Theorem

Fueter-Polya Theorem

Number Theory

The Fueter-Polya theorem, first proved by Rudolf Fueter and George Polya, states that the only quadratic polynomial pairing functions of the plane are the two Cantor polynomials that Georg Cantor introduced in 1878 to biject pairs of natural numbers with the natural numbers. Fueter initially proved the result for pairing functions satisfying an added condition, and Polya later removed that restriction to establish the theorem in its full generality.

Facts

Statement

The only quadratic polynomial pairing functions are the Cantor polynomials. 1

Proof Year

1923 1

Classification

Statement Form

Classification Theorem 1

Connections

Has Statement Form

Classification Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Proved By

George Polya

Source Fueter-Polya theorem (Wikipedia)

Sources

1. Fueter-Polya theorem (Wikipedia)

Introduction
The only quadratic polynomial pairing functions are the Cantor polynomials.
History
Fueter and Polya published their joint work in 1923
Proved By: George Polya, Lead paragraph
The Fueter-Pólya theorem, first proved by Rudolf Fueter and George Pólya, states that the only quadratic polynomial pairing functions are

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Fueter-Polya Theorem

Has Statement Form

Proved By