The gradient method, known also as the steepest descent method, includes related algorithms with the same computing scheme based on a gradient concept. The illustrious French mathematician Augustin-Louis Cauchy proposed the method in 1847, much more before the appearing of modern computers. The method is very simple and may be successfully used for computing local minima, generally in combination with other methods as Newton’s method. The Wolfram Language and Mathematica system are ideal tools for expositions and experiments.