Identify the source
Choose a problem already listed in the AIM GitHub repository, even if someone has explained it before. Record its problem ID, statement, status and source revision.
View the AIM collection ↗Open problems from the AIM GitHub repository
Readable accounts of open problems
Papers and videos explaining open applied mathematics problems in the AIM GitHub repository, including partial results and later resolutions.
A contribution can explain the mathematics, develop a worked example or clarify an application. A new theorem or a solved conjecture is not required. Authors receive credit for their explanations and cite the mathematical work they draw on.
Papers and videos are both welcome. Explanations of open, partial, claimed, solved and formally verified entries are eligible for the library, independently of the optional competition.
About the project
Understanding the mathematics
Following a proof does not always explain why an approach works, where an assumption matters or what the result is useful for. Examples, context and connections to applications can help make those ideas clear.
A clearer understanding of an application can be a paper’s entire contribution. A paper might explain how mathematics connected to an AIM problem describes a phenomenon, clarifies a model’s assumptions or supports a computational method. It need not introduce a new theorem or solve the conjecture.
Contributions may also explain the statement, historical context, known cases or proof of a repository problem. State what is established and what remains open, cite the problem record and your sources, and credit the mathematical authors. For new problems, corrections or additional solutions, follow the contribution procedure in the source repository.
This AIM project is not affiliated with the American Institute of Mathematics.
The library
Preparing an explanation
Contributions can cover a problem’s statement, known cases, proofs or applications. The examples and level of detail should suit the intended audience.
Explain the ideas
Develop your account of the problem, its mathematics or an application. Use examples to explain the ideas, and distinguish established results from conjectures.
Guidance for contributors →Submit for review
Send a link to your paper or video and a plain-text overview through the common submission form. Organisers review submissions privately and agree any public version with the author before publication.
Submission guidance →The library
Published explanations
Accepted explanations receive their own library pages with author credit and citations to the AIM problem record and sources. Multiple explanations of the same conjecture are welcome: different perspectives can help different readers. Contributions are welcome throughout the year; entering the competition is not required.
View the explanation library →Competition
Enter the AIM competition
Entries close on . Eligible contributors may opt in when submitting a paper or video to the library. Winning entries receive a cash prize and a certificate, and selected explanations form a curated publication with author credit.
Competition arrangements →The team
Website maintainers
For general enquiries about AIM, explained, contact any of the researchers below.
- Steven L. BruntonUniversity of Washington
- Matthew J. ColbrookUniversity of Cambridge
- Maarten V. de HoopRice University
- George StepaniantsUniversity of CambridgeVisiting faculty, New York University (2026–27)
- Alex TownsendCornell University
- Rachel WardThe University of Texas at Austin