For one, wouldn’t that mean they have a volume of zero? how does that work?
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A “singularity”, in math, is a discontinuity. It’s a place where the math just doesn’t work–think, dividing by zero.
Presumably you’re talking about black holes. In that case, we can’t describe the singularity directly. Instead, we describe what happens as we *approach* the singularity. If you’ve ever taken any calculus, it’s just a limit–“what’s the behavior as we approach some value?” (EDIT: because I neglected to draw the connection. In the same way dividing by zero is a numerical discontinuity, a black hole singularity is a *topological* discontinuity. )
Our math does really well at explaining what happens almost arbitrarily close to the singularity, in the same way the math works as we divide by a number arbitrarily close to zero. But that specific point is indescribable with our current understanding.
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