This project aims to centralize, organize, and document the various mathematical problems posed by the legendary mathematician Paul Erdős.
Erdős offered cash prizes for the solution of many of these problems, which range from graph theory and combinatorics to number theory. This repository is structured to track the current status of these problems.
This repository is primarily maintained in English (default), but a French version is also available. Please look for .fr.md files (like README.fr.md) for the French version of any document.
The repository is organized into three main directories, representing the current status of the problems:
resolved/: Contains problems that have been fully solved. Each problem is located in a sub-folder named in the formatN-Problem-Labelwhere N is the number and Problem-Label is its short title (e.g.,01-Erdos-Discrepancy). Inside, you will find detailed explanations of the problem, the solution, and references.inprogress/: Contains problems that are well advanced but only partially solved, with significant ongoing research and open leads. The folder structure follows the same format as above.todo/: Contains a listing of all open Erdős problems. Each folder follows the formatN-Problem-Labeland contains the formal statement of the problem and any relevant background information.
Contributions are highly encouraged! Whether you are providing a new solution, updating the status of an open problem, translating a document into French, or simply fixing typos, your help is welcome.
When adding a new problem or updating an existing one, please ensure you provide both an English (README.md) and a French (README.fr.md) version.
- [2026-06-18]: Resolution of Lemma 13 - Representation Function Estimation for Erdős-Turán. Probabilistic proof of the unboundedness of r_B(n). Status: In progress.
- [2024-06-17]: Initial research on Erdős-Turán.
This project is open-source. Please check the LICENSE file for more details.