I used to think that the Sturm–Liouville theory of second-order ordinary differential
equations was one of the most beautiful areas of mathematics. Its simplicity,
together with the power of the comparison and oscillation theorems, shed a different
light on second-order ordinary differential equations. However, while reading a
transcription of a talk of G.C. Rota, I realized something: there are many interesting
problems, both of theoretical and applied origin, that cannot be analyzed with the
Sturmian tools