Hello, I am new here and this is my first post. Kindly let me know if my post is off topic. My question is about the applicability of singularities of a function in Physics. By singularity I mean one of the higher derivatives (>2) of a function jumping at a point. Is there any conceptual use of such singularities in a physical theory. Could they be used to represent the subatomic particles. Can this be helpful for a unified theory (of large and small scale)? I'd be glad to hear some discussion on it.