Erdos-Szekeres Theorem
Statement
Any sequence of more than (r-1)(s-1) distinct reals contains a monotone subsequence of length r or s.
About this Problem
Proved when Erdos was 22. The paper also posed the Happy Ending problem, named because it led to the marriage of Szekeres and Esther Klein.
About the Lean 4 Prover
Lean 4 is a theorem prover and programming language. When a proof compiles in Lean, it is mathematically certain to be correct — the type checker verifies every logical step. This is the gold standard for formal verification.
Our platform uses fal.ai serverless compute to run Lean verification, and Gemini to generate proof strategies that are then formally checked. ShinkaEvolve provides the evolutionary backbone for automated mathematical discovery.
Mathematical Art
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