Radioactive decay is random and our math cannot handle it at the most basic level, the individual nucleus.
That's probably a matter of technology and physics and theories, not of math. It's not like math can't get small enough or something: it can get infinitely small!
In general, regarding randomness, I think that randomness = ignorance. If I flip a coin and say that the result of the flip will be random, what I mean is that I personally can't predict the result. But surely if we knew all environmental conditions down to the atom, we'd be able to predict it. So saying "X is random" is saying "at the moment, I don't know what causes X".
If there is actual non-deterministic randomness in the universe (uncaused causes) then I don't think we can really understand what that means or how it could be. Everything we know in our life can be traced back to earlier causes. The concept of something that literally happens for no reason I think completely escapes us. The question "why did it happen rather than not happen?" will forever taunt us.
I was reading an article last night that might interest you, kinda similar to yours in general theme but different in content: https://blog.usejournal.com/has-physics-gone-astray-60cfca8ad62c