Erdos-Straus Conjecture
Statement
For every integer n >= 2, the fraction 4/n can be expressed as a sum of three unit fractions.
About this Problem
One of the most famous open problems in number theory. Verified computationally for n up to 10^17. Connects to Egyptian fraction representations and Diophantine equations. No AI system has yet made definitive progress.
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.