AI achieves silver-medal standard solving International Mathematical Olympiad problems

Acknowledgements

We thank the International Mathematical Olympiad organization for their support.

AlphaProof development was led by Thomas Hubert, Rishi Mehta and Laurent Sartran; AlphaGeometry 2 and natural language reasoning efforts were led by Thang Luong.

AlphaProof was developed with key contributions 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, Grace Margand. Alex Davies and Daniel Zheng led the development of informal systems such as final answer determination, with key 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 advised 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, Felix Gimeno. This work was advised by David Silver and Pushmeet Kohli.

The development of AlphaGeometry 2 was led by Trieu Trinh and Yuri Chervonyi, with key contributions by Mirek Olšák, Xiaomeng Yang, Hoang Nguyen, Junehyuk Jung, Dawsen Hwang and Marcelo Menegali. The development of the natural language reasoning system was led by Golnaz Ghiasi, Garrett Bingham, YaGuang Li, with key contributions by Swaroop Mishra, Nigamaa Nayakanti, Sidharth Mudgal, Qijun Tan, Junehyuk Jung, Hoang Nguyen, Alex Zhai, Dawsen Hwang, Mingyang Deng, Clara Huiyi Hu, Jarrod Kahn, Maciej Kula, Cosmo Du. Both AlphaGeometry and natural language reasoning systems were advised by Quoc Le.

David Silver, Quoc Le, Demis Hassabis, and Pushmeet Kohli coordinated and managed the overall project.

We’d also like to thank Insuk Seo, Evan Chen, Zigmars Rasscevskis, Kari Ragnarsson, Junhwi Bae, Jeonghyun Ahn, Jimin Kim, Hung Pham, Nguyen Nguyen, Son Pham, and Pasin Manurangsi who helped evaluate the quality of our language reasoning system. Jeff Stanway, Jessica Lo, Erica Moreira, Petko Yotov and Kareem Ayoub for their support for compute provision and management. Prof Gregor Dolinar and Dr Geoff Smith MBE from the IMO Board, for the support and collaboration; and 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 support and advice.

Finally, we’d like to thank the many contributors to the Lean and Mathlib projects, without whom AlphaProof wouldn’t have been possible.