OpenAI says it solved 100 open math problems

Top engineers at Anthropic and OpenAI say AI now writes 100% of their code.

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1.  OpenAI claims 100 open math problems and forms a panel to check its work. OpenAI announced that the internal model behind its Navier-Stokes claim has now resolved more than 100 long-standing open problems across most areas of mathematics, and named an independent advisory group of nine mathematicians, including Timothy Gowers, Martin Hairer and Edward Witten, to assess results and advise on how to publish them. The group is unpaid, can speak publicly, and, as TechCrunch points out, has no say over how fast OpenAI pushes ahead. Twenty-five Fields Medalists signed an open letter this month objecting to labs racing each other on famous problems; only one of them is on the panel. None of the 100 has been independently verified yet.

2.  Amazon blocks Meta's Muse; Shopify invites it in. Amazon cut off Meta's agent from Amazon.com, telling users that access by an unauthorized agent violates its conditions of use. Amazon says Muse never asked permission, does not identify itself when browsing, and stores customer credentials; Meta says it never sees passwords. The same day Shopify announced that Muse can browse and check out at Shopify stores through Shop Pay. Our Frontier section below has the rest.

3.  Google launches a laptop line built for Gemini. Google unveiled the Googlebook, a range of laptops from HP, Dell, Lenovo, Acer and ASUS starting at $899 and sold as the first laptop designed for Gemini. The two features Google leads with: Magic Pointer, where wiggling the cursor summons Gemini to act on whatever you select, and Rambler, which turns messy dictation into clean, formatted text. Preorders are open; a ship date is not.

4.  Grok 4.7 arrives with a larger base model and the same price. SpaceXAI released Grok 4.7, built on a new larger base model with longer reinforcement training on tasks that take hours, at the same $2 per million input tokens and $6 per million output as 4.6. A fast variant runs twice the speed at twice the price. It scores 46.3% on CursorBench 4.0 and is available in Cursor, Grok Build and the API today.

The setup. Two weeks after launch, Meta's Muse is the top free app on the iPhone, and its whole pitch is that it does the buying for you. That works only if stores let it in. On Monday the two biggest names in online retail gave opposite answers within hours of each other.

The wall. Amazon's block is framed as a security matter, and the objections are real: an agent that browses without identifying itself, holds a customer's credentials, and reads order history is a legitimate concern for any platform. But Amazon also made more than $68 billion from advertising last year, nearly all of it from humans scrolling past sponsored products. An agent that fetches the cheapest matching item and checks out never sees an ad. Amazon is protecting its customers and its ad business at the same time, and it is hard to say which motive is bigger.

The door. Shopify went the other way and wired Muse into Shop Pay, so the agent can discover and buy across Shopify stores in one tap, inside Muse or WhatsApp. Tobi Lutke called it partnering deeply. Shopify's logic is the inverse of Amazon's: it sells tools to merchants, not ads to shoppers, so every new channel that brings a buyer to a Shopify checkout is pure upside. The company's own numbers say Shop Pay lifts conversion by roughly 80%; an agent that skips straight to it is the dream customer.

The stakes for sellers. If agents take off, the question for every merchant is who owns the customer. On Amazon the customer already belonged to Amazon. On a Shopify store the customer is yours, and Muse arriving at your checkout with a ready-to-pay buyer is a gift, right up until Meta decides which store its agent visits first. The Muse connector program launched last week is where that ranking will be decided.

The reframe. This is the first real test of whether agentic shopping is a channel or a threat, and the answer depends on your business model. Ad-funded marketplaces will fight it. Merchant-funded platforms will court it. If you sell online, the practical move this week is simple: check whether your store is reachable by Muse, decide whether you want it to be, and watch which side wins the first holiday season.

You cannot trust the video call. A demo on r/ChatGPT swaps a person's identity mid-livestream convincingly enough that the thread turned into a debate about whether any video evidence still counts (3K upvotes). Worth showing anyone in your company who approves wire transfers over a call.

Apple owes you $25. If you bought an iPhone 15 Pro or any iPhone 16 in the US between June 2024 and March 2025 expecting the Siri features Apple advertised and delayed, you are in the $250M settlement. Claims pay $25 per device, up to $95 depending on how many people file, and the deadline is December 21.

Jev in the wild. Two demos of TypeSafe's no-text model are circulating: a copy-and-paste that understands what it is pasting into and fills forms accordingly, and a browser agent that found and booked a flight in seven seconds. Both are on Superhuman's archive only, so no link, but the form-filler is the one to watch.

Ducks and fish. The AI-generated culture corner this week: a fan-made DuckTales live-action trailer passed 2M views, and someone rewired a Big Mouth Billy Bass to deliver motivational speeches (16K likes). Neither is linkable outside the archive; both are exactly what you think.

Three tools worth a look. Hoogly turns employee voice notes into tracked actions, Sai is an AI secretary that works your screen autonomously, and Streva does instant translation for meetings. All early; try them on low-stakes work first.

Audit any onboarding flow in one pass

Most products lose the majority of new users before they reach the moment the product becomes useful, and most teams have never written down what that moment is. This prompt makes ChatGPT or Claude walk your onboarding one screen at a time, name the reason people quit at each step, and rewrite the whole thing with fewer steps and better copy. Paste your screens as text; you do not need screenshots.

Swap [ACTIVATION MOMENT] with something concrete like "first order placed", "first invoice sent" or "first teammate invited"; a vague goal produces a vague audit. Advanced tip: run it twice, once as written and once with "assume the user is on a phone and has 90 seconds", and compare which steps survive both.