What is the difference between Newtonian Mechanics and Relativity
Newtonian mathematics is deterministic, as in, everything that is or will happen can be calculated if you know what did happen and is happening now.
Relativity is not deterministic and operates under the principles of statistics and probability. It accounts for the seemingly random movements of particles. The Heisenberg uncertainty principle is a staple of such thought, and it states that you cannot know certain pairs of physical proprerties (like position and momentum) simultanesouly.
Realitivty accounts for uncertainty; in Newtonian mathematics, everything is certain.
On macro scales Newtonian mathematics works fine, on micro scales it falls apart. The atomic level is defined by relativty, yet, together this uncertainty creates a quite predictable macro scale.
Some believe that this "uncertainty" does not exist at all, and it is merely our limitations in understanding that make it appear that way.