The article discusses how the two mathematicians (Spielman and Teng) came up with Smoothed Analysis for Algorithms (as opposed to Worst case) which gives insigh

The article discusses how the two mathematicians (Spielman and Teng) came up with Smoothed Analysis for Algorithms (as opposed to Worst case) which gives insight into why Simplex works well. We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simplex algorithm has polynomial smoothed complexity https://arxiv.org/abs/cs/0111050 https://arxiv.org/abs/cs/0111050 The two authors won the Godel prize in 2008 for this work.