Good morning. It's Thursday, May 28th, 2026. Here's your morning download.

**Three AI labs walked into a math problem — and walked out with history.** The Erdős unit-distance problem, sitting unsolved in discrete geometry since 1946, has been obliterated in a span of six days, and what's really wild is that three different AI teams did it completely independently.

OpenAI went first on May 20th with a general-purpose reasoning model — not a math-specialized system — that worked through the problem using nothing but natural language reasoning, no formal proof checker. Their solution ran 125 pages of chain-of-thought in a single context window. US mathematician Will Sawin then took their insight and produced an improved version within days.

Then Google DeepMind dropped AlphaProof Nexus over the weekend. An agentic system that works with the Lean formal proof system, it autonomously solved nine open Erdős problems out of 353 attempted — some of them half a century old. Cost: a few hundred dollars in compute per proof. The agent reads a problem in Lean, breaks it into sub-goals, calls its AlphaProof solver recursively, and refines failed branches until everything checks. It's systematic, scalable, and open-sourced on GitHub.

And then Anthropic, working with the still-unreleased Claude Mythos, cracked the original unit-distance problem over a single weekend — reportedly finding OpenAI's solution AND a second, shorter proof that mathematician Daniel Litt called more elegant. They published the result via Opus 4.7. Three labs, three different approaches, same target. The era of AI as mathematical co-researcher isn't coming. It's already here.

**The FAA has formally grounded SpaceX's Starship following Flight 12.** The agency declared Friday's V3 launch a "mishap" after Super Heavy Booster 19 suffered a cascade of Raptor V3 engine failures during boostback, sending it to an uncontrolled splashdown in the Gulf. Ship 39 itself completed its orbital test and deployed mock Starlink payloads successfully — but booster reuse remains the hard part.

A SpaceX-led investigation is required before any future flights, and the timing is awkward. The company's S-1 IPO filing went public two days before the launch, targeting a $1.75 trillion valuation with an expected roadshow around June 4th. Reuters says the Flight 12 results delivered "enough progress to keep momentum intact" behind the IPO, while warning that full reusability remains unfinished work. US space stocks rallied anyway on Wednesday — the market isn't waiting for the FAA to green-light Flight 13.

**Apple is developing AirPods with built-in cameras.** According to Bloomberg, the company is in late-stage testing of prototypes with tiny cameras along the stem, designed to capture visual information for on-device AI responses. Think of it as a Vision Pro's world-awareness compressed into something that fits in your ears.

The AI would use the visual input to respond to real-time context — describe what's in front of you, read text, identify objects — all locally processed according to Apple's privacy model. The privacy backlash is already forming. Critics are calling it a surveillance risk, and understandably so. A camera-wearing earbud changes the social contract around recording in ways that glasses never did, since they're invisible.

There's already a first-mover in this space: Guangfan's Lightwear earbuds use IR cameras for gesture detection and spatial audio, not open vision queries — which may be the smarter approach. Apple's full reveal is expected at WWDC, coming up in a few weeks.

**And finally, the BEYOND Expo kicked off today in Macau** with nearly 800 exhibitors and the theme "AI: Digital to Physical." Four days of humanoid robots, autonomous systems, and real-world AI deployment — the shift from chatbots to robots doing actual work.

The timing is notable. This comes right on the heels of Unitree Robotics' IPO hearing on the Shanghai STAR Market, where the Chinese humanoid maker is valued at $6.2 billion and would become China's first publicly-traded humanoid robotics company. The hearing is scheduled for June 1st.

What's happening — across Macau, across the robotics sector — is a transition that was invisible to most people eighteen months ago. AI isn't just getting smarter at writing code. It's getting bodies. And those bodies are starting to show up in factories, airports, and warehouses.

That's all for this morning. We'll see you tomorrow.