Researchers have proven, using mathematical techniques and a heavy amount of computing power, that 20 is the maximum number of moves necessary to solve any Rubik’s Cube configuration by the shortest method. This value is known as God’s number. They were able to mathematically reduce the number of unique patterns from 43,252,003,274,489,856,000 to a mere 1,090,175,792,696,524,800 (one quintillion). Then they used something on the order of 35 CPU years of processing to verify that each of the remaining combinations could be solved in 20 moves or less.
Thanks to Josh for this link.