Accelerating Scientific Research with Gemini: Case Studies and Common Techniques
This work addresses the challenge of accelerating scientific research for experts in theoretical domains by demonstrating AI's potential as a creative partner, though it is incremental in building on existing human-AI collaboration methods.
The paper tackles the problem of using large language models like Gemini for novel, expert-level mathematical discovery by presenting case studies where AI collaborated with researchers to solve open problems, refute conjectures, and generate new proofs across fields such as theoretical computer science, economics, optimization, and physics, resulting in successful applications like detecting flaws in proofs and verifying complex derivations.
Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.