Announcing a new project: problemsilike.com, a website collecting open problems that I, personally, like, with comments on their context, difficulty, and interest.
The goal is to track progress on mathematical questions that I think are important, and to measure human understanding of these questions, as well as the usefulness of AI tools in helping to resolve them. It is also a step for me towards thinking about what mathematics, and the dissemination of mathematics, will look like in a world of “proof abundance,” as Terence Tao put it, where generating proofs may become easier than verifying and understanding them.
Public problem lists seem to be becoming increasingly important as AI tools become more mathematically capable. In combinatorics, discrete geometry, etc.—broadly speaking, areas Erdős liked—one reason progress has been visible is the amazing Erdős Problems repository developed by Thomas Bloom, along with survey papers and problem lists that give researchers and AI tools concrete targets.
On the other hand, while they are rapidly becoming more useful for my work, the impact of AI tools—especially working autonomously—on questions that I care most about has been minimal thus far, despite my own attempts to use them. So I decided to make the kind of problem list I would like to see, with a near-infinite amount of help from Thomas Bloom in setting up the website.
There are currently ~10 problems on the site, and I hope to add a few more each week. Each problem is accompanied by some mathematical remarks, and my own view of their difficulty and interest. I think this last is especially important: I’m committing in advance to a position on the interest of these problems, to prevent goalpost-moving. And I’m trying to say something about their difficulty, to help non-experts understand what it means if progress is made.
The problems are meant to have a wide range of difficulty, with the aim of producing a sensitive instrument, though they are all open. Resolving some of them would constitute a major breakthrough; others are mostly the product of idle curiosity, and I suspect would fall quickly were they to receive sustained attention from an expert.
I’m also happy to consider submissions from research mathematicians. Please see the submission guidelines on the site.
Looking forward to seeing some progress on these questions! Check out the site here: problemsilike.com