An AI solution to an 80-year-old problem has shocked mathematicians
Summary
OpenAI's general-purpose AI model recently discovered a counterexample to the 80-year-old planar unit distance problem, also known as Erdős problem 90, originally conjectured by Paul Erdős in 1946. This significant breakthrough, described by mathematician Daniel Litt as "the first result produced autonomously by an AI that I find interesting in itself", disproved the long-held intuition that grid-like arrangements were optimal for maximizing unit-distance pairs. The AI's solution, leveraging algebraic number theory, demonstrates patterns yielding more unit-distance pairs for infinitely many values of *n*. Following this, US mathematician Will Sawin achieved an improved result, and Google DeepMind resolved nine other open problems by Erdős. Experts like Fields Medallist Timothy Gowers lauded the AI's sophistication, noting it would warrant publication in prestigious journals and was achieved with minimal human prompting, highlighting AI's growing impact on mathematical research by exploring vast idea spaces.
Key takeaway
For research scientists exploring complex mathematical conjectures, this development signals a shift in problem-solving paradigms. You should consider integrating general-purpose AI models into your research workflow to autonomously explore vast solution spaces and synthesize existing literature. While AI's capacity for genuine conceptual leaps remains uncertain, its ability to identify counterexamples and resolve open problems with minimal human intervention can significantly accelerate discovery and challenge long-held intuitions.
Key insights
AI can autonomously solve long-standing mathematical conjectures by exploring vast solution spaces and combining existing knowledge.
Principles
- AI excels at exploring numerous speculative lines of inquiry.
- AI can synthesize existing mathematical literature effectively.
- General-purpose AI models can achieve specialized mathematical breakthroughs.
Method
The AI model was given an initial prompt and then conducted a "chain of thought" to explore mathematical ideas, combining existing literature to find a counterexample using algebraic number theory.
In practice
- Use AI to explore complex mathematical problem spaces.
- Apply general AI models to specific scientific challenges.
- Integrate AI for synthesizing disparate research findings.
Topics
- OpenAI
- Erdős Conjecture
- AI in Mathematics
- Counterexample Discovery
- Algebraic Number Theory
- Discrete Geometry
Best for: AI Scientist, Research Scientist
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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial intelligence (AI) – The Conversation.