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AlphaGeometry
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<h2 id="alphageometry-2">AlphaGeometry 2</h2> <p>AlphaGeometry 2 is an improved version of AlphaGeometry, published on February 5, 2025. They added more features to the representation language to describe more geometry problems that involve movements of objects, and problems containing linear equations of angles, ratios, and distances. They targeted IMO geometry questions from 2000 to 2024. The expanded representation language allowed them to cover 88% of the questions.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p><p>It uses <a href="/facts/Gemini_(language_model)/eD5D8xBo">Gemini</a> finetuned on a synthetically generated dataset of problems and solutions in the representation language. The model is used for making auxiliary constructions like lines and points, to help the tree search. It is also used for autoformalization, i.e. converting a problem in English to a problem in the representation language.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"AlphaGeometry: An Olympiad-level AI system for geometry". Deepmind. Retrieved 26 January 2024. <a href="https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/" target="_blank">https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Roberts, Siobhan (17 January 2024). "A.I.'s Latest Challenge: the Math Olympics". The New York Times. Retrieved 26 January 2024. <a href="https://www.nytimes.com/2024/01/17/science/ai-computers-mathematics-olympiad.html" target="_blank">https://www.nytimes.com/2024/01/17/science/ai-computers-mathematics-olympiad.html</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Trinh, Trieu H.; Wu, Yuhuai; Le, Quoc V.; He, He; Luong, Thang (2024). "Solving olympiad geometry without human demonstrations". Nature. 625 (7995): 476–482. Bibcode:2024Natur.625..476T. doi:10.1038/s41586-023-06747-5. PMC 10794143. PMID 38233616. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10794143" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10794143</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>"Google DeepMind's new AI system can solve complex geometry problems". MIT Technology Review. Retrieved 26 January 2024. <a href="https://www.technologyreview.com/2024/01/17/1086722/google-deepmind-alphageometry/" target="_blank">https://www.technologyreview.com/2024/01/17/1086722/google-deepmind-alphageometry/</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Zia, Tehseen (January 24, 2024). "AlphaGeometry: DeepMind's AI Masters Geometry Problems at Olympiad Levels". Unite.ai. Retrieved 2024-05-03. <a href="https://www.unite.ai/alphageometry-how-deepminds-ai-masters-geometry-problems-at-olympian-levels/" target="_blank">https://www.unite.ai/alphageometry-how-deepminds-ai-masters-geometry-problems-at-olympian-levels/</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>"AI achieves silver-medal standard solving International Mathematical Olympiad problems". Deepmind. Retrieved 15 August 2024. <a href="https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/" target="_blank">https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Castelvecchi, Davide (2025-02-07). "DeepMind AI crushes tough maths problems on par with top human solvers". Nature. 638 (8051): 589. Bibcode:2025Natur.638..589C. doi:10.1038/d41586-025-00406-7. ISSN 1476-4687. <a href="https://www.nature.com/articles/d41586-025-00406-7" target="_blank">https://www.nature.com/articles/d41586-025-00406-7</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Chervonyi, Yuri; Trinh, Trieu H.; Olšák, Miroslav; Yang, Xiaomeng; Nguyen, Hoang; Menegali, Marcelo; Jung, Junehyuk; Verma, Vikas; Le, Quoc V.; Luong, Thang (2025). "Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2". arXiv:2502.03544 [cs.AI]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Chervonyi, Yuri; Trinh, Trieu H.; Olšák, Miroslav; Yang, Xiaomeng; Nguyen, Hoang; Menegali, Marcelo; Jung, Junehyuk; Verma, Vikas; Le, Quoc V.; Luong, Thang (2025). "Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2". arXiv:2502.03544 [cs.AI]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> </ol>