OpenAI’s Mathematical Breakthrough and Building a Notion Project Database

• Mathematical Milestone: OpenAI claims its internal model has solved more than 100 open math problems, a feat currently under review by an external advisory group of mathematicians.
• Hardware Innovation: Alphabet has launched pre-orders for the Googlebook, an AI-first laptop featuring Magic Pointer and Rambler voice transcription, alongside Android integration.
• Model Upgrades: xAI released Grok 4.7, offering enhanced capabilities for knowledge work, including longer task duration and improved self-correction, at the same price point as its predecessor.
• Agent Economy Dynamics: Meta’s Muse agent has driven a 20% stock increase, prompting Amazon to block agent purchases for privacy reasons while Shopify partners with Meta to enable agent-led checkouts.
• Notion AI Workflow: Users can build project intelligence databases in Notion by using specific AI prompts to auto-generate fields like risks and priorities via custom agents.

OpenAI has announced that the same model behind its previously disputed Navier-Stokes claim has successfully cracked more than 100 other long-standing open math problems. This development has shocked the mathematics community, prompting the lab to collaborate with an outside advisory group of mathematicians. The group’s role is to review, verify, and determine how best to communicate these findings to the public.

In parallel developments within the model landscape, xAI has dropped its most capable model for knowledge work yet: Grok 4.7. This update offers the same price and speed as Grok 4.6 but delivers a significant jump in capabilities. The developers state that the new model can work longer on challenging tasks, check its own work more carefully, and create better documents and presentations. It is available now through Grok Build, Cursor, or the API.

Alphabet has unveiled the Googlebook, described as Android’s biggest move in years. This new line of AI-powered laptops is now open for pre-orders. The device includes several AI-first features, such as Magic Pointer, which summons Gemini anywhere on the screen, and Rambler, a voice transcription feature. Additionally, the laptop links up with Android phones, allowing users to launch and switch between apps on both devices seamlessly.

Meanwhile, Meta’s stock climbed over 10% following the success of its Muse agent, contributing to an industry rally that also pushed semiconductor firm AMD into the $1 Trillion Club. Muse is on track to be one of Meta’s biggest successes in years, having dethroned ChatGPT to claim #1 on Apple’s App Store and helping Meta’s stock soar 20% since its launch. This success suggests a mainstream moment for personal agents, though it has triggered a power struggle in e-commerce.

Amazon has blocked Muse from making purchases, citing privacy and security concerns for its customers. This decision also protects Amazon’s $68B ad business, which relies on real humans doing the shopping, as agents do not click ads. In contrast, Shopify made the opposite bet by partnering with Meta to let Muse power customer checkouts across Shopify stores. This standoff serves as an early test of who sets the rules for agentic shopping; if agents can buy freely, retailers might lose control of customer relationships and ad revenue.

To create a project intelligence database using Notion AI, follow these steps:

1. Open Notion and create a new page. Choose the Table view, then select "Build with AI."
2. Ask Notion AI to create a project database with fields like Project, Owner, Status, Due Date, Priority, Summary, Risks, and Keywords. Use this sample prompt: “Create a project tracker for my team with Project, Owner, Status, Due Date, Priority, Summary, Risks, and Keywords. I want AI to help summarize each project and surface potential risks from the information stored in each project page.”
3. Add each project as a database entry. Place relevant briefs, notes, decisions, and updates inside its respective page.
4. For the Summary field, open the property settings and choose AI Autofill > Basic > Summary. Use AI Autofill for Keywords and other structured fields you want Notion to extract automatically.
5. For fields like Risks or Priority, use AI Autofill > Custom Agent with instructions such as: “Identify the biggest current risk and classify priority as High, Medium, or Low.” Set AI properties to update manually, when pages change, or on a schedule so the database stays current.

Recent social media trends highlight the rapid integration of AI into daily life. Hobbyists are testing TypeSafe’s new Jev model, with one user building a smarter copy/paste tool that automatically fills forms, and another creating a browser agent that finds flight tickets in 7 seconds. On the creative side, an AI-enhanced Big Mouth Billy Bass has gone viral for screaming motivational speeches during workouts, while a fan-made DuckTales trailer has pulled in over 2 million views due to its realistic quality.

Trust issues are also emerging, with a viral Reddit demo showing how easily identity can be swapped during live video streams. In legal news, Apple has agreed to a $250M settlement over allegations that it marketed Siri AI features that arrived later than buyers expected. Some US iPhone owners can now file claims for a portion of this settlement.

The current landscape is defined by rapid advancements in mathematical reasoning, hardware integration, and agentic commerce strategies. OpenAI’s verification process for its 100 solved math problems will be closely watched, while the divergent paths of Amazon and Shopify regarding agent purchases highlight the stakes of the new agent economy. For professionals seeking to manage complex workflows, leveraging tools like Notion AI for automated project tracking offers a tangible way to harness these technological shifts for improved productivity.