Computers Might Never Be Able To Solve These Three Problems
An "undecidable" problem in computer science is one that requires a yes or no answer, but that is impossible for any known computer to reliably solve. Three of these problems are the halting problem, Kolmogorov complexity, and the Wang tile problem. The halting problem refers to whether a computer can determine if a program will ever finish running, whereas Kolmogorov complexity deals with compression, and the impossibility of perfectly compressing any given file. Wang tiles are square tiles with a color on each side. Infinitely placing them next to each other so that the colors of each side match the colors on the adjacent squares is called "tiling the plane," and there is currently no computer that can predict whether a given set of Wang tiles will tile the plane.
Key Facts In This Video
The halting problems states that no computer can always determine if a program will continue to run or eventually stop. (0:32)
Thus far, no program can perfectly compress any given file due to Kolmogorov complexity. (1:23)
There can be no method that can take any given set of Wang tiles and tell you whether or not it will tile the plane. (2:05)