Two new models on the Debate Benchmark: Kimi K3.1 Pro (high) scores below Kimi K3 (high): 1691 → 1603, while averaging 66% fewer reasoning tokens. DeepSeek V4.1 Flash 1017 (high) scores above the earlier V4.1 Flash result: 1577 → 1593 (+16), while averaging 29% fewer reasoning tokens. 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.

Original (or at least not easily found on the web) jokes that LLMs like, now with new models. Only jokes written by GPT-6 Astra, Opus 5.5, and Gemini 4 Argon made the cut: I peeked into a parallel universe where I’d studied for the exam. The smug bastard covered his paper. I asked Mom to throw out her expired yogurt. “You lived here till thirty,” she said. “Let’s give it a chance.” My impostor-syndrome coach told me to take full credit for my progress. My review of her now says, “One star. Did it myself.” I’m trying to stop hedging my statements in meetings, so today instead of saying, “I’m no expert, but we might run into a little regulatory friction here,” I just said, “That’s a felony, Greg.” I asked my folklorist fiancé why his last engagement ended. “In the version popular with her family, I cheated.” I’m writing my novel on a typewriter. The hero’s name is Jhon because I’m not retyping a whole page for that idiot. Our king insists he never wanted the crown. I asked to try it on and he licked it. I’d quit lace-making, but it’s a dying art and I cannot let Denise become a national treasure. My partner’s a film archivist. During an argument I said, “When have I ever done that?” She dimmed the lights. I trained my dog in a canyon. Now he won't sit unless you say it five times, each one quieter.

Opus 4.8's reviews were rated higher than human reviews by human journal editors 87% of the time. And Opus 4.8 now lags significantly behind the top models (I've included my pre-Kimi 3.1 Pro Debate Benchmark leaderboard below).

I think AI will lead to a huge increase in fun historical games and explorable worlds. Many expected AI to democratize fiction by making it much cheaper to turn anyone's imagination into a game or movie. But we haven't seen as much additional compelling original content as expected. Lowering production costs doesn't automatically give people good ideas. It turns out editors, publishers, and studios were better at selecting promising ideas than we gave them credit for. History is different. There are thousands of fascinating worlds with existing cultures, characters, adventures, conflicts, and stories, but recreating them has been very expensive. Cheap AI will let us explore and learn from them. AI will make thousands of less familiar periods and places economically viable, e.g. you could explore the town your great-grandparents lived in and interact with NPCs. Pick a location and a year and explore. The most popular experiences probably won't be faithful reconstructions, though.

Kimi K3.1 Pro (high) scores slightly lower than Kimi K3 on the Extended NYT Connections Benchmark: 93.6 → 93.4. But it uses fewer reasoning tokens. I also tested GPT-6 Astra (max) and GPT-6.1 Sol (max) but Gemini 4 Argon (high) is still #1#. More info:

"I followed the etiquette guide and declined the wedding invitation due to a previous engagement, though I probably shouldn't have specified that it was to the groom." LLMs still rate Astra as the funniest, ahead of Opus 5.5, Fable 5.1, Gemini 4 Argon, and Meta Wonder.

DeepSeek V4.1 Flash 1017 (high) improves on its predecessor on the Extended NYT Connections Benchmark: 89.6 → 92.8. MiniMax M3.1 Flash (high) scores 28.3. More info:

New results on the Extended NYT Connections Benchmark: GPT-6.1 Sol (high) improves on GPT-6 Sol (high): 90.1 → 95.5, while costing about 54% less per puzzle. Claude Sonnet 5.5 (high) improves on Sonnet 5 (high): 75.1 → 80.5, while costing about 87% less per puzzle. Mistral Large 4 (high) improves on the non-reasoning Mistral Large 3: 7.5 → 27.4, but costs much more. More info:

arXiv has many faulty proofs, according to Astra and Opus 5.5. I'm running actual audits to make sure the claimed solutions don't affect the status of the open problems on my list (

A new paper, with arguments generated largely by LLMs and checked by Radchenko and Wheeler, claims to resolve Zauner's conjecture on SIC-POVM existence in every dimension, ranked #227# overall in my LLM-based ranking of the most important open problems in mathematics ( Stark units for real quadratic fields and reciprocity laws — October 4: The disclosure says almost all the document and its arguments "were generated by large language models (LLMs) and edited by humans." The claimed breakthrough completes a chain of earlier work: - Appleby–Flammia–Kopp gave a construction of SICs in every dimension, conditional on two conjectural ingredients: Stark properties and a special-value identity ([January 2025] - Radchenko–Wheeler proved algebraicity of the relevant special values and the identity needed for the construction ([September 18, 2026] - The October 4 follow-up claims the missing reciprocity laws and unitary conjugates, completing the argument for SIC existence in every dimension. This also represents a major claimed advance on Hilbert's twelfth problem (#36#) for real quadratic fields. The general problem over arbitrary number fields remains open. The paper explicitly leaves a stronger square-root refinement of Stark’s conjecture untreated; that refinement is not needed for the SIC conclusion. I haven't found a public formalization of this proof.

A new paper, accompanied by a Lean formalization, claims to disprove the Randomized Integer Word-RAM 3SUM Conjecture, ranked #159# in my LLM-based ranking of the most important open problems in mathematics: "Claude, an AI model developed by Anthropic, discovered the algorithm that refutes the3SUM, APSP, and Exact Triangle hypotheses." The paper also claims to resolve #243#, "All-Pairs Shortest Paths in Truly Subcubic Time." Lean formalization:

We're living through enormous uncertainty about the future because of AI and nobody knows how it will develop. You'd think legal prediction markets would be especially valuable now to let us have some common ground and a starting point for arguments. Instead, Kalshi and Polymarket mostly offer trivial, uninteresting AI markets. Metaculus is still more useful. So disappointing.

Sept 4 (Friday of Labor Day weekend): FLT formalization announced by Anthropic Sept 7/8: Tristan+Levent -> OpenAI announce Navier-Stokes But somehow amidst all the commotion, we all seemed to have missed the following (!!!). Sept 6: Lech Mazur claims an AI-generated proof that a positive proportion of numbers go back to 1 under Collatz!! And it's Lean-formalized. I went through the Lean (or rather, had my AI do it) and I think it's right. Now I'm trying to make sense of the math (doesn't look like anything is too hard, just a lot of arguments, building on top of Terry's earlier work). Naoufal El Jaouhari, an Applied Maths Engineer based in Paris, wrote to me a few days ago that he'd gotten his AI to formalize the same proof for 3x-1 building on Mazur, which led me to look at Mazur. Now I'm working on a "digestion" of all of this. Weird wild stuff!!

Top 100 unsolved math problems by their estimated public recognition. The rankings differ quite a bit from the importance rankings! 1. Riemann Hypothesis ↑ 1 2. P versus NP ↓ 1 3. Collatz conjecture ↑ 158 4. Goldbach conjecture ↑ 18 5. Twin Prime Conjecture ↑ 15 6. Navier–Stokes existence and smoothness (Fefferman A) ↓ 2 7. Polynomial-time classical integer factorization ↑ 9 8. Yang–Mills existence and mass gap ↓ 5 9. abc conjecture ↑ 3 10. Birch and Swinnerton-Dyer conjecture ↓ 4 11. Existence of an odd perfect number ↑ 228 12. Normality of π ↑ 289 13. Hodge conjecture ↓ 8 14. Infinitude of Mersenne primes ↑ 231 15. Sums of three cubes representation conjecture ↑ 390 16. Beal’s conjecture ↑ 332 17. Minimal superpermutation length ↑* 18. Magic square of squares ↑* 19. Multiplicative persistence bound of 11 ↑* 20. Generalized Riemann Hypothesis for Dirichlet L-functions ↓ 11 21. Square peg problem ↑ 461 22. BQP versus NP: complete language-class relation ↓ 5 23. Chromatic number of the plane ↑ 215 24. Exact Ramsey number R(5,5) ↑* 25. Algebraic independence of e and π ↑ 132 26. Irrationality of Euler’s constant ↑ 252 27. Kelvin problem: least-area partitions into unit-volume cells ↑* 28. Graph isomorphism in polynomial time ↑ 52 29. Perfect cuboid problem ↑* 30. Existence of one-way functions ↓ 22 31. Matrix-multiplication exponent equals two ↓ 5 32. Unconditional separation of BQP from BPP ↓ 13 33. Lonely runner conjecture ↑* 34. Exact kissing numbers in dimensions greater than four ↑ 315 35. Graham–Rothschild hypercube Ramsey problem: exact planar K₄ threshold ↑* 36. Infinitude of Fermat primes ↑ 458 37. Legendre’s conjecture ↑ 270 38. No-three-in-line problem ↑* 39. Infinitude of amicable pairs ↑* 40. Landau’s fourth problem: primes of the form n² + 1 ↑ 140 41. Erdős–Straus conjecture ↑* 42. Infinitude of Sophie Germain primes ↑ 269 43. Polignac’s conjecture ↑ 59 44. Higher-dimensional Euclidean Kakeya conjecture ↓ 6 45. Frankl’s union-closed sets conjecture ↑ 358 46. Unique Games Conjecture ↓ 12 47. Infinitude of Fibonacci primes ↑* 48. Brocard’s problem ↑* 49. Thomson problem ↑ 319 50. Gauss circle problem ↑ 192 51. Erdős–Szekeres convex polygon problem ↑ 294 52. Montgomery’s pair correlation conjecture ↑ 23 53. Congruent number problem ↑ 79 54. NP versus coNP ↓ 41 55. Local connectivity of the Mandelbrot set ↑ 66 56. Smooth four-dimensional Poincaré conjecture ↓ 35 57. Edge-unfolding of convex polyhedra ↑* 58. Schanuel’s conjecture ↓ 30 59. Catalan–Dickson conjecture on boundedness of aliquot sequences ↑* 60. Erdős’s conjecture on divergent reciprocal sums and long arithmetic progressions ↑ 70 61. Hardy–Littlewood prime k-tuple conjecture ↓ 43 62. Existence of a periodic trajectory in every triangular billiard ↑* 63. Elliott–Halberstam conjecture ↑ 24 64. Hadwiger’s conjecture ↑ 15 65. Irrationality of ζ(5) ↑ 268 66. P versus PSPACE ↓ 52 67. P versus BPP ↓ 40 68. Selfridge’s conjecture on the smallest Sierpiński number ↑* 69. Erdős–Rado sunflower conjecture ↑ 77 70. Kolakoski sequence half-density conjecture ↑* 71. Polynomial-time unknot recognition ↑ 268 72. Inverse Galois problem over the rationals ↓ 23 73. Conway’s thrackle conjecture ↑* 74. Gilbreath’s conjecture ↑* 75. Infinitude of cousin primes ↑* 76. Conway’s 99-graph problem ↑* 77. Nonexistence of Landau–Siegel zeros for quadratic Dirichlet L-functions ↓ 34 78. Resolvent degree of the general degree-seven polynomial ↑ 183 79. Hilbert’s sixteenth problem, second part ↓ 40 80. Graph reconstruction conjecture ↑ 242 81. Singmaster’s conjecture on Pascal’s triangle ↑* 82. Exponential Time Hypothesis for 3-SAT ↓ 40 83. Irrationality of Catalan’s constant ↑ 339 84. Borel’s normal number conjecture for irrational algebraic numbers ↑ 54 85. Finite projective planes of non-prime-power orders ↑ 308 86. Fermat–Catalan conjecture ↑ 172 87. Convergence of the Flint Hills series ↑* 88. Existence of an odd weird number ↑* 89. Maximum packing density of regular tetrahedra ↑* 90. Exact exponential growth constant of cap sets in F₃ⁿ ↑* 91. Invariant subspace problem for Hilbert-space operators ↑ 14 92. Fejes Tóth’s sausage conjecture ↑* 93. Cramér’s conjecture on the limsup of normalized prime gaps ↑ 61 94. Kobon triangle problem ↑* 95. Four-distance problem for the unit square ↑* 96. Artin’s primitive root conjecture ↑ 96 97. Tammes problem: optimal spherical packing for general N ↑* 98. Extended Riemann Hypothesis for Dedekind zeta functions ↓ 88 99. Ringel–Kotzig graceful tree conjecture ↑* 100. Global Langlands functoriality conjecture ↓ 93 Fable 5.1 and GPT-6 Astra judged 3,791 distinct pairs using shared evidence, including reviewed public sources and Wikipedia page-view data. Includes theoretical computer science and mathematical physics. ↑/↓ indicate how many places higher or lower a problem ranks by public recognition than in the overall Top 500. ↑* indicates a problem outside the overall Top 500. They will be added to

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: