Hilbert's Entscheidungsproblem

Hilbert's Entscheidungsproblem, posed by mathematician David Hilbert, asked whether there exists a general method to determine whether any mathematical statement about natural numbers is true or false—essentially, a decisive algorithm for all mathematical questions. It aimed to find a systematic way to settle the truth of any statement within a formal system. In the 1930s, Alan Turing and others proved such a universal method cannot exist, showing that some problems are inherently undecidable, meaning no algorithm can resolve all questions about natural numbers.