AI Reaches Silver Medal Level in Solving Problems from the International Mathematical Olympiad

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<h2>Acknowledgements</h2>
<p>We thank the International Mathematical Olympiad organization for their support.</p>
<p>AlphaProof development was led by Thomas Hubert, Rishi Mehta, and Laurent Sartran; AlphaGeometry 2 and natural language reasoning efforts were led by Thang Luong. Key contributions to AlphaProof came from Hussain Masoom, Aja Huang, Miklós Z. Horváth, Tom Zahavy, Vivek Veeriah, Eric Wieser, Jessica Yung, Lei Yu, Yannick Schroecker, Julian Schrittwieser, Ottavia Bertolli, Borja Ibarz, Edward Lockhart, Edward Hughes, Mark Rowland, and Grace Margand. Alex Davies and Daniel Zheng played significant roles in the development of informal systems, including final answer determination, with contributions from Iuliya Beloshapka, Ingrid von Glehn, Yin Li, Fabian Pedregosa, Ameya Velingker, and Goran Žužić. Oliver Nash, Bhavik Mehta, Paul Lezeau, Salvatore Mercuri, Lawrence Wu, Calle Soenne, Thomas Murrills, Luigi Massacci, and Andrew Yang acted as advisors and contributed as Lean experts. Past contributors include Amol Mandhane, Tom Eccles, Eser Aygün, Zhitao Gong, Richard Evans, Soňa Mokrá, Amin Barekatain, Wendy Shang, Hannah Openshaw, and Felix Gimeno. This work was guided by David Silver and Pushmeet Kohli.</p>
<p>The development of AlphaGeometry 2 was led by Trieu Trinh and Yuri Chervonyi, with key contributions from Mirek Olšák, Xiaomeng Yang, Hoang Nguyen, Junehyuk Jung, Dawsen Hwang, and Marcelo Menegali. The natural language reasoning system was guided by Golnaz Ghiasi, Garrett Bingham, and YaGuang Li, with contributions from Swaroop Mishra, Nigamaa Nayakanti, Sidharth Mudgal, Qijun Tan, Junehyuk Jung, Hoang Nguyen, Alex Zhai, Dawsen Hwang, Mingyang Deng, Clara Huiyi Hu, Jarrod Kahn, and Maciej Kula. Both the AlphaGeometry and natural language reasoning systems received advice from Quoc Le.</p>
<p>David Silver, Quoc Le, Demis Hassabis, and Pushmeet Kohli coordinated and managed the overall project. We’d also like to acknowledge Insuk Seo, Evan Chen, Zigmars Rasscevskis, Kari Ragnarsson, Junhwi Bae, Jeonghyun Ahn, Jimin Kim, Hung Pham, Nguyen Nguyen, Son Pham, and Pasin Manurangsi for their contributions to evaluating the quality of our language reasoning system. Additionally, we appreciate the support from Jeff Stanway, Jessica Lo, Erica Moreira, Petko Yotov, and Kareem Ayoub in compute provision and management. Special thanks to Prof. Gregor Dolinar and Dr. Geoff Smith MBE from the IMO Board for their collaboration, and to Tu Vu, Hanzhao Lin, Chenkai Kuang, Vikas Verma, Yifeng Lu, Xinyun Chen, Denny Zhou, Vihan Jain, Henryk Michalewski, Xavier Garcia, Arjun Kar, Lampros Lamprou, Kaushal Patel, Kelvin Xu, Ilya Tolstikhin, Olivier Bousquet, Anton Tsitsulin, Dustin Zelle, CJ Carey, Sam Blackwell, Abhi Rao, Vahab Mirrokni, Behnam Neyshabur, Ethan Dyer, Keith Rush, Moritz Firsching, Dan Shved, Ihar Bury, Divyanshu Ranjan, Hadi Hashemi, Alexei Bendebury, Soheil Hassas Yeganeh, Shibl Mourad, Simon Schmitt, Satinder Baveja, Chris Dyer, Jacob Austin, Wenda Li, Heng-tze Cheng, Ed Chi, Koray Kavukcuoglu, Oriol Vinyals, Jeff Dean, and Sergey Brin for their guidance and support.</p>
<p>Finally, we extend our gratitude to the numerous contributors to the Lean and Mathlib projects, as their support has been invaluable to the success of AlphaProof.</p>