Exponential Time Hypothesis

The Exponential Time Hypothesis says that for a famous kind of puzzle, called SAT (finding values that make a logical statement true), there is no clever shortcut. In the worst case, the time needed roughly doubles with every extra variable, which becomes impossible very quickly.

Nobody has proven it, but hundreds of research papers assume it is true and build on it. If someone really disproved it, those papers would lose a foundation, even though their results might still be right.