Case Study: A Mathematical Research Agent System
The case study describes an agent system built to support mathematical research over an Obsidian vault of roughly 11,600 notes.
System requirements
- Preserve source material and distinguish it from generated summaries.
- Expose uncertainty rather than silently inventing mathematical facts.
- Keep the researcher in control of priorities and final judgments.
- Keep dates, task status, note links, theorem statements, and proof artifacts reproducible.
Workflows
Daily research scheduling
- Goal: convert recent work and priorities into a manageable daily assignment.
- Patterns: plan-and-execute, memory management, human-in-the-loop.
- Pipeline: recent work → candidate tasks → prioritized plan → human adjustment → daily sheet.
Paper encoding and note construction
- Goal: turn a paper into structured notes without losing theorem statements or raw proofs.
- Patterns: prompt chaining, tool use, memory management, reflection.
- Pipeline: paper → metadata → outline → theorem notes → proof notes → verification and revision.
Mathematical proof checking
- Goal: check a written argument against definitions, hypotheses, and known results.
- Patterns: router, tool use, reflection, human-in-the-loop.
- Pipeline: proof claim → identify dependencies → retrieve notes → check steps → report gaps → human decision.
Redesign log
For at least two failures, record:
- original design;
- observed failure;
- diagnosis of the violated interface;
- revised pattern;
- evidence that the revision helped.
Final lesson
The vault is not merely a context window. It is an external memory and source of truth. The agent patterns make operations around that source of truth repeatable, inspectable, and revisable.
Suggested figure
12-math-research-case-study.svg in the Agent design pattern illustration folder.