Can everything be explained by using mathematics?

Answer 1

No. The structure of the physical universe, and the events that occur there, can be defined or approximated by various mathematical formulas (see also algorithm). However, the actual state or operation of an given thing is subject to enormously complex variables which interact in a very large number of ways. So while mathematics easily explains that putting one apple and another apple into a box will yield a box with two apples, it cannot completely explain all the steps that occurred before and after the two apples were placed together. A good example of the complexity of the real world is in weather forecasting, where complex mathematical models will approximate the actual progression of weather systems. Very seldom are these forecasts perfectly and consistently correct. Metaphysics, spirituality, psychology and similar fields will occasionally use math to create models for non-physical situations.