Together with Bernd Sturmfels we made a new word yesterday:
theoremoid
We live in the times where a tired dentist instead of playing fruit ninja or scrolling insta now copies open math problems into chatgpt in the evening and gets back solutions that are probably true and have lean formalization.
Does everybody understand this state of research math? 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. It is for humans by human authors and 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 immediatly noticed that it is useful to have a word! I might say, "I have 5 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 btw. Most matroids are not realizable.
#math #ai