"all NP-complete problems can be converted to one another using a polynomial-time conversion" To a mathematically-challenged reader (like me), this sounds like a line from Star Trek.

In computational complexity theory, P and NP are two classes of problems. P is the class of decision problems that a deterministic Turing machine can solve in polynomial time. In useful terms… ...

NP verification Although NP-complete problems are hard to solve efficiently, once solutions are found, they can be verified trivially.

With NP-complete problems you could discover a fast algorithm to solve Sudoku puzzles that could also break the encryption schemes that protect our digital economy.

Routing and Rerouting Beyond cryptography research, the knapsack problem and its NP complete cousins are everywhere in real life.

Biological molecules that help muscles contract could one day be used to solve intractable problems that traditional supercomputers would take lifetimes to crack, new research finds.