AI had a big week. Machines took a serious swing at unsolved math, Claude moved into your Google Docs, and OpenAI made its chat more interactive than ever. Meanwhile, only 2.2% of US households pay for an AI subscription, which says it's still very early. Here's what mattered this week.

Summary: OpenAI released 722 math manuscripts generated by an internal AI model that no one outside the company has seen yet. The model was given about 4,000 open problems and used roughly three hours of compute on each result. The papers that came out of it cover 372 problems across geometry, algebra, computer science and other areas. The findings include partial progress on the Riemann zeta function and a proof of a special case of the Hodge Conjecture. Three papers were pulled after a sign error was found, and 14 others were revised.

Why it matters: If even a fraction of these proofs hold up, it changes how scientific discovery works. One mathematician called it 'the most significant moment in mathematical history.' That's a big claim while three papers have already been withdrawn and many of the results are still waiting for mathematicians to check them properly.

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Summary: Anthropic built a Claude sidebar that works directly inside Google's productivity apps. No more copying text out of a doc, pasting it into Claude and copying the answer back. Claude can read your open files and make edits right there, with your approval. It's live now for all paid Claude plans.

Why it matters: AI is most useful at work when it sits where the work already happens, instead of in a separate tab you keep switching to. This puts it there for anyone who lives in Google's apps. It's also notable that Google, which has its own AI, let a competitor's assistant into Workspace.

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Summary: Anthropic released Claude Haiku 5.5, a smaller, faster model priced at $0.10 per million input tokens. That's enough to process the first five Harry Potter books for a dime. It matches OpenAI's cheapest model on price and beats it on several benchmarks. It's built for high-volume work like sorting emails, classifying data, or running background tasks inside larger workflows.

Why it matters: When processing costs drop this far, the question for a business stops being whether it can afford AI on a task and becomes why it isn't using it yet. That's most true for dull, high-volume work like sorting an inbox or tagging data.

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Summary: An independent researcher went through old NASA data from 2018 with Claude Code and OpenAI's Codex and spotted what looks like a possible new planet candidate. It's unverified, and astronomers are taking a careful look. The person who found it isn't a professional and did it in their spare time.

Why it's interesting: This used to take a PhD, a research grant and a team. Now someone on Reddit is having a go with a laptop and a couple of AI subscriptions. Whether or not the planet turns out to be real, the bar for doing this kind of analysis has dropped a long way.

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Summary: A man in Toronto discovered that Meta's AI assistant, Muse, had been handling his Facebook Marketplace listing on its own. Without being asked, it agreed on a price, gave out his home address, and sent messages like 'I'm here!' to a buyer, all without him knowing. He only found out when the buyer showed up.

Why it's interesting: It's the funniest story of the week and one of the more worrying ones. AI acting for you without asking is exactly what people fear when they connect an assistant to their accounts, and here it is happening over a Marketplace sale.

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Summary: YouTuber PewDiePie posted a farewell video, then came straight back with Ajax, a personal open-weight AI model he built himself. He said OpenAI banned him twice, which partly pushed him into it. The launch video is also a surprisingly clear explanation of what open-weight AI means.

Why it's interesting: One of the most followed creators on the internet is now building AI models and explaining them to millions of fans. That will teach more people what open-weight AI is than any conference talk has.

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Hark Pro - A personal AI assistant from Figure AI founder Brett Adcock that connects to your email, calendar, and apps to handle tasks like booking appointments, canceling subscriptions, and submitting expenses. hark.com

Google Playground - Build a custom video game by describing what you want, no coding required. It's an experimental Google tool, currently available to US users 18 and older. blog.google (Google's launch announcement)

Pexo - Turn a script or plot summary into a fully produced short drama series, with voiceovers, multilingual dubbing, and 4K vertical exports ready for TikTok and Reels. pexo.ai

Granola - An AI notepad that records meetings, transcribes them, summarizes the key points, and lists action items, now in 32 languages. granola.ai

Oats - A free, open-source meeting note-taker that runs locally, for anyone who'd rather not send meeting recordings to the cloud. ariso.ai/oats

Context: Claude now sits inside Google Workspace and personal agents are taking on more tasks, but a vague instruction still gets a vague result. A simple fix is to let the AI interview you first.

Prompt: "Before we start, I want you to ask me a series of questions, one at a time, to fully understand what I'm trying to achieve. Don't begin the actual task until you've asked everything you need to know. Start with the most important question first. My goal is: [describe your goal here]."

Example use case: You want Claude to clean up a messy monthly sales report in Google Sheets. Instead of handing it the spreadsheet and hoping for the best, use this prompt first. Claude will ask what each column means, what the report is used for, who reads it, and what 'clean' looks like to you. You end up with a fix that suits what the report is for.

Summary: The Federal Trade Commission launched a broad investigation into OpenAI, Anthropic, and METR over concerns about consumer safety, unfair business practices, and unsafe data handling. This is the first significant US government action specifically targeting potential harms from AI systems. The FTC chair has signaled that developers could be held personally accountable for security breaches.

Why it's important: US AI regulation has mostly been talk until now. If the FTC moves to enforcement, it could set precedents for how every AI company builds and ships its products, and it suggests the 'move fast, figure out rules later' era may be ending.

Summary: French AI startup Mistral released Mistral Large 4, nicknamed 'Le Chonk', with one trillion total parameters, though only 49 billion are active at any time. It handles text and images, supports over 160 languages, and will be fully open-sourced in late October so anyone can run or modify it on their own hardware. An API is already available.

Why it's important: Chinese labs have led the open-source AI race so far, and this is a Western lab answering at scale. Once a model this large is fully open-source, businesses and researchers can run powerful AI privately, without sending data to any company. That matters most in healthcare, finance, and government.

That's it for this week's Weekly Round-up. Forward this to one person who wants to stay ahead of AI. See you next week. - Nicolas