OpenAI's GPT solves 80-year-old Erdős problem for under $1,000
General-purpose LLM produces 125 pages of reasoning, surprising mathematicians.
OpenAI announced that a general-purpose reasoning model (not a dedicated math system) disproved the planar unit distance problem, a discrete geometry conjecture from Erdős (1946). The model produced 125 pages of output for under $1,000 in compute, with mathematician Timothy Gowers calling it the first really clear example of AI solving a well-known open math problem. OpenAI emphasized the model was not pushed to its limit and is intended for public use, with observers noting this as evidence of inference-time scaling driving progress.
Cohere released Command A+ as Apache 2.0 open weights, its most permissive and powerful model yet. With 218B total parameters (25B active), multimodal support, and 48 languages, it can run on 2× H100s at W4A4 with vLLM day-0 support. Benchmarks place it around Claude 4.5 Haiku on the Artificial Analysis Intelligence Index, with strong non-hallucination behavior but weaker scientific reasoning and coding. The architecture includes parallel transformer blocks and LayerNorm, making it a notable open enterprise-grade release.
- OpenAI's general-purpose LLM solved the Erdős planar unit distance problem in <32 hours for <$1,000, producing 125 pages of reasoning.
- Timothy Gowers called it the first clear AI solution to a well-known open math problem, signaling a shift beyond olympiad-level math.
- Cohere released Command A+ as Apache 2.0 open weights: 218B MoE / 25B active, runs on 2× H100s, with vLLM support and strong non-hallucination benchmarks.
Why It Matters
OpenAI shows LLMs can advance formal science; Cohere's open model lowers barriers for enterprise deployment.