Erdos Discrepancy Problem
Statement
For any infinite +/-1 sequence, partial sums along arithmetic progressions are unbounded.
About this Problem
Open for 83 years. A 2010 Polymath project used SAT solvers for partial progress. Tao proved it in 2015 using entropy methods and the Elliott conjecture.
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
Generate a unique AI illustration of this problem using fal.ai FLUX.