Course Overview 

Artificial intelligence has helped researchers discover novel algorithms and construct counterexamples to open mathematical conjectures. This advanced graduate research seminar explores the frontier of generative AI and autonomous agentic workflows for scientific discovery. Moving decisively beyond general-purpose chatbot prompting, this course examines how modern language models, neuro-symbolic architectures, and programmatic feedback loops can be transformed into rigorous partners for scientific inquiry, mathematical reasoning, and fact-finding. The course equally emphasizes the current limitations of these systems, including hallucinations, false novelty claims, evaluation failures, benchmark contamination, reproducibility challenges, and the distinction between research assistance and genuine scientific discovery.

Students will critically investigate selected topics on how AI systems:

1. Automate Literature Synthesis and Fact-Checking: Audit technical claims with verifiable citation grounding, rigorous hallucination detection, citation validation, and novelty assessment.

2. Formulate In Silico Hypotheses and Experiments: Systematically explore parameter spaces, generate causal graphs, and design simulation protocols.

3. Advance Formal Mathematics and Symbolic Logic: Interface with interactive theorem provers (Lean 4) and rediscover fundamental physical equations via symbolic regression.

4. Discover Novel Algorithms and Discrete Heuristics: Leverage evolutionary LLM search loops (e.g., FunSearch) to break bounds in combinatorial optimization and extremal combinatorics.

5. Orchestrate Autonomous Scientific Agents: Implement and evaluate end-to-end multi-agent research loops that code, test, critique, and write computational scientific workflows.

This course is tailored for research-oriented STEM graduate students, who will gain expertise in building and evaluating the next generation of AI scientific tools. Required work includes:

• Research Paper Presentations: Each participant presents and leads critical seminar discussions on about two milestone research papers selected from the course syllabus.

• Hands-on Capstone Project: Students propose and build an autonomous agent, algorithmic pipeline, or evaluative benchmark tailored to a concrete scientific challenge in their disciplinary domain, including a rigorous analysis of reliability, validity, and failure modes.

The recommended preparation is knowledge of programming (such as Python, Matlab, Java, etc.).