Draft:Erdős's problems

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Erdős's problems are a set of over 893 mathematical problems posed by Hungarian mathematician Paul Erdős from his mathematical career spanning from the 1930s to the 1990s.

History

In contrast to many mathematicians who collect their problems into a single list or publication, Erdős posed his problems throughout his career in various papers, lectures, and personal communications. He often offered monetary prizes for solutions, ranging from a few dollars to thousands of dollars depending on the problem's difficulty and his assessment of its importance.

Many of these problems became central challenges in combinatorics, graph theory, and number theory. Erdős continued posing problems until his death in 1996, with some of his final problems appearing in posthumous publications.

Prize system

Erdős would pay those who solved his problems. The amounts ranged from $25 to several thousand dollars, with the value reflecting both the problem's difficulty and its mathematical significance. This system helped motivate research and brought attention to important mathematical questions. As of 2024, several of his problems remain unsolved with their prizes unclaimed. The Erdős Prize Committee, established after his death, maintains and administers these prize offers.

Notable problems

Number theory

The Erdős–Turán conjecture on arithmetic progressions