AI solves Erdős planar problem, speeds genomics 275x

OpenAI and Hugging Face made two separate research claims this week that were later bundled together in a social-media thread: one in pure mathematics, the other in genomics. On May 20, OpenAI said an internal reasoning model had disproved a longstanding conjecture in the planar unit-distance problem, an Erdős question first posed in 1946. About three days later, Hugging Face Biology released Carbon, a family of genomic foundation models, and said its 3-billion-parameter model matched Arc Institute’s Evo 2 7B on benchmark win rate at roughly 275 times the throughput. The X post that circulated Saturday added broader claims about weather forecasting and drug discovery, but those appear to be extrapolations from the releases rather than results demonstrated in the cited materials. ### What exactly did OpenAI say it solved? OpenAI said the result concerns the planar unit-distance problem: given \(n\) points in the plane, how many pairs can be exactly distance 1 apart? The company said mathematicians had long believed “square grid” constructions were essentially optimal, and that its model disproved that conjecture by producing an infinite family of examples with a polynomial improvement. (openai.com) Paul Erdős posed the problem in 1946, and OpenAI described it as one of the best-known questions in combinatorial geometry. The company said the proof was checked by a group of external mathematicians and published alongside a companion paper explaining the argument and its context. ### Was this an AI assistant helping a human, or something stronger? (openai.com) OpenAI said the proof came from “a new general-purpose reasoning model,” not from a system trained specifically for mathematics or targeted only at the unit-distance problem. The company called it “the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI.” (openai.com) Tim Gowers, a Fields Medalist quoted by OpenAI, called the result “a milestone in AI mathematics.” Arul Shankar, identified by OpenAI as a leading number theorist, said the paper showed current AI models are capable of “original ingenious ideas” and carrying them through. ### What is Carbon, and where does the 275x figure come from? (openai.com) Hugging Face Biology said Carbon is “a family of causal language models” trained on 1 trillion tokens, or 6 trillion DNA base pairs, from a curated DNA and RNA corpus. The public repository lists three sizes — 500M, 3B and 8B parameters — and says the 3B model “matches or beats Evo2 7B.” Hugging Face’s Carbon demo page gives the clearest version of the speed claim. (openai.com) It says Carbon 3B matches Evo 2 7B’s benchmark win rate at “roughly 275× the throughput,” measured in base pairs per second. That is a benchmarking claim about model inference efficiency, not a blanket statement that all genome analysis is now 275 times faster. ### Is “biology’s carbon model” the same thing as Evo 2? (github.com) Arc Institute’s Evo 2 and Hugging Face’s Carbon are different models from different groups. Arc Institute says Evo 2 is a genomic foundation model for prediction and design across DNA, RNA and proteins, and Nature described it as trained on 9 trillion DNA base pairs spanning all domains of life. The Carbon repository explicitly compares itself with Evo 2 in evaluation and installation notes, including an optional Evo 2-backed evaluation setup. (huggingface.co) That supports the reading that the viral post was referring to Carbon as a new open-source competitor or alternative in genomic modeling, not to a single combined system. ### What about the thread’s claims on weather forecasting and drug discovery? (arcinstitute.org) The X post’s references to weather forecasting and drug discovery were not substantiated in the OpenAI math announcement or the Hugging Face Carbon materials reviewed here. Carbon is presented as a genomic model for tasks such as sequence recovery, variant-effect prediction and perturbations, while Evo 2 is described as supporting biological prediction and design tasks. (github.com) Any link from these releases to weather forecasting or broader computational pipelines is therefore an inference from the general usefulness of faster foundation models, not a reported result in the source documents. The materials that are public now are the OpenAI proof and companion remarks, plus Hugging Face’s code, weights, benchmarks and demo. (github.com) OpenAI’s proof materials were posted on May 20, 2026, and Hugging Face’s Carbon release pages and repository were updated within the past several days. Readers looking for the next concrete step can check the published proof and companion remarks on OpenAI’s site and the Carbon demo, model cards and GitHub repository from Hugging Face Biology. (openai.com)