The greatest unsolved problem in computer science...

TL;DR

P vs NP asks whether problems easy to verify are also easy to solve — and no one has proven it in 50 years.

Key Points

• 1.P (Polynomial time) = problems a computer solves efficiently as input grows (e.g., sorting a list scales ~10–20x when input grows 10x); NP = problems whose solutions can be *verified* quickly but may take until the heat death of the universe to *find* (e.g., factoring 69,420 into primes)
• 2.The Traveling Salesman Problem illustrates NP perfectly: finding the shortest route through 15 cities requires checking ~87 billion possibilities, yet handing someone the answer to verify takes seconds
• 3.NP-Complete problems (first defined by Steven Cook in 1971 with the Boolean Satisfiability problem) are the hardest class — solving *any one* in polynomial time would instantly solve *all* of them, meaning P = NP
• 4.If P = NP, every encryption key, password, and crypto wallet becomes instantly crackable; it would also theoretically accelerate drug discovery and resource optimization — the Clay Mathematics Institute offers $1 million to anyone who proves it either way