Mathematics is Not Science or Art, But like the Both
Mathematics is not science. Science seeks to understand some aspect of phenomena from empirical observations, while math seeks to use logic to understand and often prove relationships between quantities and objects which may not relate to any real phenomena. Scientific theories may be supported by evidence from observations, but not proven, while we can actually prove things in math.
On the other hand, mathematics is like science. For example, in number theory, we gather data by computing a lot of examples. Then we search for a pattern, make a hypothesis, and test it against additional data. If the hypothesis doesn’t match the new data, we revise it. After some iterations, when new data matches our hypothesis, we finally try to prove the hypothesis.
What about Statistics?
Statistics seeks to understand and process information/data. It is a branch of applied mathematics, and is ultimately judged by how well it serves the world of applications. In the 250+ years of Statistics, it has been subtly changed from application focused to mathematically logical and computationally heavy. But the center of the field maintains the philosophical cohesion.
“Mathematics” here is shorthand for the mathematical/logical justification of statistical methods. “Computation” stands for the empirical/numerical approach.
Reference: Bradley Efron, Trevor Hastie 2016. Computer Age Statistical Inference.