Working with experts on 18 research questions, the advanced version of Gemini Deep Think has helped solve long-standing bottlenecks across algorithms, ML and combinatorial optimization, information theory, and economics. Highlights of the “Accelerating Research with Gemini” paper include (corresponding section numbers within the paper):
Crossing mathematical boundaries in network puzzles: Progress on classic computer science problems such as “Max-Cut” (efficiently partitioning networks) and “Sreiner Trees” (connecting high-dimensional points) has been slow. Gemini has broken both deadlocks by thinking outside the box. It solved these discrete algorithmic puzzles by drawing sophisticated tools such as the Kirsch-Brown theorem, measure theory, and the Stone-Weierstrass theorem from completely unrelated areas of continuous mathematics. See Sections 4.1 and 4.2. Putting to rest a decade of speculation in online submodular optimization: A 2015 theoretical paper proposed seemingly obvious rules for data streams. Making a copy of an item when it arrives is always less valuable than simply moving the original. Experts struggled for ten years to prove this. Gemini created a counterexample for a very specific three-item combination, rigorously proving that long-held human intuitions were wrong. See Section 3.1. Machine learning optimization: Training AI to remove noise typically requires engineers to manually adjust mathematical “penalties.” Researchers have developed a new technique to do this automatically, but they haven’t been able to explain mathematically why. Gemini proved this method to be successful by analyzing the equation and secretly generating its own “adaptive penalty” on the fly. See Section 8.3. Upgrading the economic theory of AI: The recent “revelation principle” for auctioning AI-generated tokens worked mathematically only if bids were restricted to rational numbers. Extending the domain to continuous real numbers invalidates the original proof. Gemini employed advanced topology and ordering theory to extend the theorem to accommodate real-world continuous auction dynamics. See Section 8.4. Physics of cosmic strings: Calculating gravitational radiation from cosmic strings requires finding analytical solutions to difficult integrals involving “singularities.” Gemini found a new solution using Gegenbauer polynomials. This naturally absorbed the singularity and collapsed the infinite series into a finite sum in closed form. See Section 6.1.
Results across a variety of disciplines, from information and complexity theory to cryptography and mechanism design, demonstrate how AI is fundamentally changing research. See the paper for more details.
Given computer science’s fluid and conference-driven publication pipeline, we discuss these results based on academic trajectories rather than rigid taxonomies. Approximately half are targeted at high-powered conferences, including acceptance at ICLR ’26, and most of the remaining findings will form future journal submissions. Whether identifying mistakes (Section 3.2) or refuting assumptions (Section 3.1) to course-correct in the field, these results highlight the value of AI as a high-level scientific collaborator.
The future of human-AI collaboration
Building on Google’s previous breakthroughs (1, 2, 3, 4, 5), this work demonstrates that common-based models leveraging agent inference workflows can serve as powerful scientific companions.
Under the guidance of expert mathematicians, physicists, and computer scientists, Gemini Deep Think mode has proven its usefulness across fields where complex mathematics, logic, and reasoning are central.
We are witnessing fundamental changes in scientific workflows. As Gemini evolves, it acts as a “power multiplier” for human intelligence, handling the search and rigorous verification of knowledge, allowing scientists to focus on conceptual depth and creative direction. Whether refining proofs, finding counterexamples, or connecting divided fields, AI is becoming a valuable ally in the next chapter of scientific progress.
Acknowledgment
We would like to thank the community of professional mathematicians, physicists, and computer scientists who supported this project.
This project was a major collaboration across Google, and its success is the combined effort of many individuals and teams. Thang Luong and Vahab Mirrokni led the overall research direction, leveraging the deep technical expertise of Tony Feng and David Woodruff.
The authors of the first paper, “Towards autonomous mathematical research,” include Tony Feng, Trieu H. Trinh, Garrett Bingham, Dawsen Hwang, Yuri Chervonyi, Junehyuk Jung, Joonkyung Lee, Carlo Pagano, Sang-hyun Kim, Federico Pasqualotto, Sergei Gukov, Jonathan N. Lee, Junsu Kim, Kaiying Hou, and Golnaz. Contains. Gyashi, Yi Tai, Yaguan Lee, Chengkai Kuan, Yuan Liu, Hangjiao (Maggie) Lin, Evan Zelan Liu, Nigamaa Nayakanti, Xiaomeng Yang, Hentze Chen, Demis Hassabis, Korai Kabukkuolu, Kuok V. Lee, and Tan Luong. We would like to thank the following experts for feedback and discussion on this work: Jarod Alper, Kevin Barreto, Thomas Bloom, sourav Chatterjee, Otis Chodosh, Michael Harris, Michael Hutchings, Seongbin Jeon, Youngbeom Jin, Aiden Yuchan Jung, Jiwon Kang, Jimin Kim, Vjekoslav Kovač, Daniel Litt, Ciprian Manolescu, Mona Merling, Agustin Moreno, Karl Schildkraut, Johannes Schmidt, Insook Seo, Jaehyun Seo, Chengcheng Tsai, Ravi Vakil, Zhiwei Yun, Shentong Zhang, Wei Zhang, Yufei Zhao.
The authors of the second paper, “Accelerating Scientific Research with Gemini: Case Studies and Common Techniques” include David P. Woodruff, Vincent Cohen-Addad, Lalit Jain, Jieming Mao, Song Zuo, MohammadHossein Bateni, Simina Branzei, Michael P. Brenner, Lin Chen, Ying Feng, Lance Fortnow, Gang Fu, Ziyi Guan, Zahra Hadizadeh, Mohammad T. Hajiagai, Mahdi Jafariraviz, Adel Javanmar, Kartik CS, Kenichi Kawarabayashi, Ravi Kumar, Silvio Latanzi, Wiun Lee, Yi Li, Ioannis Panagias, Dimitris Paparas, Ben. Jamin Przybocki, Bernardo Sverkasso, Ola Svensson, Shayan Tahelijam, Xuan-Wu, Eilon Yogev, Morteza Zadimoghaddam, Samson Chow, Yossi Mathias, Jeff Dean, James Manyika, Vahab Mirakni. This list includes researchers at Google who are building agent inference on Gemini, as well as academic collaborators who are validating and collaborating with Gemini. We would also like to thank Corinna Cortes for her careful review of this paper.
We would like to thank other members of the DeepThink team for their essential support: Anirudh Baddepudi, Michael Brenner, Irene Cai, Kristen Chiafullo, Paul Covington, Rumen Dangovski, Chenjie Gu, Huan Gui, Vihan Jain, Rajesh Jayaram, Melvin Johnson, Rosemary Ke, Maciej Kula, Nate Kushman, Jane Labanowski, Steve Li, Pol Moreno, Sidharth Mudgal, William Nelson, Ada Maksutaji Offraza, Sahitya Potluli, Navneet Potti, Shubha Raghvendra, Shiamak Shakeri, Archit Sharma, Shinyin. – Song, Mukund Sundararajan, Qijun Tang, Zak Tsai, Theophane Weber, Winnie Xu, Jicheng Xu, Junwen Yao, Xunyu Yao, Adams Yu, Lijun Yu, Honglei Zhuan.
Thanks to Quoc Le, Koray Kavukcuoglu, Demis Hassabis, James Manyika, Yossi Matias, and Jeff Dean for sponsoring this project.
Last but not least, we would like to thank Divy Thakkar, Adam Brown, Vinay Ramasesh, Alex Davies, Thomas Hubert, Eugénie Rives, Pushmeet Kohli, and Benoit Schillings for their feedback and support on the project.
