https://github.com/0bserver07/bourbaki
An autonomous agent for mathematical reasoning and proof
https://github.com/0bserver07/bourbaki
ai-agent arxiv autonomous-agent computer-algebra fastapi lean4 math-research mathematics oeis proof-assistant pydantic-ai sympy theorem-proving
Last synced: about 1 month ago
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An autonomous agent for mathematical reasoning and proof
- Host: GitHub
- URL: https://github.com/0bserver07/bourbaki
- Owner: 0bserver07
- License: mit
- Created: 2026-02-09T04:26:34.000Z (4 months ago)
- Default Branch: master
- Last Pushed: 2026-05-12T02:50:57.000Z (about 1 month ago)
- Last Synced: 2026-05-12T04:09:24.267Z (about 1 month ago)
- Topics: ai-agent, arxiv, autonomous-agent, computer-algebra, fastapi, lean4, math-research, mathematics, oeis, proof-assistant, pydantic-ai, sympy, theorem-proving
- Language: Python
- Homepage: https://yad.codes/posts/building-bourbaki/
- Size: 710 KB
- Stars: 3
- Watchers: 0
- Forks: 0
- Open Issues: 8
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
Awesome Lists containing this project
README
An autonomous agent for mathematical reasoning and proof.
How It Works ·
Quick Start ·
Tools ·
Skills ·
Autonomous Mode ·
Commands
---
[Claude Code](https://docs.anthropic.com/en/docs/claude-code/overview) gives an LLM a shell and dev tools so it can write and run code. Bourbaki does the same thing for math: it gives an LLM a computer algebra system (SymPy), a proof assistant (Lean 4), and research APIs (OEIS, arXiv).
You ask a question in the TUI, the agent computes, verifies, looks things up, and streams the answer back. If it writes a proof, it can formalize it. If it makes a claim, it can check it.
## How It Works
1. You ask a question in the TUI
2. The backend agent reasons about the approach
3. It calls tools: SymPy for computation, Lean for verification, OEIS/arXiv for lookup
4. Results feed back into the agent, which iterates if needed
5. A scratchpad enforces limits and deduplicates repeated calls
6. The final answer streams back to the TUI as it's generated
The TUI is a pure display client. All reasoning, tool calls, and state live in the Python backend.
## Quick Start
```bash
# Clone the repo
git clone https://github.com/0bserver07/bourbaki.git
cd bourbaki
# Start the backend
cd backend
pip install -e .
uvicorn bourbaki.main:app --reload --port 8000
# In another terminal — start the TUI
bun install
bun start
```
The TUI connects to `localhost:8000` by default. Override with `BOURBAKI_BACKEND_URL`.
### Prerequisites
- [Python 3.11+](https://python.org)
- [Bun](https://bun.sh) v1.0+
- An LLM API key (set `ANTHROPIC_API_KEY`, `OPENAI_API_KEY`, or `GOOGLE_API_KEY`)
- [Lean 4](https://lean-lang.org/) with Mathlib (optional, for formal verification)
## Tools
| Tool | What it does |
|------|-------------|
| **Symbolic Compute** | Native SymPy: simplification, integration, solving, 30+ operations |
| **Lean Prover** | Lean 4 + Mathlib, machine-checked formal proofs |
| **Sequence Lookup** | OEIS: identify and explore integer sequences |
| **Paper Search** | arXiv: find relevant papers and results |
| **Web Search** | Exa: search the web for mathematical references |
## Skills
Skills are proof techniques loaded from `SKILL.md` files. They tell the agent how to approach a specific type of proof step by step, instead of letting it improvise.
21 built-in skills across five categories:
- **Basic:** induction, strong induction, direct proof, contradiction, pigeonhole, counting
- **Analysis:** epsilon-delta, convergence tests, sequence limits, inequality chains
- **Geometry:** coordinate proof, synthetic construction, transformations
- **Algebra:** group homomorphisms, ring ideals, polynomials
- **Advanced:** extremal arguments, probabilistic method, conjecture exploration, formalization, proof explanation
Skills can be added at three levels: built-in (`src/skills/`), user (`~/.bourbaki/skills/`), or project (`.bourbaki/skills/`).
## Autonomous Mode
Long-running proof search via a proposer-builder-reviewer loop driven by GLM-5.1 and a warm `LeanREPLSession`. One proposal per iteration, bounded by `max_iterations` (default 50, 8 for interactive). Every reported solve is gated by a `lean_prover` whole-file compile — no REPL-only claims.
Drive the loop from `backend/bourbaki/benchmarks/minif2f.py::attempt_proof_loop` or from the FastAPI `/query` endpoint with `use_loop=True`. (The TUI's `/prove ` command still points at the legacy `/autonomous/start` route, which now returns HTTP 410 Gone — the legacy pipeline was deleted in commit `2113629`. Rewiring the TUI to the new loop is tracked separately.)
## Results
Verified pass rates on miniF2F valid (every solve confirmed by `lean_prover` standalone compile — see [`docs/REALITY_CHECK.md`](docs/REALITY_CHECK.md) for the audit of the earlier REPL-only era):
| Date | Approach | Verified | Sample |
|------|----------|---------:|--------|
| 2026-02-22 (audit) | v0.2.1 code, lean_prover-gated | 6.2% (15/244) | full 244 |
| 2026-03-08 (v0.2.2) | + REPL pipe-recovery + tactic blocklist | 25.8% (63/244) | full 244 |
| 2026-04-01 | + HILBERT decomposer + in-context solving | 50.0% (5/10) | 10-problem |
| 2026-04-25 | **proposer-builder-reviewer loop (GLM-5.1)** | **90.0% (9/10)** | 10-problem · 0 false positives |
| 2026-05-09 | same loop on a wider sample | **62.9% (22/35)** | 35-problem stratified · 0 false positives |
The 2026-02-17 v0.2.0 and 2026-02-18 v0.2.1 releases claimed 91.8% / 94.3% on the valid/test splits. Both numbers were inflated ~15× by REPL false positives and were retracted in the v0.2.2 audit (both GitHub releases now read "RETRACTED (inflated numbers)" in their titles). The current proposer-builder-reviewer architecture (commits `49211ce` through `2113629`) replaces the prior HILBERT-style pipeline; the full 244-problem run with the new architecture is pending (tracked in [issue #14](https://github.com/0bserver07/bourbaki/issues/14)).
## Example Usage
**Prove a theorem:**
```
❯ Prove that the sum of the first n integers equals n(n+1)/2
⏺ Thinking...
⏺ Symbolic Compute (expression=Sum(k, (k, 1, n)))
⎿ Computed result
⏺ Lean Prover
⎿ ✓ Verified in 2.3s
Proof by induction. Base case: n = 1, sum = 1 = 1·2/2. ✓
Inductive step: assume ∑_{k=1}^{n} k = n(n+1)/2.
Then ∑_{k=1}^{n+1} k = n(n+1)/2 + (n+1) = (n+1)(n+2)/2. ∎
```
**Compute symbolically:**
```
❯ Factor 84 and find its divisors
⏺ Symbolic Compute (operation=factor, expression=84)
⎿ Computed result
84 = 2² × 3 × 7
Divisors: {1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84}
```
**Identify a sequence:**
```
❯ What sequence is 1, 1, 2, 3, 5, 8, 13?
⏺ Sequence Lookup (query="1,1,2,3,5,8,13")
⎿ Found 1 results
A000045 — Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.
```
## Commands
| Command | What it does |
|---------|-------------|
| `/help` | Show all commands |
| `/model ` | Switch LLM model |
| `/skills` | List available proof technique skills |
| `/problems` | Browse the problem database |
| `/prove ` | Start proof attempt (legacy TUI handler still POSTs to `/autonomous/start`, which now returns 410; use the `attempt_proof_loop` driver or `/query` with `use_loop=True` for the new loop) |
| `/pause` | Pause proof search (legacy, 410) |
| `/progress` | Show proof search progress (legacy, 410) |
| `/sessions` | List saved sessions |
| `/new` | Start a new session |
| `/export [format]` | Export last answer (latex, lean, markdown) |
| `/debug` | Toggle debug mode |
| `/clear` | Clear the screen |
## Architecture
```
src/ React + Ink TUI (display client)
├── components/ UI components (Input, AgentEventView, AnswerView)
├── hooks/ useAgentRunner (SSE bridge), useModelSelection
└── skills/ 21 SKILL.md proof technique files
backend/bourbaki/ Python backend (owns all state)
├── agent/ Pydantic AI agent, prompts, scratchpad, event mapper
├── tools/ SymPy, Lean 4, OEIS, arXiv, Web Search, Skills
├── sessions/ Persistence + context compaction
├── prover/ Proposer-builder-reviewer-memory loop
├── autonomous/ Phase-3 vestige — only `tactics.py` survives (blocklist)
├── benchmarks/ miniF2F + PutnamBench runners
├── problems/ 13 classic problems database
└── server/routes/ FastAPI endpoints (query, sessions, skills, ...)
```
## Tech Stack
- **Backend:** Python, FastAPI, Pydantic AI, SymPy, httpx
- **TUI:** Bun, React + Ink, TypeScript
- **Verification:** Lean 4 + Mathlib
- **Sequences:** OEIS API
- **Papers:** arXiv API
## Credits
Named after [Nicolas Bourbaki](https://en.wikipedia.org/wiki/Nicolas_Bourbaki), the collective pseudonym of a group of mathematicians who tried to rewrite all of mathematics from scratch using set theory.
## License
[MIT License](LICENSE)