The State-of-the-Art Intelligence
🎓 Breakthrough Achievement: Revolutionary AI system demonstrating autonomous mathematical research and complex problem solving through hierarchical multi-agent orchestration.
⚡ Current Status: Open-sourced complete implementation including core Self-Evolve mechanism and production-ready web application.
Prompt ≙ Policy Parameters | Feedback ≙ Reward
We optimize the context itself, not the model weights.
- 9,000+ lines of internal reasoning
- 1+ hour of continuous problem-solving
- Complete mathematical proof with rigorous methodology
📄 View Solution - The final output showcasing Crux's unique approach to complex mathematical problems.
Starting from only the hypothesis, Crux autonomously derived:
- ✅ 9 systematic lemmas with complete mathematical rigor
- ✅ Full convergence proofs for the theoretical framework
- ✅ δ-bookkeeping methodology for practical implementation
- ✅ Research-grade theoretical foundations matching peer-reviewed standards
- 📄 View Research
- Hierarchical orchestration inspired by graduate school research structures
- Recursive depth capabilities for arbitrarily complex problems
- Dynamic specialist allocation based on problem complexity
- Proven scaling behavior similar to deep neural networks 📄 View Research - Complete independent mathematical derivation and analysis.
Paradigm Shift: Crux doesn't just reproduce existing work—it conducts original mathematical discovery through autonomous reasoning.
| Feature | Description |
|---|---|
| 🧮 Mathematical Reasoning | Deep mathematical understanding with proof generation |
| 🔍 Problem Analysis | Systematic breakdown of complex mathematical problems |
| 📊 Theoretical Framework | Independent development of mathematical theories |
| 🎯 USAMO-Level Solutions | Solving competition-grade mathematical problems |
| 🔬 Research Methodology | Autonomous mathematical research and discovery |
- Competition mathematics (USAMO, IMO level)
- Abstract algebra and number theory
- Combinatorics and graph theory
- Mathematical analysis and proofs
- Test-Time Reinforcement Learning (TTRL)
- Mathematical reasoning architectures
- Autonomous theorem proving
- AI-driven mathematical discovery
- Independent hypothesis verification
- Rigorous proof construction
- Systematic lemma development
- Mathematical framework derivation
Problem Solving Capability:
- Input: Mathematical problems, hypotheses, research questions
- Processing: 9,000+ lines of internal reasoning
- Output: Complete solutions with rigorous proofs
- Time: 1+ hours for complex problems
Research Methodology:
- Systematic lemma development
- Convergence proof construction
- Independent framework derivation
- Peer-reviewed quality standards
We welcome contributions to advancing AI-driven mathematical research! Feel free to:
- 🔬 Propose new mathematical challenges
- 📊 Share research insights and methodologies
- 🧮 Contribute to theoretical frameworks
- 📚 Help document research findings
- Current: Advanced mathematical reasoning and problem solving
- Q1 2025: Expanded theoretical framework development
- Q2 2025: Multi-domain mathematical applications
- Future: Revolutionary advances in AI-driven mathematical discovery
Our mission is to push the boundaries of AI-driven research and mathematical discovery. Crux represents a breakthrough in autonomous mathematical reasoning. Visit tooliense.com to learn more about our research initiatives.
The heart of Crux - implementing the IC-RL algorithm with enhanced multi-agent hierarchical architecture.
Key Features:
- Basic Self-Evolve mechanism (Generator → Evaluator → Refiner)
- Enhanced Professor-Specialist architecture
- Recursive deep agent hierarchies
- Dynamic function calling for optimal team composition
Production-ready FastAPI + Next.js application for experiencing Crux capabilities.
Key Features:
- RESTful API with async processing (FastAPI + Celery)
- Modern React frontend with real-time updates
- Multi-provider LLM support (OpenAI, OpenRouter, DeepSeek)
- Supabase integration for authentication and persistence
# Clone and setup
git clone https://github.com/your-org/crux.git
cd crux/self-evolve
# Install dependencies
pip install -r requirements.txt
# Set API keys
export OPENAI_API_KEY="your-key-here"
# Run basic example
python -m self-evolve.exampels.example_usage.py
# Run enhanced Professor-Graduate architecture
python -m self-evolve.examples.professor_graduate_example# Navigate to agent directory
cd crux/crux-agent
# Setup backend
pip install -r requirements.txt
cp .env.example .env
# Edit .env with your API keys
# Start services
redis-server # Terminal 1
python worker.py # Terminal 2
uvicorn app.main:app --reload # Terminal 3
# Setup frontend (new terminal)
cd crux-mvp
pnpm install
pnpm devVisit http://localhost:3000 to access the web interface.
- Treats prompts as trainable policy parameters
- Uses natural-language feedback as reward signals
- Achieves optimization through context refinement, not weight updates
🎓 Professor Agent
├── 🔬 Math Specialist → [Sub-specialists...]
├── 🔬 Logic Specialist → [Sub-specialists...]
└── 🔬 Domain Specialist → [Sub-specialists...]
Each specialist can recursively become a professor, creating fractal-like intelligence hierarchies.
- Depth-1: Single agent for simple tasks
- Depth-2: Professor + 3-4 specialists for complex reasoning
- Depth-3+: Recursive hierarchies for research-grade problems
| Metric | Basic Self-Evolve | Enhanced Architecture |
|---|---|---|
| Problem Complexity | Medium | Ultra-High |
| Reasoning Depth | ~100 lines | 9,000+ lines |
| Success Rate | Good | Exceptional |
| Scaling Ability | Limited | Unlimited |
We welcome contributions! Areas of interest:
- Automated specialist discovery algorithms
- Cross-domain transfer learning
- Resource optimization for dynamic teams
- Integration with ML frameworks
See Contributing Guidelines for details.
@misc{tooliense2025crux,
title = {CRUX: Autonomous Mathematical Research through Hierarchical Multi-Agent Orchestration},
author = {Tooliense Team},
year = {2025},
note = {IC-RL Implementation with Self-Evolve Mechanism},
url = {https://github.com/tooliense/crux}
}MIT License. Please respect the terms of your model provider (OpenAI, DeepSeek, etc.).