"The Revolutionary Mindset of Alan Turing: Harnessing the Power of Negative Thinking"

Alan Turing, the pioneering computer scientist, proved the existence of "uncomputable" problems using a counterintuitive strategy called diagonalization. Diagonalization is a mathematical technique that builds up a missing string bit by bit, ensuring that the new string differs from every string on the original list. Turing used this technique to construct an obstinate problem that would thwart every algorithm on an infinite list of possible algorithms. While diagonalization has its limitations, it remains a key tool in complexity theorists' arsenal and has been used to make significant progress in understanding computational complexity.