Recently one can observe the increasing popularity of experimental mathematics, namely the use of modern computer programs and equipments in theoretical mathematical research. It is very popular to use such tools in number theory, algebra, analysis, geometry and even topology, to perform calculus manipulations, to test conjectures and visualize results. The authors describe some of the key techniques used in experimental mathematics such as the PSLQ algorithm of \textit{H. R. P. Ferguson} and \textit{D. H. Bailey} and \textit{S. Arno} [Math. Comput. 68, 351--369 (1999; Zbl 0927.11055)] and arbitrary digit calculation formulas. They give several interesting examples of experimental mathematics and discuss its implications. The most important is that there are many mathematical truths that they have no good reasons in traditional rational sense and ``computer experiments can provide precisely the sort of evidence that is required''. The paper is must-read for anyone who wants to use computers in pure mathematical research.