Gold-medalist Performance in Solving Olympiad Geometry with
  AlphaGeometry2
Authors: name: Yuri Chervonyi, name: Trieu H. Trinh, name: Miroslav Olšák, name: Xiaomeng Yang, name: Hoang Nguyen, name: Marcelo Menegali, name: Junehyuk Jung, name: Vikas Verma, name: Quoc V. Le, name: Thang Luong

We present AlphaGeometry2, a significantly improved version of AlphaGeometry
introduced in Trinh et al. (2024), which has now surpassed an average gold
medalist in solving Olympiad geometry problems. To achieve this, we first
extend the original AlphaGeometry language to tackle harder problems involving
movements of objects, and problems containing linear equations of angles,
ratios, and distances. This, together with other additions, has markedly
improved the coverage rate of the AlphaGeometry language on International Math
Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process
of AlphaGeometry2 has also been greatly improved through the use of Gemini
architecture for better language modeling, and a novel knowledge-sharing
mechanism that combines multiple search trees. Together with further
enhancements to the symbolic engine and synthetic data generation, we have
significantly boosted the overall solving rate of AlphaGeometry2 to 84% for
all geometry problems over the last 25 years, compared to 54%
previously. AlphaGeometry2 was also part of the system that achieved
silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not
least, we report progress towards using AlphaGeometry2 as a part of a fully
automated system that reliably solves geometry problems directly from natural
language input.