title: Gold-medalist Performance in Solving Olympiad Geometry with
    AlphaGeometry2
summary: 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.
paper_authors._id: 67a589ebb16fabcdd2dea1eb
paper_authors.name: Yuri Chervonyi
paper_authors._id: 67a589ebb16fabcdd2dea1ec
paper_authors.name: Trieu H. Trinh
paper_authors._id: 67a589ebb16fabcdd2dea1ed
paper_authors.name: Miroslav Olšák
paper_authors._id: 67a589ebb16fabcdd2dea1ee
paper_authors.name: Xiaomeng Yang
paper_authors._id: 67a589ebb16fabcdd2dea1ef
paper_authors.name: Hoang Nguyen
paper_authors._id: 67a589ebb16fabcdd2dea1f0
paper_authors.name: Marcelo Menegali
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-02-07T10:41:38.940Z
paper_authors._id: 60cc0c3494ab6115ab6ecf12
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/1623985197562-noauth.jpeg
paper_authors.fullname: Marcelo Menegali
paper_authors.type: user
paper_authors.user: mmenegali
paper_authors._id: 67a589ebb16fabcdd2dea1f1
paper_authors.name: Junehyuk Jung
paper_authors._id: 67a589ebb16fabcdd2dea1f2
paper_authors.name: Vikas Verma
paper_authors._id: 67a589ebb16fabcdd2dea1f3
paper_authors.name: Quoc V. Le
paper_authors._id: 67a589ebb16fabcdd2dea1f4
paper_authors.name: Thang Luong
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2025-02-07T10:42:08.011Z
paper_authors._id: 65ee0b97306927c125d65779
paper_authors.avatarUrl: /avatars/637129308a95efdf8faac9fb81a66589.svg
paper_authors.fullname: Thang Luong
paper_authors.type: user
paper_authors.user: lmthang
paper_title: Gold-medalist Performance in Solving Olympiad Geometry with
    AlphaGeometry2
paper_summary: 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.