In 1981 David Singmaster published "Notes on Rubik's 'Magic Cube'", which is one of the first mathematical articles about the Rubik's Cube. In this paper he defines a notation to denote the basic operations F, U, R, L, B, D. He also describes a method of solving the cube, known as Singmasters (Layer by Layer) method, which is still very popular and intuitive for beginners. This method begins to solve an outer layer, followed by the middle layer, and then the final and bottom layer is to be solved. This can easily be done in less than 3 minutes for any experienced solver. There are many improvements for the layer-by-layer method, so the cube can be solved in fewer moves and thus fewer time. Ofcourse, all these improvements are more difficult as they require more algorithms to be memorized. For instance, Fridrich's solution requires learning roughly 120 algorithms but allows the Cube to be solved in only 55 moves on average.
For as long as God's Number was undetermined, we could still give a lower- and upper bound for it. In 1982, David Singmaster and Alexander Frey hypothesised that the number of moves needed to solve the Rubik's Cube, given an ideal algorithm, might be in "the low twenties". In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3*3*3 Rubik's Cube configuration can be solved in 26 moves or less. In 2008, Tomas Rokicki lowered that number to 22 moves, and in July 2010, a team of researchers including Rokicki, working with Google, proved the so-called "God's number" to be 20. This is optimal, since there exist some starting positions which require at least 20 moves to solve.