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)}")