📐 A 1946 Math Problem Finally Has an Answer

A 1946 math problem that resisted generations of mathematicians just got disproved by an AI that wasn't even built for math. Paul Erdős posed the planar unit distance conjecture nearly 80 years ago. A general-purpose OpenAI model found a bridge between algebraic number theory and geometry that nobody had spotted, and external mathematicians have already verified it. AI is starting to see math from angles humans missed. Let's dive in!

In today’s insights:

LATEST DEVELOPMENTS

Evolving AI: An internal OpenAI model autonomously disproved a famous Erdős conjecture from 1946.

OpenAI revealed that one of its general-purpose reasoning models tackled the planar unit distance problem and found a novel disproof. The problem asks how many pairs among n points on a plane can be exactly one unit apart. Square grids had long been assumed optimal. The model produced an infinite family of arrangements giving a polynomial improvement, drawing on algebraic number theory. External mathematicians have verified the result independently.

Erdős posed this in 1946. Generations of mathematicians have circled it, AI has been writing proofs and winning IMO golds for a couple of years, and still nobody, human or machine, had cracked it. Then a general-purpose model, not even a math-specific one, found a connection between algebraic number theory and geometry that nobody had drawn. The interesting part isn't that AI did math, it's that the answer was hiding in a place nobody thought to look.

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Evolving AI: Anthropic is set to post its first operating profit while other frontier labs keep losing billions.

Anthropic shared the numbers with investors as part of a fresh funding round, and the jump is pretty wild. Q2 revenue is on track to more than double quarter over quarter, a 130% lift that would deliver the company's first ever operating profit of roughly $559 million. Growth is reportedly outpacing what Zoom did during the pandemic and what Google and Facebook posted on the way to their IPOs. Heavy compute spending could pull things back into the red later in the year, but for now the math is finally working.

Anthropic's numbers land at a moment when investors are starting to ask harder questions about AI economics. OpenAI's $14 billion projected loss and xAI's reported burn have shifted the mood from growth-at-all-costs to something more cautious. A profitable quarter gives the market its first real proof that frontier AI revenue can outrun frontier AI costs.

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Evolving AI: SpaceX filed its S-1 on Wednesday, opening up the largest IPO in market history.

SpaceX filed for its IPO on Wednesday, confirming Nasdaq as its listing venue. Reports peg the raise near $75 billion at a valuation around $1.75 trillion, which would top every prior offering on record. The company's AI exposure is now central to the pitch. SpaceX absorbed xAI in February, spent $12.7 billion on AI infrastructure in 2025, and is anchoring the Terafab chip project with Tesla, xAI, and Intel.

What used to be two separate trades, AI and hard infrastructure, is starting to look like one, and SpaceX is the cleanest example of it. Satellites, models, launch capacity, and chip plans now sit inside one filing, with Musk holding 85% voting control. Public investors are getting a single ticker that covers more of the AI stack than any name currently listed.

OpenAI’s video of computer use inside Codex feels like a glimpse at what AI agents may actually look like in daily work. Instead of only generating code, Codex can interact with terminals, browsers, and apps to complete multi-step tasks while you supervise. The demo makes it clear we’re moving beyond chatbots toward AI systems that can actively operate software on your behalf, which could completely change how developers, marketers, and knowledge workers use AI tools day to day.

QUICK HITS

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