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import sys
from swarms import Agent, ConcurrentWorkflow
import os
import pathlib
from pathlib import Path
from dotenv import load_dotenv
import asyncio
import json
from datetime import datetime
import math
load_dotenv()
sys.path.insert(0, str(Path(__file__).parent))
def create_riemann_hypothesis_agents():
"""Create specialized agents for Riemann Hypothesis proof."""
# Agent 1: Mathematical Analysis Agent
math_analysis_agent = Agent(
agent_name="Riemann-Math-Analysis-Agent",
system_prompt="""You are a specialized mathematical analysis agent focused on the Riemann Hypothesis. Your mission is to:
1. **Understand the Riemann Hypothesis**: ζ(s) = 0 has non-trivial zeros only at s = 1/2 + it for real t
2. **Analyze the Zeta Function**: ζ(s) = Σ(n=1 to ∞) 1/n^s for Re(s) > 1
3. **Calculate Critical Values**: Use MCP tools to compute ζ(1/2 + it) for various t values
4. **Verify Zeros**: Check if ζ(1/2 + it) = 0 for specific t values
5. **Analyze Patterns**: Look for patterns in the distribution of zeros
CRITICAL: You MUST use MCP tools for all mathematical calculations. Focus on:
- Computing ζ function values
- Analyzing the critical line Re(s) = 1/2
- Checking for non-trivial zeros
- Statistical analysis of zero distributions
Use precise mathematical reasoning and provide detailed analysis of each calculation.""",
model_name="gpt-4o-mini",
streaming_on=True,
print_on=True,
max_loops=10,
error_handling="continue",
tool_choice="auto",
verbose=True,
mcp_url="stdio://examples/mcp/working_mcp_server.py",
)
# Agent 2: Computational Verification Agent
computational_agent = Agent(
agent_name="Riemann-Computational-Agent",
system_prompt="""You are a computational verification agent for the Riemann Hypothesis. Your mission is to:
1. **Numerical Verification**: Use MCP tools to compute ζ function values numerically
2. **Zero Detection**: Identify when ζ(s) ≈ 0 within computational precision
3. **Critical Line Analysis**: Focus on s = 1/2 + it values
4. **Statistical Testing**: Analyze the distribution of computed zeros
5. **Error Analysis**: Assess computational accuracy and error bounds
CRITICAL: You MUST use MCP tools for all computations. Focus on:
- High-precision calculations
- Error estimation
- Statistical analysis of results
- Verification of known zeros
- Discovery of new patterns
Provide detailed computational analysis with error bounds and confidence intervals.""",
model_name="gpt-4o-mini",
streaming_on=True,
print_on=True,
max_loops=10,
error_handling="continue",
tool_choice="auto",
verbose=True,
mcp_url="stdio://examples/mcp/working_mcp_server.py",
)
# Agent 3: Proof Strategy Agent
proof_strategy_agent = Agent(
agent_name="Riemann-Proof-Strategy-Agent",
system_prompt="""You are a mathematical proof strategy agent for the Riemann Hypothesis. Your mission is to:
1. **Proof Strategy Development**: Develop systematic approaches to prove RH
2. **Analytic Continuation**: Analyze ζ(s) beyond Re(s) > 1
3. **Functional Equation**: Use ζ(s) = 2^s π^(s-1) sin(πs/2) Γ(1-s) ζ(1-s)
4. **Zero-Free Regions**: Identify regions where ζ(s) ≠ 0
5. **Contradiction Methods**: Use proof by contradiction approaches
CRITICAL: You MUST use MCP tools for all mathematical operations. Focus on:
- Functional equation analysis
- Contour integration methods
- Analytic number theory techniques
- Complex analysis applications
- Proof strategy validation
Develop rigorous mathematical arguments and validate each step computationally.""",
model_name="gpt-4o-mini",
streaming_on=True,
print_on=True,
max_loops=10,
error_handling="continue",
tool_choice="auto",
verbose=True,
mcp_url="stdio://examples/mcp/working_mcp_server.py",
)
# Agent 4: Historical Analysis Agent
historical_agent = Agent(
agent_name="Riemann-Historical-Analysis-Agent",
system_prompt="""You are a historical analysis agent for the Riemann Hypothesis. Your mission is to:
1. **Historical Context**: Analyze previous attempts to prove RH
2. **Known Results**: Review verified properties of ζ function
3. **Computational History**: Study previous numerical verifications
4. **Failed Approaches**: Learn from unsuccessful proof attempts
5. **Modern Techniques**: Apply contemporary mathematical methods
CRITICAL: You MUST use MCP tools for all calculations. Focus on:
- Historical verification of known results
- Analysis of previous computational efforts
- Statistical analysis of historical data
- Pattern recognition across different approaches
- Synthesis of historical insights
Provide comprehensive analysis of historical context and its relevance to current proof attempts.""",
model_name="gpt-4o-mini",
streaming_on=True,
print_on=True,
max_loops=10,
error_handling="continue",
tool_choice="auto",
verbose=True,
mcp_url="stdio://examples/mcp/working_mcp_server.py",
)
return [math_analysis_agent, computational_agent, proof_strategy_agent, historical_agent]
def create_riemann_workflow():
"""Create a comprehensive Riemann Hypothesis workflow."""
# Create the specialized agents
agents = create_riemann_hypothesis_agents()
# Create concurrent workflow
workflow = ConcurrentWorkflow(
name="Riemann-Hypothesis-Proof-Attempt",
agents=agents,
show_dashboard=True,
auto_save=True,
output_type="dict",
max_loops=5,
auto_generate_prompts=False,
)
return workflow
def riemann_hypothesis_proof_attempt():
"""Main function to attempt Riemann Hypothesis proof."""
print(" RIEMANN HYPOTHESIS PROOF ATTEMPT")
print("=" * 80)
print("Mission: Calculate and prove the Riemann Hypothesis")
print("Hypothesis: All non-trivial zeros of ζ(s) have Re(s) = 1/2")
print("=" * 80)
# Create workflow
workflow = create_riemann_workflow()
# Comprehensive Riemann Hypothesis task
riemann_task = """
MATHEMATICAL MISSION: PROVE THE RIEMANN HYPOTHESIS
The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function ζ(s)
have real part equal to 1/2. This is one of the most important unsolved problems in mathematics.
TASK BREAKDOWN:
1. **Riemann-Math-Analysis-Agent**:
- Define and analyze the Riemann zeta function ζ(s) = Σ(n=1 to ∞) 1/n^s
- Understand the critical line Re(s) = 1/2
- Analyze the functional equation: ζ(s) = 2^s π^(s-1) sin(πs/2) Γ(1-s) ζ(1-s)
- Use MCP tools to compute ζ function values
- Identify patterns in zero distribution
2. **Riemann-Computational-Agent**:
- Perform high-precision numerical calculations of ζ(1/2 + it)
- Verify known zeros (first few: t ≈ 14.1347, 21.0220, 25.0109, 30.4249, 32.9351)
- Compute ζ function values for various t values
- Analyze statistical distribution of computed values
- Provide error analysis and confidence intervals
3. **Riemann-Proof-Strategy-Agent**:
- Develop systematic proof strategies
- Use analytic continuation techniques
- Apply complex analysis methods
- Explore proof by contradiction approaches
- Validate each mathematical step computationally
4. **Riemann-Historical-Analysis-Agent**:
- Review historical attempts and known results
- Analyze computational verification history
- Study failed proof approaches
- Apply modern mathematical techniques
- Synthesize historical insights with current methods
MATHEMATICAL REQUIREMENTS:
- Use MCP tools for ALL calculations
- Provide rigorous mathematical reasoning
- Include error analysis and confidence intervals
- Verify each step computationally
- Document all assumptions and limitations
EXPECTED DELIVERABLES:
- Comprehensive analysis of ζ function behavior
- Numerical verification of known zeros
- Statistical analysis of zero distribution
- Proof strategy development
- Historical context and insights
- Computational evidence supporting or refuting RH
CRITICAL: This is an attempt to contribute to one of mathematics' greatest unsolved problems.
Provide thorough, rigorous analysis with full computational validation.
"""
print(" Executing Riemann Hypothesis Proof Attempt...")
print("=" * 80)
# Execute the workflow
results = workflow.run(riemann_task)
print("\n" + "=" * 80)
print("Riemann Hypothesis Proof Attempt Complete!")
print("=" * 80)
# Display results
if isinstance(results, dict):
for agent_name, result in results.items():
print(f"\n {agent_name}:")
if isinstance(result, str):
print(f" Result: {result[:500]}...")
else:
print(f" Result: {str(result)[:500]}...")
print("-" * 60)
elif isinstance(results, list):
for i, result in enumerate(results):
print(f"\n Agent {i+1}:")
if isinstance(result, str):
print(f" Result: {result[:500]}...")
else:
print(f" Result: {str(result)[:500]}...")
print("-" * 60)
else:
print(f"\n Results: {results}")
return results
def test_individual_riemann_agent():
"""Test a single Riemann Hypothesis agent."""
print(" Testing Individual Riemann Hypothesis Agent...")
print("=" * 80)
# Create a single agent for focused analysis
riemann_agent = Agent(
agent_name="Riemann-Single-Analysis-Agent",
system_prompt="""You are a specialized Riemann Hypothesis analysis agent. Your mission is to:
1. **Define the Problem**: ζ(s) = Σ(n=1 to ∞) 1/n^s, find all s where ζ(s) = 0
2. **Critical Line Focus**: Analyze s = 1/2 + it (the critical line)
3. **Numerical Verification**: Use MCP tools to compute ζ(1/2 + it) values
4. **Zero Detection**: Identify when |ζ(1/2 + it)| ≈ 0
5. **Statistical Analysis**: Analyze patterns in zero distribution
CRITICAL: You MUST use the specific mathematical MCP tools for ALL calculations:
- Use 'compute_zeta' tool to calculate ζ function values (NOT the calculate tool)
- Use 'find_zeta_zeros' tool to search for zeros of the zeta function
- Use 'complex_math' tool for complex number operations
- Use 'statistical_analysis' tool for data analysis
DO NOT use the simple 'calculate' tool. Use the specialized mathematical tools.
Focus on:
- Computing ζ function values numerically using compute_zeta
- Analyzing the first few known zeros using find_zeta_zeros
- Statistical analysis of results using statistical_analysis
- Error estimation and confidence intervals
- Pattern recognition in zero distribution
Provide detailed mathematical analysis with full computational validation using the proper mathematical tools.""",
model_name="gpt-4o-mini",
streaming_on=True,
print_on=True,
max_loops=8,
error_handling="continue",
tool_choice="auto",
verbose=True,
mcp_url="stdio://examples/mcp/working_mcp_server.py",
)
# Test task focused on Riemann Hypothesis
test_task = """
RIEMANN HYPOTHESIS ANALYSIS TASK:
The Riemann Hypothesis states that all non-trivial zeros of ζ(s) have Re(s) = 1/2.
CRITICAL INSTRUCTIONS: You MUST use the EXACT mathematical MCP tools listed below:
TOOL 1: compute_zeta
- Purpose: Calculate Riemann zeta function values
- Parameters: real_part (number), imaginary_part (number), precision (integer)
- Example: compute_zeta with real_part=0.5, imaginary_part=14.1347, precision=1000
TOOL 2: find_zeta_zeros
- Purpose: Find zeros of the zeta function
- Parameters: start_t (number), end_t (number), step_size (number), tolerance (number)
- Example: find_zeta_zeros with start_t=0.0, end_t=50.0, step_size=0.1, tolerance=0.001
TOOL 3: complex_math
- Purpose: Perform complex mathematical operations
- Parameters: operation (string), real1 (number), imag1 (number)
- Example: complex_math with operation="exp", real1=0.0, imag1=3.14159
TOOL 4: statistical_analysis
- Purpose: Analyze data statistically
- Parameters: data (array), analysis_type (string)
- Example: statistical_analysis with data=[1,2,3,4,5], analysis_type="descriptive"
DO NOT use the 'calculate' tool. Use ONLY the tools listed above.
REQUIRED ACTIONS (execute these in order):
1. Use compute_zeta tool to calculate ζ(1/2 + 14.1347i)
2. Use compute_zeta tool to calculate ζ(1/2 + 21.0220i)
3. Use compute_zeta tool to calculate ζ(1/2 + 25.0109i)
4. Use find_zeta_zeros tool to search for zeros in range [0, 50]
5. Use statistical_analysis tool to analyze the results
Execute these actions using the EXACT tool names and parameters shown above.
"""
print(" Executing Riemann Hypothesis Analysis...")
result = riemann_agent.run(test_task)
print("\n" + "=" * 80)
print(" Individual Riemann Agent Test Complete!")
print("=" * 80)
print(f" Result: {result}")
return result
def riemann_hypothesis_main():
"""Main function to run the Riemann Hypothesis proof attempt."""
print(" RIEMANN HYPOTHESIS PROOF ATTEMPT")
print("=" * 80)
print("This is an attempt to contribute to one of mathematics' greatest unsolved problems.")
print("The Riemann Hypothesis: All non-trivial zeros of ζ(s) have Re(s) = 1/2")
print("=" * 80)
try:
# Test individual agent first
print("\n1️ Testing Individual Riemann Agent...")
individual_result = test_individual_riemann_agent()
# Then test the full workflow
print("\n2️ Testing Full Riemann Hypothesis Workflow...")
workflow_results = riemann_hypothesis_proof_attempt()
# Summary
print("\n" + "=" * 80)
print(" Riemann Hypothesis Proof Attempt Summary")
print("=" * 80)
print(" Individual Agent Test: COMPLETED")
print(" Full Workflow Test: COMPLETED")
print(" Mathematical Analysis: PERFORMED")
print(" Computational Verification: EXECUTED")
print(" Proof Strategy: DEVELOPED")
print(" Historical Analysis: CONDUCTED")
print("=" * 80)
print(" Note: This is a computational exploration of the Riemann Hypothesis.")
print(" The actual proof remains one of mathematics' greatest challenges.")
print("=" * 80)
return {
"individual_result": str(individual_result) if individual_result else "No result",
"workflow_results": str(workflow_results) if workflow_results else "No results",
"status": "COMPLETED",
"timestamp": datetime.now().isoformat(),
"mathematical_mission": "Riemann Hypothesis Analysis",
"note": "This is a computational exploration, not a formal proof"
}
except Exception as e:
print(f"\n Error during Riemann Hypothesis analysis: {e}")
import traceback
print(f"Full traceback: {traceback.format_exc()}")
return {
"error": str(e),
"status": "FAILED",
"timestamp": datetime.now().isoformat(),
"mathematical_mission": "Riemann Hypothesis Analysis"
}
if __name__ == "__main__":
result = riemann_hypothesis_main()
print(f"\n Final Results: {json.dumps(result, indent=2)}")
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