On October 20, 2026, Balázs Patkós posted on arXiv a counterexample, found by ChatGPT 6.1 Sol, to a conjecture of Frankl, Ota and Tokushige on intersecting families.
On October 20, 2026, Ludovic Patey posted on arXiv an answer to an open question in mathematical logic about the Ordered Variable Word theorem, with a core lemma proved by Claude Opus 5.5.
On October 17, 2026, Jędrzej Hodor, Piotr Micek and William T. Trotter posted on arXiv new bounds on the dimension of posets excluding a standard example, with proofs found by ChatGPT-6 Astra.
On October 16, 2026, Alexander Divoux and Shouda Wang posted on arXiv the asymptotic value of the maximum number of Hamiltonian cycles in a tournament, which would prove a conjecture of Wormald, from proofs found by GPT-5.6.
On October 15, 2026, Simon Becker and Benjamin Lawton posted on arXiv counterexamples to the ordinary Fried conjecture in dimension 3, built with GPT-6.1 Sol and partly formalised in Lean with Claude Code.
On October 14, 2026, Manjul Bhargava posted on Hexagon a proof, written up and formalised in Lean with GPT-6, that every non-square integer other than −1 is a primitive root modulo a positive proportion of primes.
On October 13, 2026, four probabilists posted on arXiv a central limit theorem for the high-temperature SYK model, proved with ChatGPT 5.5 Pro and 5.6 Pro and then formalised in Lean under one assumption.
On October 13, 2026, Nicolas Monod and Andreas Thom posted on arXiv a proof that every Lie group can be realised by permutations of a countable set, a question of Ulam, building on a construction found by GPT 6 Astra.
On October 13, 2026, Saint Wesonga posted on arXiv the resolution of two open problems on torus polynomials and the Majority function, results discovered and formalised in Lean with GPT-6 Astra.
Meta introduces Muse Wonder and Muse Wonder Full, its most capable models, available via the Meta Model API and Muse Code (Wonder) and to Muse Code subscribers (Full).
Dean Cureton and Jesse Thorner posted on Hexagon, on October 12, 2026, a proof obtained with the AxiomProver system that no Dedekind zeta function would vanish when the real part exceeds 31/32 (version of October 14).
On October 11, 2026, a contributor to the integer-mult-bounds project proposed a conditionally improved theoretical bound for multiplying very large integers.
TheoPhysEval: five AI agents on 50 unpublished theoretical physics problems
Physicists post on arXiv 50 unpublished theoretical physics problems with numerical answers and test five AI agents on them. The best, GPT-6-Astra with Codex, gets 49 of 50 problems right with web access, 46 without. Preprint not peer-reviewed; one run per agent, no timed humans.
Google DeepMind published its AlphaProof Nexus study in Science on October 8, 2026: the authors report 9 of 353 open Erdős problems and 44 of 492 OEIS conjectures solved in Lean.
Anthropic releases Claude Haiku 5.5, its small model, the first Haiku with an adjustable effort setting and an average cost about 75% lower than Haiku 4.5.
On October 7, 2026, OpenAI withdrew three manuscripts from its mathematics release, on Weil classes, Kuga-Satake K3 and the rational Hodge conjecture, after a sign error. Status: withdrawn.
Google geospatial models applied to five public-health cases
Google Research posts a preprint and blog where place embeddings improve epidemiological models (MMR vaccination, dengue in Mexico, cholera in DRC, etc.).
Mistral opens a public preview of Mistral Large 4, a natively multimodal 1-trillion-parameter model with 52 billion active parameters, weights promised by end of month.
On October 6, 2026, OpenAI released 722 mathematics manuscripts at once, written by an unreleased internal model; three were withdrawn the following day.
Visionary AI: predicting pre-eclampsia from retinal imaging (Nature Biotechnology)
Nature Biotechnology publishes a retinal vascular graph model that predicts pre-eclampsia before clinical onset, with external validation without retraining.
Arc Institute presents PIE, which predicts which genes change after a perturbation, with AUPRC 1.2 to 3.2 times that of the strongest competitor on the Replogle-Nadig dataset.
BootLoops: LLM-driven toolkit for exact quantitative science
Matthew Schwartz (Harvard) posts on arXiv a toolkit for exact computation (Feynman integrals, completeness proofs) operable by AI agents, applied to genomics, ecology and other fields.
Boston Dynamics: new 13-degree-of-freedom hand for Atlas
Boston Dynamics presents Atlas's new hand: 13 degrees of freedom, directly actuated, built for high-fidelity simulation and mass manufacturing (7 degrees on the previous generation).
Pretrained model for neutrino detectors (Nature Machine Intelligence)
Nature Machine Intelligence publishes a pretrained sparse Vision Transformer that, on simulated FASERCAL events, matches scratch training with an order of magnitude more data using about 10^3 labelled events.
Space-weather risk forecast for 66,935 power substations
A Microsoft Research post describes a system estimating space-weather risk per US substation and detecting nearly 80% of major events in the evaluation period.
Google DeepMind publishes in Nature watermarking methods for AI-generated protein sequences and structures; watermarked binders tested in the lab matched unwatermarked ones.
OpenAI releases GPT-6.1 Sol, an upgrade of GPT-6 Sol that it says nearly matches Astra on agentic coding, computer use and professional work at one fifth of the price.
Quine: AI system for biology tested on pancreatic cancer
Microsoft Research introduces Quine, a biology world model with a tool harness, and says its top-ranked compounds produced the largest shifts in tumour cell states.
AGENT: AI-designed mRNA vaccines stable at 37 °C (Nature Biotechnology)
Nature Biotechnology publishes a Bayesian-optimisation framework that found solid-state mRNA-LNP formulations in six iterations that kept bioactivity at 37 °C.
GenFocal: fine-scale weather from climate projections (Nature Machine Intelligence)
Nature Machine Intelligence publishes GenFocal, a generative framework producing fine-scale heatwaves and cyclones from coarse climate projections without temporally aligned training pairs.
Ben Antieau and colleagues, working with a language model, posted an algebraic geometry text on Hexagon on September 26, 2026. The platform labelled it "Primarily AI-generated". Status: not yet evaluated.
Claude identifies an enzyme system with CRISPR-like repeats
Anthropic reports that Claude agents spotted, in DNA data, a system (ART) pairing a reverse transcriptase, a partner gene and a repeat array, whose function is unknown.
FDA: ProNova VIRTUE QA cleared via 510(k) with a predetermined change control plan
The FDA lists a Substantially Equivalent decision on 2026-09-23 for VIRTUE QA (ProNova, K260597), AI quality assurance for proton therapy, with an authorized change control plan.
Meta: Ray-Ban Display glasses, landmark-based navigation and call hologram
Meta announces for Ray-Ban Display glasses navigation that cites visible landmarks, a voice-driven face hologram for WhatsApp calls, and expansion to five countries.
Meta: Ray-Ban Meta Audio glasses and Muse agent announced for AI glasses
Meta presents 43 g audio glasses with an AI assistant (pre-order from USD 349, shipping October 13) and announces its Muse agent coming to its AI glasses in the coming months.
Minerva: genome language model to find non-coding RNAs
A Stanford/Arc preprint introduces Minerva, which predicts interactions from sequence and describes prophage reverse transcriptase systems encoding arrays of non-coding RNAs.
Anthropic introduces Claude Opus 5.5, first model of the Claude 5.5 family, which it says matches Fable 5.1 on most work at 40% lower cost than Opus 5.
EAGLE: AI detection of oesophageal cancer on CT (Nature Medicine)
Nature Medicine publishes an AI model for oesophageal cancer screening on non-contrast chest CT, validated on 80,612 patients in 12 centres across three countries.
OpenAI adds two faster, cheaper models to the GPT-6 family, Sol and Luna, trained like Astra, with API prices cut 50% versus GPT-5.6 promotional pricing.
Xiaomi publishes on Hugging Face, under MIT licence, MiMo-V2.6-Pro-RL, an omnimodal model of 1.02T total and 42B active parameters with 1M-token context.
RetroChimera: chemical retrosynthesis model (Nature)
Microsoft Research publishes in Nature a retrosynthesis model that ensembles two complementary models; chemists accepted about 90% of its complete routes.
FDA: Epic Deterioration Index Version 2 cleared via 510(k)
The FDA 510(k) database lists a Substantially Equivalent decision on 2026-09-18 for Deterioration Index Version 2 (Epic Systems, K260008), an AI clinical-deterioration risk score.
Figure: Helix 2.5, whole-body behaviors tested in 30 unseen homes
Figure presents Helix 2.5, a model pretrained on its Index dataset that tidies living rooms, folds towels and makes beds in 30 homes with no data collected in them.
Virtual Biotech: 37,000 AI agents analyse clinical trials (Science)
Stanford researchers describe a system of 37,000 AI agents that analysed clinical trials and proposed a drug strategy (an antibody-drug conjugate targeting B7-H3) for lung cancer.
Gemini 3.8 Live and 3.8 Live Extended Thinking (Google)
Google launches two real-time voice models, one of which reasons and speaks simultaneously, available through the Gemini API, Workspace and the Gemini app.