Explaining computational complexity theory

Question

Assuming some background in mathematics, how would you give a general overview of computational complexity theory to the naive?

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Answer 1

Here are a few links on the subject:

• Clay Mathematics statement of P vp NP problem
• P vs NP Page
• P, NP, and Mathematics

In you are familiar with the idea of set cardinality, that is the number of elements in a set, then one could view the question like P representing the cardinality of Integer numbers while NP is a mystery: Is it the same or is it larger like the cardinality of all Real numbers?