Can you, I, or any mathematician who isn't well connected (let's say someone who is a young Maryam Mirzakhani or just someone who is in grad school) learn from the system that produced the solution to the unit distance problem? https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29a...
You will notice that it says on the first page,
"first mathematically generated in one shot by an internal model at OpenAI"
And I want to talk to models of similar aptitude and capability to help me understand nuances of the proof. Mathematicians will happy to pay for this. I've heard that people and non-profits are putting together $$$ for this to get access to these systems so that they can all interrogate them.
But the issue is that we can't. And I'm using the royal we here.
The paper says that the labs shouldn't release proofs from models that mathematicians can't interrogate. It's very clear that the models we get as users aren't the models used to produce the breakthroughs. And as LLMs display emergent capabilities, it's uncertain whether or not the model actually understands what it's explaining.
Because if I don't understand it. Professional mathematicians who are subject experts don't understand it. Then how do we know the model does? How do we know that it's correctly representing the proof produced by a more capable model? It's not logical to take any random model at its word, unless we can verify. Or, if it's the same model that produced the proof.
And that's what the mathematicians want. Access to the actual models.