Under $1,000. That's the compute bill OpenAI's GPT-next reportedly ran up to resolve the Erdős unit distance problem, a combinatorics conjecture that stumped professional mathematicians for 80 years.
The problem itself is deceptively clean: given a set of n points on a flat plane, how many pairs of those points can share exactly the same distance from each other? Hungarian mathematician Paul Erdős posed the question in 1946 and spent decades refining it. Researchers made incremental progress over the following eight decades, but no one closed it. GPT-next apparently did.
The Cost Is the Real Story
The capability gap matters, but the price tag is what reframes things. Serious mathematical research typically requires years of a skilled researcher's time, conference rounds, and peer review cycles that can stretch across careers. A compute run under $1,000 puts that output cost below a mid-tier SaaS annual subscription.
This isn't the first time AI has contributed to formal mathematics. Google DeepMind's AlphaProof system made headlines in 2024 for solving problems from the International Mathematical Olympiad. But those demonstrations involved narrower, competition-style problems with known difficulty ceilings. Erdős conjectures sit in a different category: open-ended, research-grade problems where even the path to a solution is undefined.
The Latent Space newsletter, which reported on the GPT-next result, framed it as a boundary shift - the line between AI as a research assistant and AI as an independent research contributor just moved.
What This Does and Doesn't Mean
For working mathematicians and theoretical computer scientists, the result is significant and worth scrutiny. A claimed proof needs verification from domain experts before it enters the permanent record - automated theorem provers (systems that check whether a logical argument is actually valid step-by-step) are the usual standard here, and it's not yet clear whether GPT-next's solution has cleared that bar.
For everyone else building with AI tools day-to-day, the practical takeaway is more about trajectory than this specific result. The same reasoning capabilities that let a model close a combinatorics problem translate - at varying quality levels - into tasks like data analysis, debugging complex code, or working through multi-step business problems. The models being used in productivity tools today are already several generations behind what OpenAI is running in research contexts.
The $1,000 figure will almost certainly fall further as inference costs (the cost of running a model to generate an answer) continue their two-year downward trend. If formal mathematical research can be attempted at that price point now, the economics of AI-assisted research across harder scientific domains shift considerably within the next few years.