借助Gemini加速科研进程：案例解析与常用技巧

摘要

近年来，大型语言模型（LLMs）的突破为加速科研进程开辟了新途径。尽管此类模型在处理常规任务方面日益成熟，但其在推动专家级数学新发现方面的潜力尚不明确。本文通过系列案例研究，展示研究人员如何与基于谷歌Gemini的先进AI模型（特别是Gemini Deep Think及其高级变体）成功协作，在理论计算机科学以及经济学、优化理论和物理学等多个领域解决开放性问题、推翻猜想并生成新证明。基于这些实践，我们提炼出适用于理论研究的人机协作通用技术，包括迭代优化、问题分解和跨学科知识迁移等。虽然大部分成果源于这种交互式对话方法，但我们也重点介绍了超越标准聊天接口的特殊案例：将模型部署为严格的反向评审员以发现现有证明中的细微漏洞，并将其嵌入"神经符号"循环中自主编写执行代码以验证复杂推导。这些案例共同表明，人工智能不仅可作为自动化工具，更能在科学发现的创造性过程中成为多才多艺的真正合作伙伴。

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.

借助Gemini加速科研进程：案例解析与常用技巧

Accelerating Scientific Research with Gemini: Case Studies and Common Techniques

摘要

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