Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating".
The usual definition in Physics describes it just as a source whose dimensions are negligible in comparison to another variable you're relating it to, which leads to well-behaved phenomena such as isotropic emission.
Well, if there's something I wouldn't expect from a singularity, that's well-behaving. Given that, how does that math definition of point source makes sense? How to phenomenologically relate it, lucidly, it with physics?