# GenesisGeo: Technical Report

arXiv: https://arxiv.org/abs/2509.21896 · HTML: https://mlsanity.com/paper/2509.21896/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2505.10557/) (2025)
- [Proposing and solving olympiad geometry with guided tree search](https://mlsanity.com/paper/2412.10673/) (2024)
- [Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration](https://mlsanity.com/paper/2504.12773/) (2025)
- [TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving](https://mlsanity.com/paper/2504.15780/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [Newclid: A User-Friendly Replacement for AlphaGeometry](https://mlsanity.com/paper/2411.11938/) (2024)

## Built on by (most cited first, 2 of 2)

- [GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagrams](https://mlsanity.com/paper/2603.19252/) (2026)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)

## Abstract (arXiv)

Recent neuro-symbolic geometry theorem provers have made significant progress on Euclidean problems by coupling neural guidance with symbolic verification. However, most existing systems operate almost exclusively in a symbolic space, leaving diagram-based intuition largely unused during reasoning. For humans, geometric diagrams provide essential heuristics for identifying non-trivial auxiliary constructions. Meanwhile, visual language models (VLMs) still struggle with geometry due to the lack of high-quality data with geometric diagrams and reasoning supervision. In this paper, we introduce GenesisGeo-1M, a large-scale synthetic dataset for visual geometric reasoning that contains 1M multimodal geometry problems paired with machine-checkable proof traces. Building on this dataset, we formulate geometric learning as a multi-task training paradigm that jointly optimizes text-based proof generation and diagram-grounded proof generation, encouraging models to learn visual grounding and symbolic deduction. Extensive experiments show that our GenesisGeo-2B model achieves gold-medal-level performance on Olympiad geometry benchmarks, solving 29/30 problems on IMO-30, 63/95 on IMO-95, and 278/409 on HAGeo-409.