# Why Mathematics Needs Imagination

By Vic Odarve

For many students, Math is described as a difficult course and only a few are interested; that is why imagination helps to understand, appreciate, and challenge how this course works. Unknown to many, imagination keeps various mathematical equations and formulas stay in our minds; keeping us to understand how it works in real worlds and of course, their limitations. As Mother Nature expresses her beauty through mathematics, from Newton’s law of motion and Kepler’s laws in revolving planets, imagination keeps us appreciate the beauty and grandeur of our planet and the universe we live in. And a lot more, our imagination would keep us challenged to investigate math secrets and its function in the mysteries the universe has. Understanding math is more like doing an imaginative play than anything else!

Mathematics brings anxiety and stress to students

Math consists of interwoven equations and formulas, and imagination would keep the students considering how math works in tangible worlds. Imagination adds our knowledge in quantum and cosmic worlds because variables or quantities involve in the math equations, develop only in modern science labs and scientific experiments which are often out in our real senses. In quantum mechanics, for instance, particles behave differently from the classical mechanics. In cosmic science, some mathematical formulas and equations developed from years of observation in various astronomical phenomena like an event horizon, a quantum singularity, the expanding universe, the uncertainty principle and many others. But Einstein’s equations, where time is not constant, and his conversion ratio between matter and energy, are clearly a result in imagination. Prediction formulas, too, which are the product of probability and statistics, also come from imagination. Hence, imagination helps us going to get deep into equations with mathematical relationships between different things.

There is no ugly mathematics. Math is always beautiful.

There is no ugly mathematics. Math is always beautiful. The beauty of math can be further appreciated by imagination. Mother Nature teaches us math; from the plant leaves to the cloud formations and the intricate webs of heavenly bodies stretching into the cosmic ocean are mathematical wonders. Beautiful and intricate applications of mathematics are illustrated in the complexities of our natural world such as the golden ratio, Fibonacci sequence, fractals and the honeycomb conjecture. The simple twig of a tree is a fragmented geometric shape, look like the branches which they grow on, which look like the tree itself—a math beautiful expression! Another one is a hexagonal shaped honey combs created by the bee, it is geometry in action. And these are all around us. Mathematical equations give us understanding Mother Nature’s mind and discover how the laws of physics are working. The existence of these laws keeps us appreciate the beauty of understanding mathematics.

Beautiful monuments and natural landscapes are the expression of  mathematics

And much more, imagination would keep us challenged to investigate math further; unlocks some of the secrets and discover the things we don’t yet understand. Some mathematical laws discovered are so strange that keep our mind-boggling and expanding. Through imagination, we are just like playing equations in our mind and think how it works in different circumstances and challenge to solve some of the mathematical problems. Newton and Leibnitz, for example, imagined how to solve areas of figures bounded by several curves, developed integral calculus; Laplace developed the method for solving differential equation; and probability and statistics for gambling or game of chance.

For math-intensive career like engineering, it is through the imagination that students can play around various math equations and formulas. Imagination is a driving force that leads to many inventions and innovations and what brought us to our present state of civilization. Math is not math until it is understood, appreciated, and challenged. And it needs imagination!

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