运用Gemini加速科学研究：案例研究与常用技术解析

摘要

大型語言模型（LLMs）的最新進展為加速科學研究開闢了新途徑。儘管模型在協助常規任務方面日益成熟，但其在推動專家級數學新發現方面的能力仍待探索。本文通過一系列案例研究，展示研究人員如何與基於Google Gemini架構的高級AI模型（特別是Gemini Deep Think及其進階變體）成功協作，解決了理論計算機科學、經濟學、優化理論和物理學等多個領域的開放性問題，推翻既有猜想並生成新證明。基於這些實踐經驗，我們提煉出理論研究中有效人機協作的通用技法，包括迭代優化、問題分解與跨學科知識遷移。雖然大部分成果源自這種交互式對話方法，我們也特別展示了超越標準聊天界面的創新應用：將模型部署為嚴格的對抗性評審員以檢測證明中的細微謬誤，以及將其嵌入「神經符號」循環中自主編寫並執行代碼來驗證複雜推導。這些案例共同表明，AI不僅能作為自動化工具，更能在科學發現的創造性進程中成為多功能的真實合作夥伴。

English

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.

运用Gemini加速科学研究：案例研究与常用技术解析

Accelerating Scientific Research with Gemini: Case Studies and Common Techniques

摘要

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