Abstract: One problem in classical Geometric Optics of studying "wavefronts" of a wave on an ambient space, which was addressed by Somigliana in 1919, is the starting point of a remarkable study of the so-called "isoparametric hypersurface" and their generalizations. The wavefronts in that problem are required to be "stationary" and "equidistant to each other", as an example of an "isoparametric foliation". Since its beginnings with the works of Somigliana, Levi-Civita, Segre, and Cartan, the theory of isoparametric foliations has been a fruitful area of research in differential geometry. In this talk, we will discuss the classification of isoparametric foliations on \(\mathbb{CP}^n\) based on the classification on spheres, an outstanding problem that has been investigated and contributed by many mathematicians.