The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learning

TL;DR

This paper provides a practical guide and framework for integrating AI tools into mathematical and machine learning research, emphasizing responsible use, autonomous experimentation, and real-world case studies.

Contribution

It introduces a five-level taxonomy of AI integration, an open-source framework for autonomous research assistants, and demonstrates its application through case studies in deep learning and mathematics.

Findings

Framework enables autonomous experiments over 20 hours without human intervention.

Runs inside a sandboxed container compatible with any frontier LLM.

Scales from personal laptops to multi-node GPU clusters.

Abstract

AI tools and agents are reshaping how researchers work, from proving theorems to training neural networks. Yet for many, it remains unclear how these tools fit into everyday research practice. This paper is a practical guide to AI-assisted research in mathematics and machine learning: We discuss how researchers can use modern AI systems productively, where these systems help most, and what kinds of guardrails are needed to use them responsibly. It is organized into three parts: (I) a five-level taxonomy of AI integration, (II) an open-source framework that, through a set of methodological rules formulated as agent prompts, turns CLI coding agents (e.g., Claude Code, Codex CLI, OpenCode) into autonomous research assistants, and (III) case studies from deep learning and mathematics. The framework runs inside a sandboxed container, works with any frontier LLM through existing CLI agents, is simple enough to install and use within minutes, and scales from personal-laptop prototyping to multi-node, multi-GPU experimentation across compute clusters. In practice, our longest autonomous session ran for over 20 hours, dispatching independent experiments across multiple nodes without human intervention. We stress that our framework is not intended to replace the researcher in the loop, but to augment them. Our code is publicly available at https://github.com/ZIB-IOL/The-Agentic-Researcher.