It is high time we let go of the Mersenne Twister

When the Mersenne Twister made his first appearance in 1997 it was a powerful example of how linear maps on $\mathbf F_2$ could be used to generate pseudorandom numbers. In particular, the easiness with which generators with long periods could be defined gave the Mersenne Twister a large following, in spite of the fact that such long periods are not a measure of quality, and they require a large amount of memory. Even at the time of its publication, several defects of the Mersenne Twister were predictable, but they were somewhat obscured by other interesting properties. Today the Mersenne Twister is the default generator in C compilers, the Python language, the Maple mathematical computation system, and in many other environments. Nonetheless, knowledge accumulated in the last $20$ years suggests that the Mersenne Twister has, in fact, severe defects, and should never be used as a general-purpose pseudorandom number generator. Many of these results are folklore, or are scattered through very specialized literature. This paper surveys these results for the non-specialist, providing new, simple, understandable examples, and it is intended as a guide for the final user, or for language implementors, so that they can take an informed decision about whether to use the Mersenne Twister or not.