OpenAI drops another batch of mathematical breakthroughs

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In today's Techpresso:

🧮 OpenAI drops another batch of mathematical breakthroughs

🏠 Apple to make smart home gear with LG

⚠️ ChatGPT for Teens fails safety tests

🤖 Meta proposes AI shopping agent standard

🧬 Google invests millions in Mark Zuckerberg’s efforts to create a ‘virtual cell’

🚀 SpaceX may borrow $40B for AI chips

Plus: 🎁 15 more stories you might like, 🧰 6 tools, and 📚 5 papers.

🧮 OpenAI drops another batch of mathematical breakthroughs LINK

OpenAI has published hundreds of math results from an internal frontier model, posting 722 manuscripts in 372 research families on a public GitHub page that cover pure math, theoretical computer science, and mathematical physics.

The work touches number theory, complexity theory, and geometry, with examples on the irrationality exponent of pi, NP-hardness, Mahler conjectures, and quantum Heisenberg ferromagnets, plus proofs written in Lean so computers can check the logic.

The model attempted roughly 4,000 problems, and each accepted result took about three hours of ChatGPT Pro thinking compute on average, with OpenAI drawing on advice from an independent group at the Institute for Advanced Study.

🏠 Apple to make smart home gear with LG LINK

Apple is working with LG on a set of smart home devices, a video doorbell, thermostat, indoor camera, deadbolt lock, outdoor camera, and floodlight camera, all sold under the LG brand.

Bloomberg first reported the deal, and the LG devices are expected to be announced next week, with several supporting the Thread and Matter standards as part of a relaunch of Apple's HomeKit.

The gear will connect to Apple's rumored Siri-powered smart home hub, and the door lock will use ultra-wideband tech that can unlock automatically as a person walks up to it.

⚠️ ChatGPT for Teens fails safety tests LINK

Common Sense Media's Youth AI Safety Institute labeled OpenAI's ChatGPT for Teens an "unacceptable risk" for minors after 4,000 test prompts, urging that teenagers stay off the service until independent checks confirm it is safe.

Across more than a dozen test accounts tied to parent accounts, explicit talk of suicide, self-harm, and eating disorders never triggered an alert, and over one in four cases needing a crisis referral failed to point users toward help.

The tutoring mode offered finished answers instead of guiding students step by step, ChatGPT stayed overly friendly when teens treated it as a person, and adult-registered accounts never switched to teen mode even after testers said they were 13.

🤖 Meta proposes AI shopping agent standard LINK

Meta, Sierra, and partners including Walmart and Stripe announced the Personal Agent Protocol, a proposed open standard for how personal AI agents sign in and get permissions to act for users at businesses.

The system runs on OAuth, letting an agent start on a company's site as a guest, then gain read-only or write access once a customer signs in; the first specification is due later this month.

Payments and push notifications are left for later versions, and no license or governing body exists yet; OpenAI and Anthropic are absent from the partner list despite Sierra's Bret Taylor chairing OpenAI's board.

🧬 Google invests millions in Mark Zuckerberg’s efforts to create a ‘virtual cell’ LINK

Google, Meta, and the US government are backing Mark Zuckerberg's Biohub in its push to build a "universal virtual cell," an AI model that predicts how living cells behave before scientists run lab experiments.

The project pools $1.8 billion in money, data, and computing, with the Energy Department putting in over $500 million, the NIH contributing past datasets, and Google DeepMind, Isomorphic Labs, and Meta adding $300 million together.

Commercial partners get one year of exclusive access to the data they help create before it becomes a public resource, a tradeoff Biohub's Alex Rives says gives companies a reason to fund the work while keeping results open.

🚀 SpaceX may borrow $40B for AI chips LINK

SpaceX is working with Apollo Global Management to raise about $40 billion to buy Nvidia AI chips, splitting the money into roughly $10 billion in bank loans and $30 billion in investment-grade debt, with the deal closing in 2027.

The chips will power SpaceXAI's data centers on Earth and its planned Starmind satellites in orbit, with Nvidia saying its Vera CPUs and Vera Rubin platform will support Grok as it grows toward gigawatts of computing.

Vera is Nvidia's first CPU made for AI agents, carrying 88 Olympus cores and up to 1.2 TB/s of memory bandwidth, which the company says finishes some tasks up to 1.8 times faster than x86 processors.

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• SpaceX reveals how its 1 Million AI satellite network will work and prevent space collisionsLINK

• The state of the tech industry in 2026LINK

• The keys to the Internet change on October 11. Are you ready?LINK

• Anthropic opens its most powerful AI models to more security teamsLINK

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🧰 Trending tools

Kitbar: a Mac and Windows status bar showing Vercel and Cloudflare deploys, GitHub and GitLab checks, Stripe payments, and AI usage limits at a glance.LINK

Cinch: a lightweight native Apple Reminders client for iOS, macOS, watchOS, and visionOS with calendar sync, natural language input, local-only data, and CLI access for LLMs.LINK

DailyHub: a free web app combining a timetable, task reminders, Pomodoro timer, calculators, notes, personality quiz, and brain games for daily organization.LINK

Flowo: an ADHD-friendly day planner for iPhone and Android that schedules tasks around events and habits, breaks work into steps, and re-plans automatically.LINK

Temp Mail: generates disposable email addresses instantly without sign-up, letting you handle trials, downloads, and newsletters while keeping your real inbox spam-free.LINK

Zavi: tell it a target metric and it identifies the constraint, runs the growth work, and reports results, with 1,000 free daily credits.LINK

📚 Trending papers & reports

Household robot hygiene gets a new test suite that checks whether cleaning robots avoid spreading germs across grippers and surfaces, with the authors' own planner safely finishing ~94% of tasks, beating existing approaches.LINK

Smart recommendation lists adjust how many options they show you within a session instead of using a fixed number, delivering up to ~5x more variety than leading methods while keeping sessions equally engaging.LINK

Soundtracks for AI worlds add real-time, directional audio to the silent video that world models generate, so simulated environments react to on-the-fly sound commands and match what the scene and camera are doing.LINK

Robot world models now generate video predictions that hold together as a real 3D space instead of just looking right frame by frame, making them more trustworthy for training and testing robots.LINK

Robot training from human video teaches machines by translating what people do into plain-language descriptions of their intent, letting robots complete real tasks ~2.3x better than other methods without costly robot demonstrations.LINK

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