But what's crazy is that within the last day or so, we've also gotten LLM-assisted solutions to #95, the Kannan\u2013Lov\u00e1sz\u2013Simonovits (KLS) conjecture, by three different authors in parallel (all extending Song\u2013Zhang's key criterion introduced on Oct. 1), #278, the Mumford\u2013Shah conjecture, and #227, Zauner's conjecture on SIC-POVM existence in every dimension, which also represents a major claimed advance on Hilbert's twelfth problem (#36) for real quadratic fields.
This is likely because OpenAI's solutions to 100 open conjectures are expected to drop any day, so everyone is in a hurry not to get scooped."},"story_title":{"matchLevel":"none","matchedWords":[],"value":"Subquadratic 3SUM and Subcubic APSP"},"story_url":{"matchLevel":"none","matchedWords":[],"value":"https://arxiv.org/abs/2610.06783"}},"_tags":["comment","author_zone411","story_49977437"],"author":"zone411","children":[49983790],"comment_text":"I maintain an LLM-ranked list of the 500 most important open problems in math at https://www.proofatlas.ai/open-problems/. This problem was ranked #159, and it also resolved #244, "All-Pairs Shortest Paths in Truly Subcubic Time." It is formalized in Lean.
But what's crazy is that within the last day or so, we've also gotten LLM-assisted solutions to #95, the Kannan\u2013Lov\u00e1sz\u2013Simonovits (KLS) conjecture, by three different authors in parallel (all extending Song\u2013Zhang's key criterion introduced on Oct. 1), #278, the Mumford\u2013Shah conjecture, and #227, Zauner's conjecture on SIC-POVM existence in every dimension, which also represents a major claimed advance on Hilbert's twelfth problem (#36) for real quadratic fields.
This is likely because OpenAI's solutions to 100 open conjectures are expected to drop any day, so everyone is in a hurry not to get scooped.","created_at":"2026-10-06T20:29:47Z","created_at_i":1791318587,"objectID":"49983654","parent_id":49977437,"story_id":49977437,"story_title":"Subquadratic 3SUM and Subcubic APSP","story_url":"https://arxiv.org/abs/2610.06783","updated_at":"2026-10-08T17:13:25Z"}],"hitsPerPage":20,"nbHits":2,"nbPages":1,"page":0,"params":"query=Kannan-Lovasz-Simonovits&advancedSyntax=true&analyticsTags=backend","processingTimeMS":10,"processingTimingsMS":{"_request":{"roundTrip":28},"fetch":{"query":9,"total":10},"total":10},"query":"Kannan-Lovasz-Simonovits","serverTimeMS":11}