🧠 GPT-5.2 cracked 30-year math problem

Good Morning! GPT-5.2 just crossed a line many thought was still years away, it solved a decades-old Erdős math problem, and Terence Tao confirmed it. Plus, I’ll show you how to generate high-quality images using pre-built Nano Banana Pro prompts.

In today’s AI newsletter:

• How to Generate High-Quality Images Using Pre-Built Nano Banana Pro Prompts

• GPT-5.2 Solves an Erdős Problem

• Google Unveils Universal Commerce Protocol (UCP)

• AI Bartender Tries to Replace Humans

• 4 new AI tools worth trying

AI NEWS

🧮 GPT-5.2 Solves an Erdős Problem

GPT-5.2 Pro generated an original proof for Erdős Problem #397, which was then formalized and verified in Lean using the Aristotle system, and accepted by Fields Medalist Terence Tao.

• Part of a growing streak: GPT-5.2 has now solved Erdős Problems #728, #729, and #397

• Fully verified math: Aristotle closed proof gaps and produced Lean-checked code

• Original reasoning: Tao confirmed these were not rediscoveries of existing literature

• Limits remain: Strong on “standard technique” problems, weaker on deep, insight-heavy research

This marks a shift from AI finding answers to AI creating proofs. Even if these are “low-hanging fruit,” autonomous, verified problem-solving is now real, and it’s exactly the kind of reasoning work used in law, engineering, and compliance. Once this curve steepens, every domain with long-standing “everyone knows this is hard” problems should pay attention.

AI COMMERCE

🛒 Google Unveils Universal Commerce Protocol (UCP)

Google announced a new open standard, UCP, designed to let AI agents handle the entire shopping journey, from discovery to checkout to post-purchase support, without jumping between disconnected systems.

• UCP lets AI agents work seamlessly across retailers like Shopify, Etsy, Walmart, and Target

• Google will enable in-chat checkout via Search AI mode and Gemini, using Google Pay (PayPal coming soon)

• Brands can offer real-time discounts inside AI conversations when users show buying intent

• Merchants can deploy branded AI business agents in Google Search for customer support and sales

This is Google turning AI from a recommendation engine into a transaction engine. If agents can browse, compare, negotiate discounts, and check out for you, search, shopping, and ads collapse into one flow. Commerce isn’t just moving into chat… it’s becoming agent-native.

TECHNOLOGY

🍸 AI Bartender Tries to Replace Humans

Breakreal unveiled the R1, an AI-powered cocktail machine claiming “unlimited AI-generated recipes” and LLM-driven conversation, but reality looks a bit less magical.

• Holds only 8 ingredients, making “unlimited recipes” mostly marketing fluff

• Takes 20–40 seconds per drink, with reports of liquid leaking mid-pour

• Promises “mood-sensing flavor adaptation” and interactive chat (word salad alert)

• Priced at $1,299 ($999 early access), vs $349 for non-AI competitors

The R1 is a perfect snapshot of the current AI device era, slapping “LLM-powered” onto hardware that doesn’t clearly outperform simpler tools. It shows how fast AI hype is moving into physical products… and how quickly consumers will call bluff when “intelligence” doesn’t translate into a better experience.

HOW TO AI

🗂️ How to Generate High-Quality Images Using Pre-Built Nano Banana Pro Prompts

In this tutorial, you’ll learn how to use the Nano Banana Pro Prompt Hub to generate professional-quality images without writing prompts from scratch.

🧰 Who is This For

• Creators who want high-quality portraits, avatars, and visuals

• Designers who need fast inspiration, mockups, or ready-made visual styles

• Founders and marketers creating images for landing pages, ads, and presentations

• Beginners who want professional-grade AI images without trial and error

STEP 1: Access the Nano Banana Pro Prompt Hub

Open your browser and go to YouMind. Once the page loads, you’ll see a bold header at the top labeled Nano Banana Pro Prompts.

Directly below it is a large input box where you can generate images, and underneath that is a section called Fresh Prompts.

On the right side of this section, there’s a yellow counter showing the total number of available prompts, which is well over a thousand and continuously updating. This page is the central hub where all pre-built Nano Banana prompts live.

STEP 2: Browse and Filter Prompt Styles

Scroll down into the Fresh Prompts section. Here, you’ll notice category tabs such as Profile / Avatar, Social Media Post, Infographic. Clicking on any of these filters instantly narrows the prompt library to that specific use case. Each prompt appears as a card with a preview image, a title, the creator’s name, and a short description, allowing you to visually judge the style before opening it.

This makes it easy to find a cinematic, realistic, watercolor, anime, or minimal design style without guessing.

STEP 3: Copy and Customize a Prompt

When you find a prompt card you like, click on it and make sure the PROMPT tab is selected, not the ORIGINAL tab. Inside the card, you’ll see a black-bordered text box containing the full optimized prompt. Highlight and copy the entire text exactly as it appears.

Before generating, quickly scan the prompt to identify the subject description. Replace any existing subject, such as a famous person or generic placeholder, with your own subject while keeping the rest of the prompt intact. This ensures you preserve the lighting, composition, and stylistic instructions that make the prompt work so well.

STEP 4: Generate Your Image in Nano Banana Pro

Once your prompt is customized, scroll back to the top of the page and paste it into the main input field that says “Describe the image you want to generate…”.

Alternatively, you can open Nano Banana Pro in a new tab if you prefer a clean workspace. When you’re ready, hit enter. Within moments, Nano Banana Pro will produce a high-quality image using the pre-optimized prompt, giving you professional results without trial and error.

Malaysia becomes the second country to limit access to Grok, joining Indonesia, over the chatbot's generation of sexual content.

Anthropic announces Claude for Healthcare to offer HIPAA-ready tools for providers, insurers, and consumers, and expands its life sciences offering.

Chinese AI executives say China is unlikely to eclipse the US in the AI race anytime soon, citing limited resources and US chip export curbs as key constraints.

California launched a free tool that lets residents request the deletion of their personal data from over 500 registered data brokers.

🤖 Copilot: Microsoft’s AI assistant with built-in agentic commerce features

🌌 Grok Imagine: xAI’s tool for generating images and videos

📱 Gridfy: Turn raw data into interactive website widgets

🌐 Datastripes: Build data workflows in your browser with 300+ drag-and-drop blocks

THAT’S IT FOR TODAY

Thanks for making it to the end! I put my heart into every email I send, I hope you are enjoying it. Let me know your thoughts so I can make the next one even better!

See you tomorrow :)

- Dr. Alvaro Cintas