969) both award a Pólya Prize in his honor.

**What was George Pólya's educational background?**
He attended Berzsenyi Dániel Secondary School before studying at Eötvös Loránd University (1905–1912), the University of Vienna (1910–1911), and the University of Göttingen (1912–1913).

## Why They Matter
George Pólya transformed the approach to mathematical problem-solving and education through his development of heuristics. His book *How to Solve It* is considered a classic in the field, teaching students and educators how to think about problems rather than just solve them. In research, his work in combinatorics and probability provided essential tools used in physics, statistics, and computer science. As a member of "The Martians"—a group of brilliant Hungarian scientists that included John von Neumann and others—Pólya helped shape 20th-century scientific thought. His legacy continues through the numerous awards named after him and the generations of mathematicians he taught and inspired.

## Notable For
- **Authorship of *How to Solve It*:** A landmark book in mathematical education published in 1945.
- **The Pólya Enumeration Theorem:** A fundamental theorem in combinatorics used to count objects under symmetry.
- **The Pólya Urn Model:** A statistical model describing contagion and reinforcement processes.
- **The Martians:** Member of this group of prominent Hungarian scientists.
- **Academic Memberships:** Member of the National Academy of Sciences, Hungarian Academy of Sciences, and American Academy of Arts and Sciences.
- **Awards:** The George Pólya Award (MAA), the Pólya Prize (LMS), and the George Pólya Prize (SIAM) are named in his honor.
- **Erdős Number:** Held an Erdős number of 2.
- **Multilingual:** Spoke English, Hungarian, Italian, French, Danish, and German.
- **Archives:** His papers are archived at the ETH Zurich University Archives.

## Body

### Early Life and Education
George Pólya was born on December 13, 1887, in Budapest, Hungary, to Jakab Pólya. He had a sibling, Eugen Pólya. He completed his secondary education at Berzsenyi Dániel Secondary School from 1894 to 1904. His higher education began at Eötvös Loránd University in 1905, where he studied until 1912. During this period, he also attended the University of Vienna in 1910 and 1911, followed by the University of Göttingen from 1912 to 1913. He earned his doctorate from Eötvös Loránd University in 1912 with a thesis titled *On some questions of the calculus of probabilities and certain related integrals*, under the supervision of Lipót Fejér.

### Academic Career
Pólya's academic career was distinguished by tenures at several prestigious institutions. He began as a professor at ETH Zurich in 1914, a position he held until 1940. Following his time in Europe, he moved to the United States, where he worked at Brown University from 1940 to 1942. He concluded his formal academic career at Stanford University, where he was employed from 1942 until his retirement in 1953. His archives are maintained at the ETH Zurich University Archives.

### Research and Contributions
Pólya's research interests were vast, covering mathematical analysis, combinatorics, number theory, numerical analysis, probability theory, and education. He made significant contributions to the field of heuristics, emphasizing the psychological methods of problem-solving.

**Key Theorems and Models:**
*   **Pólya Enumeration Theorem:** A major result in combinatorics that generalizes Burnside's lemma.
*   **Pólya Urn Model:** A statistical model used in probability theory to describe the process of changing probabilities as events occur.
*   **Pólya Conjecture:** A hypothesis in number theory concerning the summatory Liouville function, which was eventually disproved.
*   **Fueter–Pólya Theorem:** Establishes that the Cantor pairing function is the only quadratic polynomial pairing function.
*   **Hilbert–Pólya Conjecture:** An approach to proving the Riemann hypothesis via spectral theory.
*   **Pólya–Szegő Inequality:** An inequality in mathematical analysis.
*   **Laguerre–Pólya Class:** A class of entire functions related to real polynomials.
*   **Beta Negative Binomial Distribution:** A probability distribution he studied.

**Publications:**
His most famous work is the book *How to Solve It*, published in 1945, which outlines a systematic method for solving mathematical problems.

### Doctoral Students
Pólya supervised a large number of doctoral students who went on to have significant careers in mathematics and related fields. His notable students include:
*   Fritz Gassmann (1926)
*   Alice Roth (1938)
*   Albert Edrei (1939)
*   Hans Albert Einstein (1936)
*   Albert Pfluger (1935)
*   James J. Stoker (1936)
*   Alfred Aeppli (1924)
*   Michael Israel Aissen (1951)
*   Florian Eggenberger (1924)
*   Gottfried Grimm (1932)
*   Jeremy Kilpatrick (1967)
*   Imre Lakatos (1961)
*   Walter Saxer (1923)
*   Andrew H. van Tuyl
*   Donald Wayne Grace
*   Reinwald Jungen
*   Ernst Boller
*   Eduard Benz
*   Hermann Muggli
*   Hans Odermatt
*   Hans Arthur Meyer
*   Madeline Johnsen
*   Burnett C. Meyer
*   Grove Crawford Nooney
*   Charles McLoud Larsen
*   Madeleine Rose Ashton
*   Wilhelm Mächler
*   Victor Junod
*   Egon Moecklin
*   August Stoll
*   Emil Schwengeler

### Personal Life and Death
George Pólya was a Hungarian national who later became a citizen of the United States. He was part of the group known as "The Martians," a cohort of prominent Hungarian scientists. He was multilingual, speaking English, Hungarian, Italian, French, Danish, and German. His religion was Catholicism. Pólya passed away on September 8, 1985, in Palo Alto, California, United States. He was buried at the Alta Mesa Memorial Park, specifically in Mausoleum #2, East Wall Stars #4.

### Legacy and Honors
Pólya's influence on mathematics is recognized through numerous awards and honors. The Mathematical Association of America established the George Pólya Award in 1976. The London Mathematical Society awards the Pólya Prize (inception 1987), as does the Society for Industrial and Applied Mathematics (inception 1969). He was a member of the National Academy of Sciences, the Hungarian Academy of Sciences, and the American Academy of Arts and Sciences. His Erdős number was 2, indicating close collaboration with Paul Erdős's circle.

### Identifiers and Archives
Pólya is widely cataloged in academic and library systems with identifiers such as ISNI (0000000121491839), GND (118825321), and VIAF (120727470). His academic genealogy is recorded in the Mathematics Genealogy Project (ID: 13648). His professional papers are held at the ETH Zurich University Archives under the signature CH-001807-7:Hs 89.

## References

1. BnF authorities
2. Integrated Authority File
3. MacTutor History of Mathematics archive
4. Czech National Authority Database
5. Find a Grave
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7. Mathematics Genealogy Project
8. Virtual International Authority File
9. CiNii Research
10. [Source](https://vls.hsa.ethz.ch/client/link/de/archiv/einheit/32205a9175e143559afd26c373f80c70)
11. SNAC
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14. discovery.nationalarchives.gov.uk
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17. [Source](https://www.deutsche-biographie.de/pnd118825321.html#ndbcontent)
18. CONOR.SI
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22. George Pólya | The StoryGraph. The StoryGraph