Abstract The progress in magneto-hydrodynamics has mainly been a result of the theoretical investigations. Mathematical methods are, and will always be, one of the most important means of exploring this interesting but extremely complicated field. But this should not obscure the fact that the field must also be explored by experimental and observational methods. Even if we know the physical foundations of a certain field of research quite well, it is often impossible to explore it by mathematical methods alone, however powerful these methods are. For example, the foundations of ordinary hydrodynamics are quite simple, but it is not possible to derive from them a picture of the turbulence by mathematical methods alone. The field has been explored by experimental methods to at least the same extent as by mathematical methods, and it would not have been possible to find the structure of a turbulent state by starting from the hydrodynamic equations.