The math problem that was proven impossible to ever solve in general
In 1900, David Hilbert asked for a single algorithm that could look at any polynomial equation with integer coefficients and correctly say, in a finite number of steps, whether it has a solution in whole numbers. Does such an algorithm exist?
Reveal the answer
No -- and this was proved, not just left unsolved. Working across four decades, Martin Davis, Hilary Putnam, and Julia Robinson built the key tools, and Yuri Matiyasevich completed the proof in 1970: no such general algorithm can ever exist, for any computer, however powerful. It's one of the few of Hilbert's 23 famous problems answered with a firm impossibility rather than a solution.
— David Hilbert; solved by Yuri Matiyasevich, Hilbert's tenth problem — posed 1900, resolved 1970