Accelerating Mathematical and Scientific Discovery with Gemini Deep Think

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Accelerating Mathematical and Scientific Discovery with Gemini Deep Think

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):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.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.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.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.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 CollaborationBuilding 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.AcknowledgementsWe 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 ZhaoAuthors 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.

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.
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.
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.
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.
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.

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However, don’t expect anything anytime soon. Intel’s Director of Global Strategic Partnerships Sanam Masroor outlined the plans in a blog post. Operations are expected to begin in Q1 2026, with prototypes due in 2027 and commercial products by 2030. While Intel has not come out and said it, that memory design is almost identical to HBM used in GPU accelerators and AI data centers. HBM sits right on the GPU die for immediate access to the GPU, unlike standard DRAM which resides on memory sticks plugged into the motherboard. HBM is much faster than DDR memory but is also much more expensive to produce. It’s also much more profitable than standard DRAM which is why the big three memory makers – Micron, Samsung, and SK Hynix – are favoring production of it.

Nvidia’s $100 Billion OpenAI Bet Shrinks and Signals a New Phase in the AI Infrastructure Cycle

One of the most eye-popping figures of the AI boom – a proposed $100 billion Nvidia commitment to OpenAI and as much as 10 gigawatts of compute for the company’s Stargate AI infrastructure buildout – is no longer on the table. And that partial retreat tells the data center industry something important. According to multiple reports surfacing at the end of January, Nvidia has paused and re-scoped its previously discussed, non-binding investment framework with OpenAI, shifting from an unprecedented capital-plus-infrastructure commitment to a much smaller (though still massive) equity investment. What was once framed as a potential $100 billion alignment is now being discussed in the $20-30 billion range, as part of OpenAI’s broader effort to raise as much as $100 billion at a valuation approaching $830 billion. For data center operators, infrastructure developers, and power providers, the recalibration matters less for the headline number and more for what it reveals about risk discipline, competitive dynamics, and the limits of vertical circularity in AI infrastructure finance. From Moonshot to Measured Capital The original September 2025 memorandum reportedly contemplated not just capital, but direct alignment on compute delivery: a structure that would have tightly coupled Nvidia’s balance sheet with OpenAI’s AI-factory roadmap. By late January, however, sources indicated Nvidia executives had grown uneasy with both the scale and the structure of the deal. Speaking in Taipei on January 31, Nvidia CEO Jensen Huang pushed back on reports of friction, calling them “nonsense” and confirming Nvidia would “absolutely” participate in OpenAI’s current fundraising round. But Huang was also explicit on what had changed: the investment would be “nothing like” $100 billion, even if it ultimately becomes the largest single investment Nvidia has ever made. That nuance matters. Nvidia is not walking away from OpenAI. But it is drawing a clearer boundary around

Microsoft will invest $80B in AI data centers in fiscal 2025

And Microsoft isn’t the only one that is ramping up its investments into AI-enabled data centers. Rival cloud service providers are all investing in either upgrading or opening new data centers to capture a larger chunk of business from developers and users of large language models (LLMs). In a report published in October 2024, Bloomberg Intelligence estimated that demand for generative AI would push Microsoft, AWS, Google, Oracle, Meta, and Apple would between them devote $200 billion to capex in 2025, up from $110 billion in 2023. Microsoft is one of the biggest spenders, followed closely by Google and AWS, Bloomberg Intelligence said. Its estimate of Microsoft’s capital spending on AI, at $62.4 billion for calendar 2025, is lower than Smith’s claim that the company will invest $80 billion in the fiscal year to June 30, 2025. Both figures, though, are way higher than Microsoft’s 2020 capital expenditure of “just” $17.6 billion. The majority of the increased spending is tied to cloud services and the expansion of AI infrastructure needed to provide compute capacity for OpenAI workloads. Separately, last October Amazon CEO Andy Jassy said his company planned total capex spend of $75 billion in 2024 and even more in 2025, with much of it going to AWS, its cloud computing division.

John Deere unveils more autonomous farm machines to address skill labor shortage

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More Self-driving tractors might be the path to self-driving cars. John Deere has revealed a new line of autonomous machines and tech across agriculture, construction and commercial landscaping. The Moline, Illinois-based John Deere has been in business for 187 years, yet it’s been a regular as a non-tech company showing off technology at the big tech trade show in Las Vegas and is back at CES 2025 with more autonomous tractors and other vehicles. This is not something we usually cover, but John Deere has a lot of data that is interesting in the big picture of tech. The message from the company is that there aren’t enough skilled farm laborers to do the work that its customers need. It’s been a challenge for most of the last two decades, said Jahmy Hindman, CTO at John Deere, in a briefing. Much of the tech will come this fall and after that. He noted that the average farmer in the U.S. is over 58 and works 12 to 18 hours a day to grow food for us. And he said the American Farm Bureau Federation estimates there are roughly 2.4 million farm jobs that need to be filled annually; and the agricultural work force continues to shrink. (This is my hint to the anti-immigration crowd). John Deere’s autonomous 9RX Tractor. Farmers can oversee it using an app. While each of these industries experiences their own set of challenges, a commonality across all is skilled labor availability. In construction, about 80% percent of contractors struggle to find skilled labor. And in commercial landscaping, 86% of landscaping business owners can’t find labor to fill open positions, he said. “They have to figure out how to do

2025 playbook for enterprise AI success, from agents to evals

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More 2025 is poised to be a pivotal year for enterprise AI. The past year has seen rapid innovation, and this year will see the same. This has made it more critical than ever to revisit your AI strategy to stay competitive and create value for your customers. From scaling AI agents to optimizing costs, here are the five critical areas enterprises should prioritize for their AI strategy this year. 1. Agents: the next generation of automation AI agents are no longer theoretical. In 2025, they’re indispensable tools for enterprises looking to streamline operations and enhance customer interactions. Unlike traditional software, agents powered by large language models (LLMs) can make nuanced decisions, navigate complex multi-step tasks, and integrate seamlessly with tools and APIs. At the start of 2024, agents were not ready for prime time, making frustrating mistakes like hallucinating URLs. They started getting better as frontier large language models themselves improved. “Let me put it this way,” said Sam Witteveen, cofounder of Red Dragon, a company that develops agents for companies, and that recently reviewed the 48 agents it built last year. “Interestingly, the ones that we built at the start of the year, a lot of those worked way better at the end of the year just because the models got better.” Witteveen shared this in the video podcast we filmed to discuss these five big trends in detail. Models are getting better and hallucinating less, and they’re also being trained to do agentic tasks. Another feature that the model providers are researching is a way to use the LLM as a judge, and as models get cheaper (something we’ll cover below), companies can use three or more models to

OpenAI’s red teaming innovations define new essentials for security leaders in the AI era

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More OpenAI has taken a more aggressive approach to red teaming than its AI competitors, demonstrating its security teams’ advanced capabilities in two areas: multi-step reinforcement and external red teaming. OpenAI recently released two papers that set a new competitive standard for improving the quality, reliability and safety of AI models in these two techniques and more. The first paper, “OpenAI’s Approach to External Red Teaming for AI Models and Systems,” reports that specialized teams outside the company have proven effective in uncovering vulnerabilities that might otherwise have made it into a released model because in-house testing techniques may have missed them. In the second paper, “Diverse and Effective Red Teaming with Auto-Generated Rewards and Multi-Step Reinforcement Learning,” OpenAI introduces an automated framework that relies on iterative reinforcement learning to generate a broad spectrum of novel, wide-ranging attacks. Going all-in on red teaming pays practical, competitive dividends It’s encouraging to see competitive intensity in red teaming growing among AI companies. When Anthropic released its AI red team guidelines in June of last year, it joined AI providers including Google, Microsoft, Nvidia, OpenAI, and even the U.S.’s National Institute of Standards and Technology (NIST), which all had released red teaming frameworks. Investing heavily in red teaming yields tangible benefits for security leaders in any organization. OpenAI’s paper on external red teaming provides a detailed analysis of how the company strives to create specialized external teams that include cybersecurity and subject matter experts. The goal is to see if knowledgeable external teams can defeat models’ security perimeters and find gaps in their security, biases and controls that prompt-based testing couldn’t find. What makes OpenAI’s recent papers noteworthy is how well they define using human-in-the-middle

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