Accelerating mathematical and scientific discoveries with Gemini Deep Think

Working with experts on 18 research problems, the advanced version of Gemini Deep Think helped solve long-standing bottlenecks in algorithms, machine learning and combinatorial optimization, information theory and economics. The most engaging of ours Article “Accelerating Research with Gemini.” include (relevant section numbers in the article):

1. Pushing mathematical boundaries for online puzzles: Progress on classic computer science problems such as “Max-Cut” (capable network slicing) and “Steiner Tree” (connecting multidimensional points) has slowed. Gemini broke both impasses by thinking outside the box. He solved these discrete algorithmic puzzles by extracting advanced tools—such as Kirszbraun’s theorem, measure theory, and the Stone-Weierstrass theorem—from completely unrelated branches of continuous mathematics. See Sections 4.1 and 4.2.
2. Resolving decades of online submodular optimization conjectures: A Theoretical article from 2015 proposed a seemingly obvious rule for data streams: making a copy of an arriving item is always less valuable than simply transferring the original. Experts have been trying to prove this for a decade. Gemini has developed a very detailed three-element combinatorial counterexample, rigorously proving that long-standing human intuition is false. See Section 3.1.
3. Machine learning optimization: Training AI to filter noise typically requires engineers to manually tune a mathematical “penalty.” Scientists created a modern technique that did this automatically, but they couldn’t mathematically explain why. Gemini analyzed the equations and proved that the method worked by secretly generating its own “adaptive penalty” on the fly. See Section 8.3.
4. Improving economic theory for artificial intelligence: The recent “Revelation Rule” for AI-generating token auctions only worked mathematically when bids were restricted to rational numbers. Extending the domain to continuous real numbers invalidated the original proof. Gemini uses advanced topology and ordering theory to extend the theorem to account for continuous real-world auction dynamics. See Section 8.4.
5. Physics of cosmic strings: Calculating the gravitational radiation of cosmic strings requires finding analytical solutions to hard integrals containing “singularities”. Gemini found an groundbreaking solution using Gegenbauer polynomials. This naturally absorbed the singularities, collapsing the infinite series into a closed form, a finite sum. See Section 6.1.

Spanning fields from information and complexity theory to cryptography and mechanism design, the results show how artificial intelligence is fundamentally changing research. For details, see our paper.

Given the fluid, conference-driven publication cycle in computer science, we describe these results based on an academic trajectory rather than a unyielding taxonomy. About half of these focus on robust conferences – including acceptance of ICLR ’26 – while most of the remaining findings will form the basis for publication in future journals. Even when correcting a field by identifying errors (Section 3.2) or refuting assumptions (Section 3.1), these results highlight the value of AI as a high-level research collaborator.

The future of human and artificial intelligence cooperation

Building on Google’s previous breakthroughs (1, 2, 3, 4, 5), this work shows that general foundational models – used in agentic reasoning processes – can act as a powerful scientific companion.

Under the guidance of experienced mathematicians, physicists and computer scientists, Gemini Deep Think mode proves its usefulness in fields where elaborate mathematics, logic and reasoning are at the core.

We are witnessing a fundamental change in scientific workflow. As Gemini evolves, it acts as a “force multiplier” of human intellect, supporting knowledge retrieval and demanding verification so that scientists can focus on conceptual depth and original direction. Whether refining evidence, searching for counterexamples, or connecting unrelated fields, AI is becoming a valuable collaborator in the next chapter of scientific progress.

Thanks

We would like to thank the community of experienced mathematicians, physicists and computer scientists for supporting this project.

This project was a large-scale collaboration across Google, and its success is the result of the combined efforts of many individuals and teams. Thang Luong and Vahab Mirrokni led the overall research direction, drawing on the deep technical expertise of Tony Feng and David Woodruff.

The authors of the first paper “Towards Autonomous Mathematics Research” are: 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, Golnaz Ghiasi, Yi Tay, Yaguang Li, Chenkai Kuang, Yuan Liu, Hanzhao (Maggie) Lin, Evan Zheran Liu, Nigamaa Nayakanti, Xiaomeng Yang, Heng-tze Hassabis, Koray Kavukcuoglu, Quoc V. Le, Thang Luong. We thank the following experts for their opinions and discussions on the 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, Carl Schildkraut, Johannes Schmitt, Insuk Seo, Jaehyeon Seo, Cheng-Chiang Tsai, Ravi Vakil, Zhiwei Yun, Shengtong Zhang, Wei Zhang, Yufei Zhao

The authors of the second article, “Accelerating Scientific Research with Gemini: Case Studies and Common Techniques,” are 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. Hajiaghayi, Mahdi JafariRaviz, Adel Javanmard, Karthik CS, Ken-ichi Kawarabayashi, Ravi Kumar, Silvio Lattanzi, Euiwoong Lee, Yi Li, Ioannis Panageas, Dimitris Paparas, Benjamin Przybocki, Bernardo Subercaseaux, Ola Svensson, Shayan Taherijam, Xuan Wu, Eylon Yogev, Morteza Zadimoghaddam, Samson Zhou, Yossi Matias, Jeff Dean, James Manyika, Vahab Mirrokni. This list includes Google researchers building agentic reasoning on top of Gemini, and our academic expert collaborators validating and collaborating with Gemini. We also thank Corinna Cortes for her insightful review of the article.

We are grateful for the fundamental support of the rest of the DeepThink team: 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 Maksutaj Oflazer, Sahitya Potluri, Navneet. Potti, Shubha Raghvendra, Siamak Shakeri, Archit Sharma, Xinying Song, Mukund Sundararajan, Qijun Tan, Zak Tsai, Theophane Weber, Winnie Xu, Zicheng Xu, Junwen Yao, Shunyu Yao, Adams Yu, Lijun Yu and Honglei Zhuang.

We thank Quoc Le, Koray Kavukcuoglu, Demis Hassabis, James Manyika, Yossi Matias, and Jeff Dean for sponsoring this project.

Finally, we would like to thank Divy Thakkar, Adam Brown, Vinay Ramasesh, Alex Davies, Thomas Hubert, Eugénie Rives, Pushmeet Kohli, Benoit Schillings for their opinions and support of the project.