OpenAI just overturned an 80-year math problem

2026.06.09 · 209 readers
What's up, Carat crew here. 🤗
Today: OpenAI flipping an 80-year math problem, a fully AI-made surreal video series, a much smarter Google NotebookLM, and Kimi running a whole swarm of agents.

🔥 The 80-year math problem an OpenAI model cracked

ⓒ OpenAI
An OpenAI model just overturned a math problem that had gone unsolved for 80 years. The question: if you scatter a bunch of points on a plane, what's the most pairs that can sit exactly the same distance apart? The AI found a better counterexample than the answer mathematicians had long treated as correct.
A similar claim turned out to be fake before, so this time nine outside mathematicians verified the result. A Fields Medalist said it's good enough for a top journal, and people are calling it the first time an AI solved a hard problem humans couldn't, on its own.

📌 3 more things today

1️⃣ Wait, this is all AI-generated video?

ⓒ ArchiveInBetween
A fully AI-made surreal video series is blowing up. It builds an entire world, like a giant underwater aquarium of creatures, and it's spreading with over 2,000 likes.
It's not just one or two shots. The whole 'world,' its mood and setting, holds together across the series. You can make this kind of concept video with a video model on Carat too.
👉 Make it on Carat

2️⃣ Google NotebookLM now writes code and builds spreadsheets

ⓒ @testingcatalog
Google gave NotebookLM a big update. It now cross-reads your documents on its own to find what's missing, and keeps going with follow-up research by itself.
Inside each notebook it can write and run code, and spin up spreadsheets, docs, slides, and images you can download. It runs on Gemini 3.5 and started rolling out yesterday.

3️⃣ Kimi just started running several AI agents at once

ⓒ @testingcatalog
Moonshot AI's work tool 'Kimi for Work' got a screen reveal. Writing, coding, research, spreadsheets, the AI handles it all in one place.
The key part is running several AI agents at once. A bunch of small AIs split the work in parallel to finish complex tasks fast, reportedly up to a few hundred at a time.

🧪 Prompt of the day

Lately a 'me on a college festival stage' photo is going around on social. Drop in just one photo of yourself and you can turn it into a live performance shot. The Carat team built two versions of the prompt.
Generated with ChatGPT Image 2 Medium on Carat
Generated with ChatGPT Image 2 Medium on Carat
The first one looks like it's caught on a big jumbotron, like someone in the crowd shot the screen from far away. Here's the prompt.
Transform my photo with the following prompt using ChatGPT Image 2 Medium.
Prompt: Use the uploaded reference image as the strongest facial identity anchor. The person must look like the exact same person from the reference image. Preserve their facial identity with very high priority: same face shape, same eyes, same nose, same lips, same skin tone, same expression style, and same overall hair impression.
Create an ultra-realistic smartphone photo taken by an audience member at a Korean university festival. The photo is not a direct stage portrait. It shows a huge outdoor LED jumbotron screen, and on that screen the person is captured performing on stage during a live song. The final image must clearly feel like someone in the crowd photographed the giant screen from a distance.
On the LED screen, the person appears as a singer mid-performance, holding a microphone, not posing for the camera, not looking directly into the lens. Their gaze is toward the audience or slightly off to the side, with a natural unplanned singing expression. The moment should feel accidentally caught during a live performance.
Do not assign a specific outfit color or fixed clothing style. Let wardrobe, colors, accessories, and styling vary naturally as contemporary Korean campus festival performer fashion.
The giant LED screen should dominate most of the frame, with visible LED pixel texture, slight moire, screen glare, blown-out highlights, and mild color banding. Include subtle real-world smartphone capture imperfections: handheld framing, slight tilt, minor motion blur, digital zoom softness, night festival lighting, lens flare, and imperfect exposure. Around the edges, show hints of the real concert environment: dark sky, stage truss, colorful lights, silhouettes of audience heads or raised phones at the bottom.
Composition: 16:9 horizontal smartphone photo of a large festival jumbotron, audience POV, screen-within-screen feeling. The performer's face should be visible on the LED screen, but the image should not look like a clean studio portrait or direct AI render. It should feel like a viral fan-taken concert screenshot photo.
Photorealistic, authentic Korean university festival atmosphere, candid live-event documentation, natural skin texture as displayed on an LED screen. No captions, no overlay text, no readable university names, no brand logos, no watermark, no extra duplicated face, no celebrity resemblance, no direct eye contact, no staged idol beauty-shot posing.
Generated with ChatGPT Image 2 Medium on Carat
Generated with ChatGPT Image 2 Medium on Carat
The second one is caught straight on the stage broadcast camera.
Transform my photo with the following prompt using ChatGPT Image 2 Medium.
Prompt: Use the uploaded reference image as the strongest facial identity anchor. The person must look like the exact same person from the reference image. Preserve their facial identity with very high priority: same face shape, same eyes, same nose, same lips, same skin tone, same expression style, and same overall hair impression.
Create an ultra-realistic candid Korean university festival stage broadcast screenshot of this person performing on stage. They are a singer captured accidentally by a live event camera while in the middle of a real performance, not posing for the camera. The person must not look directly into the lens. Their gaze should be toward the audience, slightly off to the side, or downward toward the stage while singing or moving naturally. The expression should feel unplanned and mid-performance: focused, energetic, slightly breathless, with natural facial movement.
The person is on the actual stage, holding a handheld microphone or wearing a performance mic, captured during a live song moment. Do not assign a specific outfit color or fixed clothing style. Let wardrobe, colors, accessories, and styling vary naturally as contemporary Korean campus festival performer fashion. Avoid staged idol beauty-shot posing, avoid deliberate hand poses, avoid direct eye contact, avoid symmetrical studio portrait composition.
Use a realistic live broadcast / giant LED jumbotron look: telephoto compression from the audience area, imperfect off-center framing, slight motion blur from movement, mild video softness, stage haze, LED screen texture, subtle moire, strong colored stage lights, dark truss and concert lighting in the background, blurred crowd lights below the stage. The image should feel like one frame captured from a live campus festival screen while the performer was moving.
Composition: 16:9 horizontal broadcast screenshot, upper-body or half-body on-stage framing, face visible but candid, microphone visible, dynamic stage atmosphere. Photorealistic, natural skin texture, realistic event camera image quality, high-definition social media screenshot feel. No captions, no overlay text, no watermark, no brand logos, no readable university names, no extra duplicated face, no celebrity resemblance, no reference to any specific real person.
Make it yourself on Carat right now. 👉 Make it on Carat
That's it for today. We'll be back tomorrow with fresh AI news. ☺️

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