Researchleanautomated theorem provingcombinatorics
Researchers Solve Erdős Coin-Partition Problem With AI
7.0
Researchers solved Problem 1026 from the Erdős problem site in December 2025 using AI-assisted formalization and collaboration. Boris Alexeev used the AI tool Aristotle to produce a Lean proof converting the question to a rectangle-packing formulation on Dec. 7, 2025; Koishi Chan supplied an Erdős–Szekeres blow-up proof and AlphaEvolve produced sharp upper bounds and constructions.
Key Points
- 1Formalizes Problem 1026 into a rectangle-packing formulation and produces a Lean formal proof
- 2Demonstrates AI tools can automate nontrivial combinatorics proofs and facilitate collaborative mathematical refinement
- 3Enables practitioners to obtain tight bounds and constructive examples using search and blow-up techniques
Scoring Rationale
AI-assisted formal proof and bounds provide tangible progress, but results largely reproduce existing combinatorics literature.
Sources
Public references used for this report.
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