We have recently passed the 75th anniversary of one of the most important
results in solar and space physics: Hannes Alfv\'en's discovery of Alfv\'en
waves and the Alfv\'en speed. To celebrate the anniversary, this article
recounts some major episodes in the history of MHD waves. Following an
initially cool reception, Alfv\'en's ideas were propelled into the spotlight by
Fermi's work on cosmic rays, the new mystery of coronal heating and, as
scientific perception of interplanetary space shifted dramatically and the
space race started, detection of Alfv\'en waves in the solar wind. From then
on, interest in MHD waves boomed, laying the foundations for modern remote
observations of MHD waves in the Sun, coronal seismology and some of today's
leading theories of coronal heating and solar wind acceleration. In 1970,
Alfv\'en received the Nobel Prize for his work in MHD, including these
discoveries. The article concludes with some reflection about what the history
implies about the way we do science, especially the advantages and pitfalls of
idealised mathematical models.Comment: 10 pages, accepted by Solar Physic