x.com/Vvikramai/status/2084292632839385391
1 correction found
have been open and have seen no progress on the main result for at least a decade, and in most cases much longer.
That overstates how stagnant these problems were. Several of the ten areas had substantive progress in the last few years, including 2023–2025 papers that improved bounds or resolved major special cases.
Full reasoning
This clause is too sweeping for OpenAI’s 10-result package.
Several of the included topics did see important recent progress, well within the last decade:
- In binary/spherical codes and sphere packing, OpenAI’s own collection cites 2023–2025 work, including Sardari–Zargar (published 2024) and Samorodnitsky (2025). The Sardari–Zargar paper explicitly says it gives new upper bounds for spherical codes and packings, and calls itself the first such improvement since the 1978/1979 classics. That means there was notable progress very recently, not “no progress for at least a decade.”
- In extremal graph theory / the degeneracy conjecture, OpenAI’s paper says the conjecture is “known in several cases” and cites recent work such as Janzer (2023). Janzer’s paper is literally titled “Disproof of a conjecture of Erdős and Simonovits on the Turán number of graphs with minimum degree 3.” Again, that is substantial progress inside the last decade.
- OpenAI’s own chapter on the compactness conjecture also notes that the original formulation already had simple counterexamples, so the blanket “no progress” framing is inaccurate even within that chapter.
So while some of the underlying problems are longstanding, the post’s claim that these were problems with no progress on the main result for at least a decade is not accurate as a description of the set as a whole.
3 sources
- Ten Advances in Mathematics and Theoretical Computer Science
OpenAI’s paper cites recent work in these same areas, including: '[PMP23] New bounds on the size of binary codes with large minimum distance' (2023), '[SZ24] New upper bounds for spherical codes and packings' (2024), '[Sam25] On the difficulty to beat the first linear programming bound for binary codes' (2025). In Chapter 10 it also says: 'The conjecture is known in several cases' and cites Janzer (2023).
- New upper bounds for spherical codes and packings
Published: 19 October 2023. Abstract: 'We improve the previously best known upper bounds...' The paper says this is 'the first such improvement for each dimension since the work of Kabatyanskii and Levenshtein (1978) and its later improvement by Levenshtein (1979).'
- Disproof of a conjecture of Erdős and Simonovits on the Turán number of graphs with minimum degree 3
Title: 'Disproof of a conjecture of Erdős and Simonovits on the Turán number of graphs with minimum degree 3.' Abstract: 'In this paper, we disprove the conjecture...'