The term mathematics itself means “study, learning, and knowledge” and specifically refers to the topics of space, numbers, quality, structure, and change. Until around 1700 the term was commonly used to mean “astrology” as opposed to mathematics, however over time between 1500 and 1800 the definition changed into what is commonly known as mathematics today. This earlier confused translation lead to some not trusting mathematicians as they thought of them as fortune tellers.
Mathematical proofs resolve the truth of conjectures as well as formulate and predict new conjectures. Math creates structures of real phenomena in order to offer insight, understanding and assist in predicting structures in the natural world. Natural objects can be better understood using abstract logic that is born from measurement, counting, calculation, and the study of shapes and motion. Mathematics has existed as long as there has been written records and the research required to solve problems can take centuries.
The view of mathematical research is that it establishes truth through rigorous deduction from certain specific definitions and axioms. Mathematics progressed at a slow pace until the Renaissance where it began to intersect and work in concert with other schools of science and scientific discoveries. Once it joined these other institutions mathematical discoveries rapidly increased until today. Even now mathematics is growing in leaps and bounds as it develops alongside new ideas such as string theory and the idea of a multiverse.
Galileo Galilei was the first to say that the language of the universe was mathematics. He said, “The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth”. Galileo was clearly trying to impress on everyone that mathematics is much more than an interesting scientific diversion but the key to the door of understanding everything, and in this he was not alone. David Hilbert said, “Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise.” This suggests that mathematics is an absolute science to be differentiated from other more interpretive disciplines.
Without mathematics many other scientific fields would be impossible. These fields include social science, medicine, engineering, finance, natural science, and more. Statistics and game theory not only require mathematics but were born from the studying of it. Math is often studied for its own sake as opposed for a specific application many new ideas and even schools of thought may be discovered through it. So while math is fun, without it we would understand very little of the world we live in.