Internal model at OpenAI solves 5 more Erdős problems
An unreleased OpenAI model cracked five complex combinatorial problems that had stumped mathematicians for decades.
OpenAI researchers have revealed that an internal, unreleased AI model successfully solved five open problems in combinatorics related to the famous Erdős discrepancy problem. The work, detailed in a paper by researchers like Mehtaab Sawhney, shows the model didn't just find numerical solutions but constructed formal mathematical proofs and counterexamples. This represents a qualitative shift from AI as a statistical pattern-matcher to an agent capable of structured, logical reasoning in a highly constrained domain like pure mathematics.
The problems solved are variations concerning sequences of +1 and -1, exploring the limits of their 'discrepancy'—a measure of deviation from uniformity. The AI's ability to navigate this abstract space and produce verifiable proofs suggests core advancements in its reasoning architecture. While the exact model (potentially a precursor to or variant of GPT-5 or 'Strawberry') wasn't named, its performance hints at OpenAI's progress toward systems that can perform deep research and discovery, a stated goal for Artificial General Intelligence (AGI).
This breakthrough is part of a growing trend of AI tackling formal mathematics, following projects like Google's FunSearch and DeepMind's AlphaGeometry. However, solving multiple open problems autonomously sets a new benchmark. It validates the use of large language models not just as text generators but as engines for exploration in symbolic domains, potentially accelerating progress in fields like cryptography, materials science, and algorithm design where similar structured reasoning is required.
- The model autonomously provided solutions and proofs for five unsolved problems in combinatorics, a branch of pure mathematics.
- It demonstrates advanced logical reasoning and formal theorem-proving capabilities, a key step toward research-level AI.
- The achievement signals rapid progress in AI's ability to perform discovery, not just analysis, in constrained symbolic systems.
Why It Matters
It proves AI can move beyond data analysis to genuine discovery, potentially accelerating research in math, science, and cryptography.