Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation

Moonshine, an autonomous mathematical research agent, has been introduced to generate mathematical conjectures by extracting structure from classical problems. It utilizes one-hidden-layer affine-ridge sigmoid networks to explore the Jacobian conjecture, leading to the formulation of the Neural Jacobian Conjecture (NJC) and achieving independent proofs for specific cases using models like GPT-5.5-pro and DeepSeek-V4-pro. This development underscores the potential of AI in advancing mathematical research and conjecture generation, highlighting the integration of machine learning techniques in formal mathematical exploration.