OpenAI’s internal reasoning model has cracked the planar unit distance problem — a famous open question first posed by mathematician Paul Erdős in 1946. It’s the first time an OpenAI system has solved a long-standing research problem without step-by-step human guidance. External mathematicians verified the proof, which used tools from algebraic number theory and disproved the long-held belief that the best solutions looked like square grids.
The math problem solved
The planar unit distance problem asks how many times a fixed distance can appear among n points in the plane. Erdős offered a $500 prize for its solution decades ago. Until now, no one — human or machine — had found a definitive answer. The OpenAI model autonomously worked through the problem, employing algebraic number theory in ways that surprised the humans who reviewed the results. The company framed the milestone as part of a broader push toward automated research, arguing that similar reasoning could one day speed up discovery in biology, physics, materials science, and medicine.
OpenAI’s IPO plans
Separately, OpenAI is reportedly preparing an initial public offering filing as soon as this week. The move comes after a US jury cleared the company in a lawsuit brought by Elon Musk. The IPO would give the public a chance to buy into a firm that has drawn billions in investment and whose chatbot, ChatGPT, reshaped how the world thinks about artificial intelligence. Details about the offering — including the expected valuation and the number of shares — have not been disclosed.
Anthropic and talent moves
Meanwhile, rival Anthropic is on track for its first profitable quarter, with projected revenue of $10.9 billion. The company has been quietly building its own large language models and has attracted top talent from OpenAI. Former OpenAI founding member Andrej Karpathy recently joined Anthropic to focus on frontier model research, signaling that the war for AI talent remains intense.
The next frontier: agentic AI
The broader industry is shifting toward what some call “agentic” AI — systems that can act, not just answer. Citadel CEO Ken Griffin warned that agentic AI is starting to replace PhD-level finance tasks in hours rather than months. Some observers argue that the next competitive edge in AI will come from access to real-world execution data that lets these systems take action. That raises a question the industry hasn’t yet answered: who controls the data that trains the agents that will run the world?
