“OpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.”
The rumors were true. "The current catalogue contains 722 manuscripts organized into 372 families. A family groups related papers, which may include a principal result, companion arguments, consequences, or alternative proofs. Each family …
This is significant progress and released without all the drama. Some very important progress in Reinmann, Hodge and unique games theorem. Point the repo to your agent and ask for the significance! In a way this is probably 50-100 years of…
It’s fascinating to read through the reasoning traces: https://github.com/openai/math/tree/main/reasoning_traces Look at one of their examples of an initial prompt: https://github.com/openai/math/blob/main/reasoning_traces/re...
This includes a proof of Barnette's Conjecture, which is one of the graph theory conjectures that I tried attacking with SOTA models a few months ago. I like it because it is easy to understand with a basic knowledge of graph theory. I spe…
A quick check shows that this list claims to fully solve 90 of the top 500 open problems in math (https://proofatlas.ai/open-problems/). The highest ranked would be: | 22 | Hilbert’s tenth problem over ℚ | | 29 | Unique Games | | 31 | Ande…
As Kevin Buzzard recently said: > In a 2020 piece in the Notices of the AMS, I asked the following question: “If one human had an understanding of all of modern pure mathematics simultaneously, how much further would they immediately be ab…
Unique Games Conjecture [0] is a seminal conjecture in Complexity Theory, and is an underlying assumption for many, many inapproximability results. A valid proof is a big deal! [0] https://en.wikipedia.org/wiki/Unique_games_conjecture [1] …
As a TCS/scheduling person, this one is definitely of lesser importance than UGC, but it has been an open problem since the book of Garey and Johnson in 1979: A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling [1] Since some…