Muse Wonder (high) scores 1.96 on the Short Story Creative Writing Benchmark, compared with 0.56 for Muse Spark 1.3 (high). Gemini 4 Argon (high) scores 0.80, up from −2.17 for Gemini 3.1 Pro Preview. github.com/lechmazur/writing… Argon's improvement over Gemini 3.1 Pro is large. It won all 50 matched story comparisons. Required objects, abilities, and constraints more often affect what happens in the story. Characters' solutions have clearer preparation and consequences, and relationships more often involve reciprocal needs. Gemini 3.1 Pro more frequently supplies symbolic ingredients and then explains that the problem has been solved. Argon still has recognizable habits: repeated names, explanatory narration, and endings that resolve emotional conflict too neatly. Stronger construction has not eliminated repetition or made its writing consistently subtle. The Creative Writing Benchmark tests how well models turn constrained briefs into complete 600-800-word stories. Each brief specifies 10 required elements, including a character, object, setting, motivation, and tone, that must meaningfully shape the story. Judges assess prose, originality, coherence, characterization, and how effectively the required elements work together. Models write to the same prompts. The comparisons use three judges from different model families, excluding both writers' families. Each story pair is judged in both presentation orders to reduce position bias. The leaderboard covers 59 writer models and 110,748 evaluator judgments.

Gemini 4 Argon (high) takes first place on the Extended NYT Connections Benchmark with 98.6, up from Gemini 3.1 Pro's 97.4! 🏆 Cost per puzzle drops 71%. More info: github.com/lechmazur/nyt-con…

Muse Wonder (high) scores 93.4 on the Extended NYT Connections Benchmark, ahead of Muse Spark 1.3 (high) at 85.1. It's among the most expensive models tested. More info: github.com/lechmazur/nyt-con…

Mistral Large 4 (high) scores slightly higher than Mistral Large 3 on the Short Story Creative Writing Benchmark: −1.72 → −1.59. More info: github.com/lechmazur/writing…

New LLM-assisted papers claim to resolve the Kannan–Lovász–Simonovits (KLS) conjecture, ranked #95 overall and #1 in applied and computational mathematics in my LLM-based ranking of the most important open problems in mathematics. arxiv.org/abs/2610.01447 "The AI tools used in this work were GPT-6 Astra, GPT-5.6 Sol, Claude Fable 5, and Fable 5.1" arxiv.org/abs/2610.05474 "Most proofs and mathematical ideas in this paper were found by ChatGPT" - Song–Zhang introduced a key criterion and obtained a dimension-dependent bound (Oct 1). - Bizeul–Klartag–Lehec built on that criterion to claim a full proof (Oct 4). - Song–Zhang’s revised paper also claims a full proof, using a different final argument (also Oct 4). proofatlas.ai/open-problems/

New on ProofAtlas: the Collatz Explorer proofatlas.ai/explore/collat… - Follow a trajectory. Play through a journey, jump to its peak, or inspect individual steps. - Try huge numbers. Enter starting numbers thousands of digits long, with exact integer arithmetic. - See where paths merge. Discover the shared branches behind seemingly different journeys. - Compare starting numbers. Explore ranges of up to 5,000 consecutive starts. - Share a view. Send a link to your chosen numbers and chart settings. - Explore in 3D. Rotate the view to see the paths from another angle.

The Ultimate Top 500 Open Problems in Mathematics proofatlas.ai/open-problems/ Weeks of work by 4 LLM families (GPT 6, Fable 5.1, GLM-5.3, DeepSeek V4 Pro). 34,890 pairwise judgments across 1,227 candidate problems. They ran repeated discovery rounds, source checks, deduplication, and clarification of exact problem statements. Models compared problems using source-backed descriptions without seeing the existing rankings or other models' judgments. The comparisons considered the significance of a resolution, centrality to the field, connections across disciplines, scholarly and public recognition, and potential scientific or practical impact. Results were statistically combined and checked for ranking uncertainty and sensitivity to individual model families. Includes theoretical computer science, and mathematical physics. The list includes plain-language explanations, sources, notes on what remains open, and links to related research where available. Where the targets of recent AI results would rank if they were still open: #21 — Smooth-forced Navier–Stokes breakdown (Fefferman C). #32 — Unforced three-dimensional Euler blowup. #92 — The Jacobian conjecture in general dimension. #167 — Whether every group is sofic. #211 — The planar unit-distance conjecture. Note that the recently announced Navier–Stokes result concerns flow driven by a smooth external force. #4 entry is unforced three-dimensional Navier–Stokes global regularity (Fefferman's statement A), which remains open. Showing that a forced flow can develop a singularity does not settle whether singularities can arise without external forcing.

ANNOUNCEMENT: An AI milestone on one of maths' most famous unsolved problems: COLLATZ. For every sufficiently large X, at least cX positive integers n < X reach 1 within 10.46 ln(n) ordinary Collatz steps, for one fixed c > 0. Previously, lower bounds such as X^0.84 and X^0.90 left open whether the proportion of starting values reaching 1 could tend to zero. Lean-formalized (42k additional lines), building on earlier formalizations of almost-boundedness (Tao) and its natural-density extension. Developed primarily by AI agents using the ProofAtlas.ai harness and Codex, with some high-level guidance from me (which may or may not have helped). Paper: proofatlas.ai/papers/positiv… Formalization: proofatlas.ai/formalizations…

Fable 5.1 is the new Debate Benchmark Champion (+11 vs Fable 5)! 🏆 GPT-6 Astra lands below GPT-5.6 Sol (−39). GLM-5.3 (high) debuts at #4 among current models. It gains 80 points over GLM-5.2 max: 1573 → 1653. Hy4 Preview delivers the biggest generational leap: 1395 → 1590 (+195). Gemini 3.8 Flash also advances over 3.7: 1464 → 1524 (+60). Muse Spark 1.3 trails 1.1 by 46. Debate Benchmark tests how well models defend a position through sustained, adversarial, multi-turn opposition across hundreds of topics. It demands broad knowledge, factual accuracy under pressure, sharp rebuttals, and arguments that hold together round after round. Every matchup runs twice on the same motion, with PRO and CON swapped to control for side advantage. Three judges from distinct model families independently evaluate each debate’s winner and margin. More info: github.com/lechmazur/debate

Using AI, I found an explicit 12-vertex counterexample to Jackson's 1981 conjecture that every regular bipartite tournament decomposes into directed Hamilton cycles and verified it in Lean. Granet's 2022 theorem for sufficiently large regular bipartite tournaments is unaffected.

AI agents produced a Lean-verified strengthening of Tao's landmark Collatz theorem to natural density, one clock: for every f(N)→∞, almost every N has an iterate below f(N) within 436 ln N raw steps. Paper: proofatlas.ai/papers/natural… Formalization: proofatlas.ai/sources/natura…

Kimi K3 scores 95.8 on the Extended NYT Connections Benchmark, extending its lead as the top open-weights model. Kimi K2.6 scored 91.4.

Kimi K3 ranks second overall on the Debate Benchmark, trailing only Claude Fable 5! However, it is much more expensive to run than Kimi K2.6.

The LLM position-bias benchmark asks a simple question: when the same two answers are shown in opposite orders, does the model keep the same preference or does display order change the result? Fable 5 and Opus 4.8 are the strongest frontier-models. GPT-5.5 improves over 5.4.

Opus 4.8 underperforms Opus 4.7 on PACT, the multi-round buyer-seller negotiation benchmark: 1945 → 1787. Qwen 3.7 Max underperforms Qwen 3.6 Max: 1705 → 1511. Ernie 5.1 is also slightly below Ernie 5.0: 1379 → 1358. Step 3.7 Flash lands at 1453. GPT-5.5 holds the #1 spot.

GPT-5.5 improves over GPT-5.4 and overtakes Opus 4.6 to take the 2nd place behind Gemini 3.1 Pro on the Extended NYT Connections Benchmark: xhigh: 94.0→97.5 high: 93.6→96.9 medium: 92.0→95.0 no reasoning: 32.8→37.5 Kimi K2.6 improves over Kimi K2.5 (78.3→91.4) and becomes the #1 open weights model. DeepSeek V4 Pro improves over DeepSeek V3.2 (50.2→75.7). DeepSeek V4 Flash scores 53.2. Qwen 3.6 Max Preview scores 82.2 (Qwen 3.6 Plus scored 71.3). Tencent Hy3 Preview scores 30.2. Ling 2.6 1T (no reasoning) scores 10.8.

Opus 4.7 (high) takes #1 on the LLM Debate Benchmark, leading the previous champion, Sonnet 4.6 (high), by 106 BT points! Incredibly, it has not lost a single completed side-swapped matchup: 51 wins, 4 ties, and 0 losses!