Mathematics is the study of quantity, structure, space and change. Mathematicians seek out patterns and formulate new conjectures. Conjectures are either proven by a formal mathematical proof or falsified by some counterexample.
Wikipedia on the definition of mathematics
Programmers developed a language which enables them to communicate effectively and at a high level about software and their profession: creating software. It is a small language but very powerful, it is the language of design.  Mathematics, as a language, enables scientists ( astronomers, biologists, chemists, ... ) to talk and think about the patterns in the universe.
Take for example symmetry. Everybody, children included, has some notion of symmetry, i.e. reflection symmetry. When we are confronted with the art of Escher we realize that there is more to symmetry.

Circle Limit II 1959 woodcut in red and black, printed from 2 blocks 
Symmetry is real, it is a physical phenomenon we can observe from the structure of atoms to the spirals of galaxies. Symmetry is more than a property of space it is what defines the structure of everything around us.
But what is quantity, and how we describe it? Here we enter the realm of numbers and number theory. Although, I am seriously fascinated by ( prime ) numbers, we cannot see them anywhere in nature. They are not real and seem inventions by humans. If we ever pickup a signal from outer space that somehow involves prime numbers that would mean that that signal is created by extraterrestrial life.
When you study group theory you will find that there is a deep connection between groups ( i.e. symmetries ) and... prime numbers! Prime numbers are thus part of the signature of the Creator no matter what image you have of that concept.