# Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation

arXiv: https://arxiv.org/abs/2606.10806 · HTML: https://mlsanity.com/paper/2606.10806/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 8 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Built on by (most cited first, 6 of 6)

- [VALG: An Agentic System for ML Theory Research](https://mlsanity.com/paper/2608.13060/) (2026)
- [The Problem Is the Problem: Towards Scalable Mathematical Discovery](https://mlsanity.com/paper/2608.16977/) (2026)
- [MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures](https://mlsanity.com/paper/2607.27709/) (2026)
- [Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification](https://mlsanity.com/paper/2609.11319/) (2026)
- [Andy: A Mathematical Agent for Rigorous Proof and Autonomous Research](https://mlsanity.com/paper/2608.15052/) (2026)
- [Learning to Discover Interesting Mathematics](https://mlsanity.com/paper/2609.28603/) (2026)

## Abstract (arXiv)

Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures. Its core capability is to extract structure from classical problems, distill new concepts, and formulate conjectures of mathematical significance. Rather than treating the solution of a single proposition as its endpoint, Moonshine builds an extensible theoretical framework through conjecture generation, bridge building, and obstacle identification. This article uses Moonshine's exploration of the Jacobian conjecture as an example. It shows how the central logic of whether local nondegeneracy can force global injectivity is transferred to one-hidden-layer affine-ridge sigmoid networks. This leads to the formulation of the Neural Jacobian Conjecture (NJC): if such a network has strictly positive Jacobian determinant on the whole space, then it must be globally injective. By invoking GPT-5.5-pro and DeepSeek-V4-pro separately, Moonshine obtained independent complete proofs for the case (N=n+1). In addition, with the assistance of ChatGPT through interactive use of its web interface with GPT-5.5-pro, a geometric-topological proof was developed. These results provide preliminary evidence for the plausibility of the conjecture. The general higher-width case (N≥ n+2), however, remains unresolved and is left for further investigation. This work illustrates Moonshine's ability to autonomously generate meaningful mathematical problems and make rigorous progress on them.