The anatomy of the mammalian hearing apparatus will be described, followed by details of the microanatomy of the cochlea. Indications will be given of the actual size of the structures involved. The generally accepted theory of transmission and transduction of the acoustic signal will be recounted; then observational and experimental data providing difficulties in accepting current teaching will be explained. An alternative explanation will be offered in brief outline and areas where mathematical contributions to the understanding of wave motion and energy will be suggested.