“Euler’s Identity is the most beautiful math equation!”

– literally every single math professor

Euler’s identity is often regarded as “the most beautiful math equation” because of its foundational role in mathematics. It relates to many aspects of math, such as trigonometry, imaginary numbers, natural logs, etc. In a very simple and concise equation, Euler’s identity ties together many different mathematical concepts. Each one of the symbols and numbers represents a fundamental idea in math. For instance, ‘0’ is a unique and only number that represents Null or None out of all the different mathematical expressions. ‘1’ is precisely the complete opposite of 0, and all numbers is a summation of ones. ‘e’ is a unique constant that often describes many natural phenomenons. ‘i’ is the definition and stem of imaginary/complex numbers, an entirely different system of irrational numbers. ‘pi’ is the constant that is almost guaranteed to appear when dealing with rotations and waves, such as circles, spheres, traveling waves. Euler’s Identity, outside of its theoretical significance, also is a useful tool in many different disciplines; It is useful in electrical engineering, quantum physics, multivariable calculus, physics, etc.

Nonetheless, it is interesting how one equation can be used to describe many things in nature. Many different theories, disciplines, and reasoning all somehow lead to this one equation. Aesthetics is defined as “a set of principles concerned with the nature and appreciation of beauty, especially in art.” Euler’s Identity, despite its somewhat confusing mathematical representation, might be an indication that the creation of our world isn’t entirely based on chance. Perhaps, this is the beauty of math; It connects our fragmented knowledge into a cohesive understanding. Perhaps, math is just another tool for us to realize the beauty and order of nature. On this note, maybe math isn’t so different from art. This sparks a series of questions: What makes math and art different and similar? Does math has its limits? What is the end goal of scientific studies? Is it be possible that there is an unknown principle law, analogous to Euler’s Identity in math, that governs our life?