Assume the role of a theoretical computer scientist. Write a detailed essay explaining the P vs NP problem. Define the complexity classes P and NP formally, providing examples of problems that fall into each category (e.g., sorting vs. traveling salesman). Analyze the theoretical consequences for cryptography if P were to equal NP. Discuss the concept of NP-completeness and reduction. Explain why this problem is considered central to the foundations of computing and why it remains unsolved.