AI Weekly Brief
AI disproves an Erdős conjecture
A general-purpose OpenAI reasoning model disproved the 80-year-old Erdős unit distance conjecture, with a proof Gowers deemed Annals-worthy.
TL;DR
- Google I/O delivered a unified agent-first platform: Gemini 3.5 Flash as the new default model (76.2% on Terminal-Bench 2.1), Gemini Omni Flash for video from any input, Antigravity 2.0 for multi-agent orchestration, and Gemini Spark as a 24/7 personal agent.
- An internal general-purpose OpenAI reasoning model disproved Erdős's 80-year-old unit distance conjecture, with a proof Fields Medalist W.T. Gowers said he would recommend to the Annals of Mathematics without hesitation.
- Anthropic acquired Stainless, the maker of every official Anthropic SDK, and signed a global alliance with KPMG (276,000+ employees), as Bloomberg reported the Pentagon is testing OpenAI, Google, and xAI models as Claude replacements.
- Google DeepMind published Co-Scientist in Nature, a multi-agent hypothesis generator already deployed with Daiichi Sankyo, Bayer, and US National Laboratories, with lab-confirmed hits including a liver fibrosis drug-repurposing candidate that blocked 91% of a scarring response.
- OpenAI opened its first overseas Applied AI Lab in Singapore (S$300M, 200+ roles) on the same day Google signed a parallel Singapore national partnership.
Editor’s Pick
What the proof reveals about AI mathematical capability is different from what earlier results established. SU-01 reached gold-medal olympiad performance last week, but through a pipeline built to instill proof search: reverse-perplexity curriculum SFT, two-stage RL, and a generative reward model scoring complete proofs. The capability was real, but it came from optimization aimed directly at it.
The Erdős result is different. OpenAI describes the model as general-purpose, and researcher Sheryl Hsu confirmed it was not trained with the goal of doing math research. It applied algebraic number theory, specifically constructing number fields with many primes of small norm, to a problem classified as discrete geometry. No geometry specialist had brought those techniques to the unit distance problem, because the connection required knowing both bodies of mathematics well enough to see one's relevance to the other.
Gowers said the proof would go to the Annals of Mathematics without hesitation and that no previous AI-generated proof had come close. Thomas Bloom, who publicly exposed OpenAI's false Erdős claim in October 2025, co-authored the verification paper, which makes the result credible against the most informed critic of earlier AI mathematics claims.
The downstream implication: if a general-purpose reasoning model can do cross-domain mathematical synthesis at this level without targeted training, then every domain where expert judgment decomposes into verifiable steps becomes a candidate for similar autonomous contribution. Legal reasoning, software verification, drug target identification, and financial modeling all share the property that success is verifiable even when the search is opaque. The proof is less a mathematics result that happened to come from AI than an existence proof that AI can be a primary contributor to frontier knowledge in domains it was never specialized for.
Model Releases
Google's Gemini 3.5 Flash. The new default for the Gemini app and AI Mode beats Gemini 3.1 Pro on Terminal-Bench 2.1 (76.2%), GDPval-AA (1656 Elo), MCP Atlas (83.6%), and CharXiv Reasoning (84.2%) while running 4x faster than comparable frontier models; Gemini 3.5 Pro targets June.
Google's Gemini Omni Flash. The first Omni-family model generates and conversationally edits video from any mix of text, image, audio, and video, with improved physics reasoning and SynthID watermarks, available to Google AI subscribers and in YouTube Shorts.
Cohere's Command A+. Cohere's first fully open-source model, a 218B MoE with 25B active under Apache 2.0, runs on two H100s or one B200 via W4A4 quantization and folds the reasoning, vision, translation, and tool-use variants into one artifact across 48 languages.
Alibaba's Qwen3.7-Max. An API-only model built for long-horizon autonomy ran 35 hours of unsupervised kernel optimization (1,158 tool calls) for a 10x speedup versus DeepSeek V4 Pro's 3.3x, and scores 80.4% on SWE-Verified and 92.4% on GPQA Diamond.
AI Tools & Products
Google's Gemini Spark personal agent. A 24/7 agent on Gemini 3.5 Flash and the Antigravity harness runs on dedicated Google Cloud VMs so it keeps working when devices are closed, spanning Workspace and MCP-based apps, with approval gates for payments and outbound email.
Google's Antigravity 2.0. Google rebuilt its coding IDE into a multi-agent orchestration platform with a desktop app, CLI, and SDK, and now provisions isolated Linux agent sandboxes from a single Gemini API call using the harness behind its own agents, which process 3T tokens a day.
OpenAI launches Guaranteed Capacity reservations. An enterprise compute reservation program with one-, two-, and three-year commitments at rising discounts across OpenAI's portfolio, competing with hyperscaler committed-use programs and giving OpenAI forward revenue visibility ahead of a potential IPO.
Claude Managed Agents gain self-hosted sandboxes. Anthropic now lets agent workspaces run inside customer infrastructure, with MCP tunnels for private connectivity to internal tools and data, addressing the data-residency and air-gap requirements that held back adoption in regulated industries.
OpenAI and Dell bring Codex on-premises. Codex will connect to the Dell AI Data Platform so agents can work on internal codebases and systems without sending data to the public cloud, with Dell AI Factory integration for its 5,000+ enterprise customers under exploration.
Research Breakthroughs
OpenAI model disproves Erdős unit distance conjecture. A general-purpose internal reasoning model used algebraic number theory to show some planar point sets have more than n^(1+δ) unit distances, overturning Erdős's 1946 conjecture; nine mathematicians including Thomas Bloom and W.T. Gowers verified it, and Will Sawin made δ = 0.014 explicit.
Google DeepMind's Co-Scientist published in Nature. Seven specialized agents rank thousands of hypotheses in an Elo tournament; lab-validated hits include a liver fibrosis repurposing candidate that blocked 91% of a scarring response, and the system is deployed with Daiichi Sankyo, Bayer Crop Science, and US National Laboratories.
Error diversity predicts RLVR training success. EDAS amplifies advantage penalties for dominant repeated errors and softens them for rare exploratory failures, adding an average 6.29 points over DAPO on Qwen3-8B across seven math benchmarks as a drop-in for any RLVR algorithm.
HRM-Text pretrains a hierarchical recurrent model. A 1B hierarchical recurrent model trained on 40B tokens for $1,500 reaches 60.7% MMLU and 84.5% GSM8K, competitive with 2–7B Transformers trained on 100–900x more tokens with 96–432x more compute.
Workflows & Techniques
Google proposes WebMCP for browser agents. A proposed web standard lets pages expose JavaScript functions and forms as structured tools that agents can call against live UI state, unlike server-side MCP, with an origin trial in Chrome 149.
ScheduleFree+ drops learning-rate schedules for pretraining. A schedule-free optimizer that replaces the learning-rate schedule with momentum-based model averaging cuts training time to equivalent loss by 31% versus Warmup-Stable-Decay at 1,000 tokens per parameter and allows anytime stopping.
Industry & Ecosystem
Pentagon tests rivals to replace Claude. Bloomberg reported that 25 Pentagon power users have tested OpenAI, Google, and xAI models against Claude since March, after Anthropic was designated a supply-chain risk for refusing to lift restrictions on autonomous weapons and mass surveillance, a designation it is fighting in court.
Anthropic acquires Stainless. The SDK and MCP-server tooling company behind every official Anthropic SDK, used by hundreds of companies to generate client libraries and CLIs from API specs, joins Anthropic to extend Claude's agent connectivity.
KPMG signs a global alliance with Anthropic. KPMG is embedding Claude Cowork and Managed Agents in its Digital Gateway for 276,000+ employees in 138 countries and becomes Anthropic's preferred private-equity consulting partner, deploying Claude into portfolio companies of firms such as Blackstone and H&F.
OpenAI opens an Applied AI Lab in Singapore. A S$300M ($235M) agreement with Singapore's digital ministry creates OpenAI's first applied AI lab outside the US, targeting 200+ forward-deployed engineers, as Google signed a parallel national partnership the same day.
Andrej Karpathy joins Anthropic pre-training. The OpenAI founding scientist and former Tesla AI director joined Anthropic's pre-training group as part of a reported recursive self-improvement research push, its highest-profile public research hire.
Anthropic's first Project Glasswing progress update. Anthropic reported that the AI-driven software supply-chain security initiative, whose founding members include AWS, Apple, Google, Microsoft, NVIDIA, CrowdStrike, and the Linux Foundation, has moved from announcement to active deployment across the consortium.
DeepSeek V4 reportedly moves to Huawei Ascend. Chinese media report DeepSeek gave Huawei's Ascend 950PR early access to V4 ahead of NVIDIA, aiming to migrate training and inference from CUDA to CANN, with Alibaba, ByteDance, and Tencent reportedly ordering hundreds of thousands of chips contingent on the result.
Trends & Predictions
Google put Gemini Spark, Antigravity 2.0's sandboxes and SDK, and the WebMCP proposal on the harness behind its own agents, which process 3T tokens a day, while Anthropic moved Managed Agents sandboxes into customer infrastructure and bought SDK maker Stainless.
- Prediction (Nov 2026): Agent harness capabilities (sandboxing, credential management, tool connectivity, state persistence, subagent orchestration) become a required part of flagship system cards and benchmark comparisons, displacing single-turn capability as the main enterprise procurement axis.
- Resolves: Yes if by November 22, 2026 the system cards or launch posts for the latest flagship models from at least three of OpenAI, Google, Anthropic, xAI, and Meta include a dedicated evaluation of the agent harness itself (sandboxing, credential management, state persistence, or subagent orchestration).
Based on Google's Gemini Spark personal agentGoogle's Antigravity 2.0Google proposes WebMCP for browser agentsClaude Managed Agents gain self-hosted sandboxesAnthropic acquires Stainless
AI starts producing verified scientific and mathematical results
AI in scientific discoveryStrengthenedContinues fromMay 15
An OpenAI general-purpose reasoning model disproved Erdős's 1946 unit distance conjecture, verified by nine mathematicians including W.T. Gowers, and Nature published DeepMind's Co-Scientist, whose lab-validated liver fibrosis candidate blocked 91% of a scarring response.
- Prediction (Nov 2026): At least one AI-assisted result is accepted at STOC, FOCS, or the Annals of Mathematics with AI credited as a primary contributor, forcing new journal and grant-agency policies on AI authorship.
- Resolves: Yes if by November 22, 2026 STOC, FOCS, or the Annals of Mathematics accepts a paper that credits an AI system as a primary contributor to its main result, as shown in the paper or the venue's accepted-papers list.
Based on OpenAI model disproves Erdős unit distance conjectureGoogle DeepMind's Co-Scientist published in Nature
KPMG is putting Claude Cowork and Managed Agents in front of 276,000+ employees and became Anthropic's preferred private-equity consulting partner, while 25 Pentagon power users tested OpenAI, Google, and xAI models as Claude replacements after Anthropic was designated a supply-chain risk.
- Prediction (May 2027): The Anthropic-Pentagon dispute is not resolved before the phase-out deadline, and Anthropic's revenue mix tilts toward regulated commercial sectors (financial services, healthcare, legal, education) and away from defense, diverging from OpenAI and Google.
- Resolves: Yes if on May 22, 2027 the Defense Department's supply-chain-risk designation of Anthropic remains in force and Anthropic has announced no new Defense Department contract, per DoD statements, court records, and Anthropic's newsroom.
Based on KPMG signs a global alliance with AnthropicPentagon tests rivals to replace Claude
Chinese media report DeepSeek gave Huawei's Ascend 950PR early access to V4 ahead of NVIDIA to migrate from CUDA to CANN, with Alibaba, ByteDance, and Tencent reportedly ordering hundreds of thousands of chips contingent on the result.
- Prediction (Nov 2026): If DeepSeek V4 ships with confirmed training parity on Huawei chips, Chinese frontier compute procurement shifts measurably from export-controlled NVIDIA GPUs toward domestic silicon.
- Resolves: Yes if by November 22, 2026 DeepSeek states in a V4 technical report or official announcement that V4 was trained primarily on Huawei Ascend chips, and Reuters or Bloomberg reports a confirmed Ascend 950 order from Alibaba, ByteDance, or Tencent.
Alternatives to Transformers start winning at equal compute
Architecture and inference efficiencyStrengthenedContinues fromMay 15
HRM-Text's 1B hierarchical recurrent model, trained on 40B tokens for $1,500, reached 60.7% MMLU, competitive with 2–7B Transformers trained on 100–900x more tokens, and ScheduleFree+ cut time to equivalent loss by 31% versus Warmup-Stable-Decay.
- Prediction (Nov 2026): At least one frontier lab incorporates a non-standard architectural element, recurrent, hybrid, or AI-discovered, into a production model.
- Resolves: Yes if by November 22, 2026 OpenAI, Google DeepMind, Anthropic, Meta, xAI, DeepSeek, Alibaba Qwen, or Mistral ships a production model whose technical report or model card describes a recurrent-depth (looped or hierarchical recurrent) or AI-discovered architecture component.
Based on HRM-Text pretrains a hierarchical recurrent modelScheduleFree+ drops learning-rate schedules for pretraining