Collaborating with consultants on 18 analysis issues, a complicated model of Gemini Deep Suppose helped resolve long-standing bottlenecks throughout algorithms, ML and combinatorial optimization, data principle, and economics. Highlights from our “Accelerating Analysis with Gemini” paper embody (corresponding part numbers in paper):
- Crossing mathematical borders for community puzzles: Progress on basic laptop science issues like “Max-Reduce” (effectively splitting networks) and the “Steiner Tree” (connecting high-dimensional factors) had slowed down. Gemini broke each deadlocks by considering exterior the field. It solved these discrete algorithmic puzzles by pulling superior instruments—just like the Kirszbraun Theorem, measure principle, and the Stone-Weierstrass theorem—from solely unrelated branches of steady arithmetic. See Sections 4.1 and 4.2.
- Settling a decade-old conjecture in on-line submodular optimization: A 2015 principle paper proposed a seemingly apparent rule for knowledge streams: making a duplicate of an arriving merchandise is at all times much less priceless than merely transferring the unique. Consultants struggled for a decade to show this. Gemini engineered a extremely particular three-item combinatorial counterexample, rigorously proving the long-standing human instinct false. See Part 3.1.
- Machine studying optimization: Coaching AI to filter out noise normally requires engineers to manually tune a mathematical “penalty.” Researchers created a brand new approach that did this robotically, however could not mathematically clarify why. Gemini analyzed the equations and proved the tactic succeeds by secretly producing its personal “adaptive penalty” on the fly. See Part 8.3.
- Upgrading financial principle for AI: A latest ‘Revelation Precept’ for auctioning AI era tokens solely labored mathematically when bids had been restricted to rational numbers. Extending the area to steady actual numbers invalidated the unique proof. Gemini employed superior topology and order principle to increase the theory, accommodating real-world, steady public sale dynamics. See Part 8.4.
- Physics of cosmic strings: Calculating gravitational radiation from cosmic strings requires discovering analytical options to tough integrals containing “singularities.” Gemini discovered a novel resolution utilizing Gegenbauer polynomials. This naturally absorbed the singularities, collapsing an infinite sequence right into a closed type, finite sum. See Part 6.1.
Spanning various fields—from data and complexity principle to cryptography and mechanism design—the outcomes reveal how AI is essentially shifting analysis. For particulars, see our paper.
Given laptop science’s fluid, conference-driven publication pipeline, we describe these outcomes by educational trajectory moderately than a inflexible taxonomy. About half goal robust conferences—together with an ICLR ’26 acceptance—whereas most remaining findings will type future journal submissions. Even when course-correcting the sector by figuring out errors (Part 3.2) or refuting conjectures (Part 3.1), these outcomes spotlight AI’s worth as a high-level scientific collaborator.
The Way forward for Human-AI Collaboration
Constructing on Google’s earlier breakthroughs (1, 2, 3, 4, 5), this work demonstrates that normal basis fashions – leveraged with agentic reasoning workflows – can act as a robust scientific companion.
Beneath path from skilled mathematicians, physicists, and laptop scientists, Gemini Deep Suppose mode is proving its utility throughout fields the place complicated math, logic and reasoning are core.
We’re witnessing a basic shift within the scientific workflow. As Gemini evolves, it acts as “drive multiplier” for human mind, dealing with data retrieval and rigorous verification so scientists can deal with conceptual depth and artistic path. Whether or not refining proofs, trying to find counterexamples, or linking disconnected fields, AI is turning into a priceless collaborator within the subsequent chapter of scientific progress.
Acknowledgements
We thank the neighborhood of skilled mathematicians, physicists, and laptop scientists for his or her assist of this undertaking.
This undertaking was a large-scale collaboration throughout Google and its success is because of the mixed efforts of many people and groups. Thang Luong and Vahab Mirrokni led the general analysis instructions with deep technical expertises from Tony Feng and David Woodruff.
Authors of the primary paper “In direction of Autonomous Arithmetic Analysis” embody: 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 next consultants for suggestions 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 Search engine marketing, Jaehyeon Search engine marketing, Cheng-Chiang Tsai, Ravi Vakil, Zhiwei Yun, Shengtong Zhang, Wei Zhang, Yufei Zhao
Authors of the second paper “Accelerating Scientific Analysis with Gemini: Case Research and Frequent Methods” embody David P. Woodruff, Vincent Cohen-Addad, Lalit Jain, Jieming Mao, Music 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 checklist consists of Google researchers constructing the agentic reasoning on prime of Gemini, and our educational skilled collaborators verifying and collaborating with Gemini. We additionally thank Corinna Cortes for her cautious overview of the paper.
We’re grateful for the foundational assist from the remainder of the DeepThink workforce: 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 Music, 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 undertaking.
Final however not least, we thank Divy Thakkar, Adam Brown, Vinay Ramasesh, Alex Davies, Thomas Hubert, Eugénie Rives, Pushmeet Kohli, Benoit Schillings for suggestions and assist of the undertaking.
