Mathematics is a type of science that helps facts about nature be described, discovered, determined, measured, predicted, and controlled. Mathematics is a tool for training young minds how to think logically. Math is a way to understand what is seen and to envision the unseen, even predicting what may exist, and how it might behave before it is scientifically proven.
For example, theoretical physicists develop complex mathematical equations to describe and predict yet unknown realities, while experimental physicists apply the scientific method to design and conduct experiments to test whether the theoretical physicists’ hypotheses were correct. Albert Einstein and Niels Bohr were theoretical physicists who relied on math to discover reality at the quantum level. It took decades for advanced technologies to catch up so the principles of quantum mechanics could be tested by experimental physicists to determine whether they were true, and they were true. Our cell phones couldn’t have been developed without the realities of the quantum world. Math describes reality.
Mathematics, like music, is a universal language. Languages have an alphabet of letters for writing down words. We write sentences and paragraphs to convey ideas and stories. Mathematics uses combinations of symbols, letters, and numbers to make mathematical words, sentences, and paragraphs for conveying ideas and stories. Symbols convey actions (plus and minus signs, for example) for mathematical operations. Terms show relationships between objects (distance per time, or miles driven per gasoline used) to describe or represent conditions. A string of terms describes multiple relationships that exist within a system, so we can study the whole system.
With each field of mathematics, we learn more of its language. During K-12, we learn arithmetic to understand how math operates at its most basic level (+ – x ÷), how to measure lengths and volumes, and calculate portions of those lengths and volumes as fractions. We learn how to square and raise the power of a number with exponents. We learn geometry to study relationships between points, lines, shapes and dimensions; algebra to work with general relationships that can be applied to specific conditions and situations; trigonometry to understand relationships between a triangle’s points, angles and lines to determine, for example, the right pitch for a roof, distance to the sun, and the heights of the tallest mountains, to analyze waves, frequencies and oscillations, as with sound, light, and ocean waves, and even where your position is on the Earth; and calculus to describe and predict how fast and by how much conditions and situations move and change.
Rigor and complexity increase in college to learn how to apply more advanced mathematics to real-world problems industries face. To describe components of systems under analysis, statistical modeling takes into account variables, factors, and facts, every conceivable interaction and complex relationship that must be included in the terms of mathematical equations to give insight and better understand, determine, predict, manage, and/or help control large systems. Mathematics helps industries solve problems, such as finding fractal geometry equations that describe patterns in nature (to make flames in movies look more real), developing artificial intelligence, revealing more facts about dark energy and dark matter to understand what we cannot see or directly detect in the cosmos, and even predicting the course of pandemics and determine best ways to control them to help reduce casualties.
Mathematics aids every scientific discipline, and in some cases, directs the show. Mathematics provides structure for the mind to process information logically and rationally, and it helps us see reality more clearly. Mathematical ‘stories’ start out as mysteries that need to be solved. Understanding how to write and solve mathematical stories is essential for finding answers about every aspect of the Universe, including us.