Welcome back to AI Researches! 👋

This week, Claude Fable 5 made headlines after reportedly finding a counterexample to the 87-year-old Jacobian conjecture in a single evening. If verified, it would mark one of AI's biggest contributions to mathematics so far, showing that AI is beginning to tackle problems once thought to require years of human research.

There's plenty more to catch up on. We cover Kimi K3 and Thinking Machines Lab's new open models, OpenAI's latest releases, AI tutorials, this week's best AI tools, expert predictions, and the biggest AI developments you should know.

Let's dive in. 

In today’s AI researches:

• Claude Fable 5 Breaks an 87-Year Math Problem Overnight

• Moonshot AI launched Kimi K3

• Mira Murati’s Thinking Machines Lab has entered the open-model race.

• Learn How to Build a mini-SaaS from one API with ChatGPT Sites

• AI Researches case studies

• AI tip: Cut Your Claude Fable Token Usage by 60%

• wild predictions from DeepMind’s CEO, Satya Nadella

• Best performing Ai tools of the week

• More Ai news and developments

Read time: 5 minutes

 NEW 

🧮 Claude Fable 5 Breaks an 87-Year Math Problem Overnight

AI Researches: Claude Fable 5 reportedly produced a short counterexample that disproves the Jacobian conjecture, an 87-year-old math problem that has confused top mathematicians since 1939.

The Details

• Anthropic researcher Levent Alpöge posted the result on X, saying Fable worked on it during the World Cup final and found a clean counterexample.

• The Jacobian conjecture basically asks whether a certain kind of polynomial map must always have a reverse version, and mathematicians long believed the answer should be yes.

• Fable’s counterexample reportedly shows three different input points leading to the same output, which breaks the idea that the map can always be reversed.

• Other researchers quickly started checking the result, and some said the formula is short enough to verify by hand instead of needing a huge proof.

why this is important

If this holds up, it shows AI is starting to do more than assist with math homework — it can challenge old problems, find cracks humans missed, and maybe change how future research gets done.

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 iMajor AI News that Happened in this week i

Moonshot AI launched Kimi K3, its strongest open model yet.
Moonshot’s new model reportedly competes with Claude Fable 5 and GPT-5.6 Sol while offering open weights and lower pricing.

Mira Murati’s Thinking Machines Lab has entered the open-model race.
Its first model, Inkling, can be downloaded or fine-tuned through Tinker, giving developers more control over how it is trained and deployed.

OpenAI just launched a $230 control pad for managing Codex agents.
Codex Micro uses light-up keys, a joystick, and a dial to show agent status, switch between coding tasks, and adjust reasoning levels.

More than 200 AI researchers and economists say the coming job disruption could arrive within a decade. Backed by 16 Nobel winners and leaders from major AI labs, the letter urges governments to start planning for large-scale labor and economic changes immediately.

🏗️ Build a mini-SaaS from one API with ChatGPT Sites

Turn a single public API into a small hosted web app by planning the product, building an MVP in Codex, and publishing it with ChatGPT Sites.

1. Pick one API
Choose a public API and define one clear job your app should perform.

2. Create the PRD
Ask ChatGPT to turn the idea, user, goal, inputs, outputs, and limits into a short product plan.

3. Build the MVP
Send the PRD to Codex and ask it to build the first working version using Git and Sites.

4. Deploy the app
Publish it with ChatGPT Sites as private for your team or public for anyone to use.

5. Manage and improve
Use the Sites sidebar to review deployments, track analytics, and add only the next useful feature.

Tutorial link: Creating and managing ChatGPT Sites from OpenAI. ChatGPT Sites lets eligible users create, preview, publish, and share lightweight apps, with access depending on plan, region, and workspace settings.

AI research team Weco says its AI agent AIDE² improved its own research process over eight days, outperforming a version that engineers had spent two years refining. The system repeatedly tested and kept only the changes that worked, showing an early example of AI improving itself with minimal human involvement.

The AI Futures Project, the team behind AI 2027, released AI 2040, a report exploring five possible futures for advanced AI over the next decade. Their recommended plan calls for the U.S. and China to pause the most powerful AI training in 2029 while increasing transparency and global oversight to reduce the risk of losing control over future AI systems.

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⚡ Cut Your Claude Fable Token Usage by 60% With This Setup

1. Set up the orchestrator
Update Claude, open Claude Code, install the Codex plugin, and start a new session.

2. Split the work
Let Claude Fable handle planning, important decisions, and the final review, while Codex or a lower-cost Claude model takes care of browsing, coding, research, and repetitive tasks.

3. Use a lower-cost fallback
If you don't have Codex, launch Claude Code, switch to a cheaper model with /model, and use the /advisor command to keep Fable as the reviewer.

Pro Tip: Save this workflow as a reusable Claude Code template. Use Fable only when strong reasoning is needed, and let cheaper models handle the repetitive execution to dramatically reduce token usage.

🔗 Learn more→

DeepMind’s CEO proposing a U.S. AI watchdog that would test advanced models before public release for risks like deception, cyberattacks, and biological misuse, with frontier labs submitting models for review 30 days before launch.

Satya Nadella calls this the “Reverse Information Paradox”: the more a company uses AI, the more valuable internal knowledge it may reveal through prompts, feedback, and corrections. He says enterprises need private learning environments, model choice, and clear ownership of their AI-generated knowledge.

• 🎬 CueTheScene — Produces complete YouTube videos from a single topic, handling the script, voiceover, footage, captions, thumbnail, and publishing workflow.

• 🗺️ MonkeyEatingMango — Plans complete trips with daily schedules, real restaurant recommendations, mapped routes, weather details, and estimated costs.

• 📱 Whacka — Turns simple messages inside Telegram or Discord into working apps, taking care of the design, development, hosting, and deployment.

• ✍️ Humanize AI Text — Refines drafts from ChatGPT, Claude, and Gemini into smoother, more natural writing that feels less machine-generated.

• 🧹 MailSweeper — Finds inbox clutter, outdated newsletters, and storage-heavy emails, then automatically clears unwanted messages using scheduled sweeps.

• 📖 Librida — Helps turn an early book idea into a complete published work, supporting character development, plotting, structure, writing, and distribution.

• 🎨 MojoMake — Brings leading AI image and video models into one workspace for generating visuals, animating images, and testing creative ideas quickly.

The U.S. is reportedly considering new restrictions on Chinese AI models. Following Moonshot AI’s Kimi K3 release, U.S. officials are reportedly revisiting restrictions on Chinese models, despite conflicting reports about whether any action is imminent.

Anthropic has finalized how users will access Claude Fable 5. The model will remain available on Max and Team Premium plans with reduced usage limits, while lower-tier users will move to pay-per-use after receiving a one-time credit.

New York became the first U.S. state to formally pause major AI data center projects. The 12-month freeze gives regulators time to create new standards for electricity, water, and environmental impacts as AI infrastructure demand grows.

Elon Musk and Sam Altman are publicly clashing again over Apple’s lawsuit.

Apple is suing OpenAI over alleged theft of its hardware secrets. The lawsuit claims former Apple employees Tang Tan and Chang Liu took confidential designs and supplier information to help develop OpenAI’s unreleased AI device.

Unity just launched a free CLI built for AI-powered game development. It lets coding agents and CI pipelines manage Unity projects, editors, authentication, and automated workflows directly from the terminal.

Meta released Muse Spark 1.1 for AI agents and computer use. The model can operate across apps, run parallel subagents, and handle long tasks through a 1-million-token context window.

OpenAI unveiled GPT-5.6 alongside a new AI workspace called ChatGPT Work. The release introduces Sol, Terra, and Luna models, plus a work platform that combines AI agents, browser control, and desktop automation.