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May 20, 2026 • Rebecca Bellan

OpenAI's Reasoning Model Solves 80-Year-Old Math Problem

OpenAI's Reasoning Model Solves 80-Year-Old Math Problem OpenAI's Reasoning Model Solves 80-Year-Old Math Problem OpenAI's Reasoning Model Solves 80-Year-Old Math Problem

OpenAI Claims It Solved an 80-Year-Old Math Problem — For Real This Time

OpenAI's Redemption Arc in Mathematical AI

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, first posed by Paul Erdős in 1946. This announcement comes seven months after an embarrassing false claim where the company said GPT-5 had solved 10 Erdős problems—only to discover those solutions already existed in the literature.

What Changed This Time

Independent Verification: Unlike the previous incident, this claim is backed by prominent mathematicians including:

  • Noga Alon
  • Melanie Wood
  • Thomas Bloom (who maintains the Erdos Problems website and previously called out OpenAI's misrepresentation)

OpenAI published companion remarks from these mathematicians supporting the disproof.

The Mathematical Achievement

The Problem: A geometry conjecture from 1946 about unit distance configurations

The Breakthrough:

  • For nearly 80 years, mathematicians believed optimal solutions resembled square grids
  • OpenAI's model discovered an entirely new family of constructions that performs better
  • This disproves the long-standing belief about the problem's structure

Technical Significance

Why This Matters for AI Development

General-Purpose Reasoning: The proof came from a new general-purpose reasoning model—not a system specifically designed for mathematics or this particular problem.

Key Capabilities Demonstrated:

  • Holding together long, difficult chains of reasoning
  • Connecting ideas across fields in unexplored ways
  • Autonomous problem-solving in central mathematical domains

Broader Implications: These reasoning capabilities have potential applications in:

  • Biology
  • Physics
  • Engineering
  • Medicine

Historical Context

This achievement represents "the first time AI has autonomously solved a prominent open problem central to a field of mathematics," according to OpenAI.

As mathematician Thomas Bloom stated: "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries. What other unseen wonders are waiting in the wings?"

Key Takeaways

  • OpenAI's new reasoning model achieved a legitimate mathematical breakthrough after previous false claims
  • The disproof is independently verified by respected mathematicians who previously criticized OpenAI
  • This represents a milestone in AI's ability to conduct autonomous mathematical research
  • The achievement demonstrates advanced reasoning capabilities applicable beyond mathematics
  • General-purpose reasoning models may now be capable of original discoveries in complex domains