Theoremoids

Together with Bernd Sturmfels I made a new word yesterday: theoremoid.

We live in times where a tired dentist, instead of playing Fruit Ninja or scrolling Instagram in the evening, copies open math problems into ChatGPT and gets back solutions that are probably true and come with a Lean formalization.

Does everybody understand this state of research mathematics? Random strangers send us the solutions to our very hard problems from the past by email, every day. The likelihood that these mails actually contain truth is very high now, even if the senders have no idea what they are sending. They are just meat-proxying AI.

We don’t want to call this a theorem, because “theorem” has a cultural meaning. A theorem is for humans, by human authors, and it is connected to the literature. Most importantly, somebody understood it and cared.

Theorems are products of mathematics. Theoremoids anybody can make. Theoremoids need work and care to be turned into theorems.

It sounds like a joke, and frankly it started as one. But I immediately noticed that it is useful to have a word! I might say “I have five theoremoids and I don’t know which one to work on!” Or: “Oh yeah, a psychologist from Chile sent me another theoremoid today.”

The word is inspired by matroids, by the way. Most matroids are not realizable.

First posted on Mastodon on 15 September 2026.