Creating a database of motivated proofs

Summary

It’s been over three years since my last post on this blog and I have sometimes been asked, understandably, whether the project I announced in my previous post was actually happening. The answer is yes — the grant I received from the Astera Institute has funded several PhD students and a couple of postdocs, and we have been busy. In my previous post I suggested that I would be open to remote collaboration, but that has happened much less, partly because a Polymath-style approach would have been difficult to manage while also ensuring that my PhD students would have work that they could call their own to put in their theses. In general I don’t see a satisfactory solution to that problem, but in this post I want to mention a subproject of the main project that is very much intended to be a large public collaboration. A few months ago, a call came out from Renaissance Philanthropies saying that they were launching a $9m AI for Math Fund to spend on projects in the general sphere of AI and mathematics, and inviting proposals. One of the categories that they specifically mentioned was creating new databases, and my group submitted a proposal to create a database of what we call “structured motivated proofs,” a piece of terminology that I will explain a bit more later in just a moment. I am happy to report that our proposal was one of the 29 successful ones. Since a good outcome to the project will depend on collaboration from many people outside the group, we need to publicize it, which is precisely the purpose of this post. Below I will be more specific about the kind of help we are looking for. Why might yet another database of theorems and proofs be useful? The underlying thought behind this project is that AI for mathematics is being held back not so much by an insufficient quantity of data as by the wrong kind of data. All mathematicians know, and some of us enjoy complaining about it, that it is common practice when presenting a proof in a mathematics paper, or eve...