This is a curated collection of "fun" problems in, or inspired by commutative algebra. By that, we mean the statement should be short, understood by most graduate students in the field, and easy to formalize, so even the AI models can enjoy them. The solutions (if they exist) should require some real efforts or creativity.
Anyone who want to have fun thinking about commutative algebra. Or want to train their AI models (who, by 2026, have been quite mediocre at the subject). That's why we provide no solutions (even for the solved ones).
Roughly, 1 and 2 stars mean graduate level exercises (and can probably be solved by 2026 Pro AI models). 3 stars and higher mean something that can be a useful part of a research paper, or a whole paper on its own. For status, "open" means "open as far as the original proposer knows" and similarly for other statuses.
Yes! And we would love to hear from you, especially when it concerns originality, correctness, or updates on the problems. The comment box is open for anyone and supports basic latex and hyperlinks. See here for details: https://katex.org
The initial idea, problems, and coding works come from the team of Hailong Dao, Daniel Dao and Lawrence Dao. But we hope to attract mathematical contributions from the whole community in the long run.