Accelerating Mathematical and Scientific Discovery with Gemini Deep Think

Under direction from expert mathematicians and scientists, Gemini Deep Think is solving professional research problems across mathematics, physics, and computer science

In the summer of 2025, an advanced version of Gemini Deep Think achieved Gold-medal standard at the International Mathematics Olympiad (IMO) and later, an updated version, obtained similar results at the International Collegiate Programming Contest. These results demonstrated the model could reason through some of the most challenging math and programming problems designed for students. Since then, Gemini Deep Think mode has moved into science, engineering and enterprise workflows to tackle more complex, open-ended challenges.

In the last week, our teams published two papers (1, 2) detailing a cross-disciplinary effort to solve professional research problems using Gemini Deep Think mode. These results stem from deep collaboration between mathematicians, physicists, and computer scientists.

The Frontier of Pure Mathematics

Unlike IMO problems, research-level mathematics requires advanced techniques from vast literature. While foundation models have large knowledge bases, data scarcity often leads to superficial understanding and hallucinations in advanced subjects.

To solve this, we built a math research agent (internally codenamed Aletheia), powered by Gemini Deep Think mode. It features a natural language verifier to identify flaws in candidate solutions and enable an iterative process of generating and revising solutions. Crucially, this agent can admit failure to solve a problem, a key feature that improved the efficiency for researchers.

Additionally, the research agent uses Google Search and web browsing to navigate complex research, preventing spurious citations and computational inaccuracies when synthesizing published literature.

Since achieving IMO Gold-medal standard in July 2025, Gemini Deep Think has progressed rapidly, scoring up to 90% on the IMO-ProofBench Advanced test as inference-time compute scales. We demonstrated that the scaling law continues to hold as we progress beyond Olympiad level into PhD-level exercises (per our internal FutureMath Basic benchmark). Notably, Aletheia demonstrated that higher reasoning quality can be achieved at a lower inference-time compute.

For research-level math, Aletheia has already enabled several advancements, produced via varying levels of autonomous research:

• Reliable autonomous research. A research paper (Feng26) generated by AI without any human intervention, which calculates certain structure constants in arithmetic geometry called eigenweights.
• AI-guided collaboration. A research paper (LeeSeo26) demonstrating human-AI collaboration in proving bounds on systems of interacting particles called independent sets.
• An extensive semi-autonomous evaluation (Feng et al., 2026b) of 700 open problems on Bloom’s Erdős Conjectures database, including autonomous solutions to four open questions listed there. On Erdős-1051, our model autonomously solved and helped lead to a generalization reported in a research paper (BKKKZ26).

The agent also contributed intermediate propositions on two further papers, (FYZ26) and (ACGKMP26). It is also of note that there has been prior work using Gemini for research-level math at a smaller scale in terms of collaborations and the number of problems tackled.

Following extensive discussions with the mathematical community, we suggest a taxonomy to classify AI-assisted mathematics research by significance and degree of AI contribution - contributing to the wider discussion on responsible documentation, evaluation and communication of AI-generated results. Level 2 (“publishable quality”) works have been submitted to reputable journals. Currently, we do not claim any Level 3 (“Major Advance”) and Level 4 (“Landmark Breakthrough”) results.

Prompts and model outputs are available here. For discussions on AI contributions, our “Human-AI Interaction card”, and community impact, see our paper.

Expanding to Physics and Computer Science

Gemini Deep Think mode has also demonstrated promise in computer science and physics. The second paper builds on similar agentic reasoning ideas, and identifies effective "recipes" for collaboration, specifically the "Advisor" model, where humans guide AI through iterative "Vibe-Proving" cycles to validate intuition and refine proofs. We also detail tactical techniques like “balanced prompting” —requesting simultaneous proof or refutation to prevent confirmation bias—and code-assisted verification. These methods, combined with the model's ability to bridge disparate scientific fields through deep structural connections, are transforming how theoretical research is conducted. This work builds upon our successful deployment of an advanced version of Gemini Deep Think to assist in reviewing CS theory papers for STOC’26 conference.

Collaborating with experts on 18 research problems, an advanced version of Gemini Deep Think helped resolve long-standing bottlenecks across algorithms, ML and combinatorial optimization, information theory, and economics. Highlights from our “Accelerating Research with Gemini” paper include (corresponding section numbers in paper):

1. Crossing mathematical borders for network puzzles: Progress on classic computer science problems like "Max-Cut" (efficiently splitting networks) and the "Steiner Tree" (connecting high-dimensional points) had slowed down. Gemini broke both deadlocks by thinking outside the box. It solved these discrete algorithmic puzzles by pulling advanced tools—like the Kirszbraun Theorem, measure theory, and the Stone-Weierstrass theorem—from entirely unrelated branches of continuous mathematics. See Sections 4.1 and 4.2.
2. Settling a decade-old conjecture in online submodular optimization: A 2015 theory paper proposed a seemingly obvious rule for data streams: making a copy of an arriving item is always less valuable than simply moving the original. Experts struggled for a decade to prove this. Gemini engineered a highly specific three-item combinatorial counterexample, rigorously proving the long-standing human intuition false. See Section 3.1.
3. Machine learning optimization: Training AI to filter out noise usually requires engineers to manually tune a mathematical "penalty." Researchers created a new technique that did this automatically, but couldn't mathematically explain why. Gemini analyzed the equations and proved the method succeeds by secretly generating its own "adaptive penalty" on the fly. See Section 8.3.
4. Upgrading economic theory for AI: A recent 'Revelation Principle' for auctioning AI generation tokens only worked mathematically when bids were restricted to rational numbers. Extending the domain to continuous real numbers invalidated the original proof. Gemini employed advanced topology and order theory to extend the theorem, accommodating real-world, continuous auction dynamics. See Section 8.4.
5. Physics of cosmic strings: Calculating gravitational radiation from cosmic strings requires finding analytical solutions to tricky integrals containing "singularities." Gemini found a novel solution using Gegenbauer polynomials. This naturally absorbed the singularities, collapsing an infinite series into a closed form, finite sum. See Section 6.1.

Spanning diverse fields—from information and complexity theory to cryptography and mechanism design—the results demonstrate how AI is fundamentally shifting research. For details, see our paper.

Given computer science's fluid, conference-driven publication pipeline, we describe these results by academic trajectory rather than a rigid taxonomy. About half target strong conferences—including an ICLR ’26 acceptance—while most remaining findings will form future journal submissions. Even when course-correcting the field by identifying errors (Section 3.2) or refuting conjectures (Section 3.1), these outcomes highlight AI’s value 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 general foundation models - leveraged with agentic reasoning workflows - can act as a powerful scientific companion.

Under direction from expert mathematicians, physicists, and computer scientists, Gemini Deep Think mode is proving its utility across fields where complex math, logic and reasoning are core.

We are witnessing a fundamental shift in the scientific workflow. As Gemini evolves, it acts as "force multiplier" for human intellect, handling knowledge retrieval and rigorous verification so scientists can focus on conceptual depth and creative direction. Whether refining proofs, hunting for counterexamples, or linking disconnected fields, AI is becoming a valuable collaborator in the next chapter of scientific progress.

Acknowledgements

We thank the community of expert mathematicians, physicists, and computer scientists for their support of this project.

This project was a large-scale collaboration across Google and its success is due to the combined efforts of many individuals and teams. Thang Luong and Vahab Mirrokni led the overall research directions with deep technical expertises from Tony Feng and David Woodruff.

Authors of the first paper “Towards Autonomous Mathematics 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, Golnaz Ghiasi, Yi Tay, YaGuang Li, Chenkai Kuang, Yuan Liu, Hanzhao (Maggie) Lin, Evan Zheran Liu, Nigamaa Nayakanti, Xiaomeng Yang, Heng-tze Cheng, Demis Hassabis, Koray Kavukcuoglu, Quoc V. Le, Thang Luong. We thank the following experts for feedback 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

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. Hajiaghayi, Mahdi JafariRaviz, Adel Javanmard, Karthik C. S., 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 the agentic reasoning on top of Gemini, and our academic expert collaborators verifying and collaborating with Gemini. We also thank Corinna Cortes for her careful review of the paper.

We are grateful for the foundational support from 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.

Last but not least, we thank Divy Thakkar, Adam Brown, Vinay Ramasesh, Alex Davies, Thomas Hubert, Eugénie Rives, Pushmeet Kohli, Benoit Schillings for feedback and support of the project.