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.
@article{arxiv.2509.21896,
title = {GenesisGeo: Technical Report},
author = {Minfeng Zhu and Zi Wang and Sizhe Ji and Zhengtong Du and Shengqiang Tai and Junming Ke and Xiao Deng and Zanlang Yin and Xiuqi Huang and Heyu Wang and Wei Chen},
journal= {arXiv preprint arXiv:2509.21896},
year = {2026}
}