Beautiful Minds

When I sit down to study for math (especially calculus), I feel like I am drowning in so many different types of formulas and rules. However, I hadn’t yet realized how many different contributions to math came from just one person: Leonhard Euler. Euler (pronounced oil-er!) reshaped the way mathematics is studied and applied. Born on April 15, 1707, in Basel, Switzerland, he was a Swiss mathematician who was widely regarded as one of the greatest and most prolific minds in the history of mathematics. 

Euler was impressive with numbers ever since he was a child, and he studied under Johann Bernoulli, an ingenious professor. Even then, Bernoulli noticed Euler’s genius. Euler was already contributing to constructive and new theories in mathematical analysis in his early twenties, and he was suggested to join the St. Petersburg Academy of Sciences in Russia. Euler’s level of citation and achievement in his career was astounding. In 1727, he moved to St. Petersburg, where he soon gained a reputation as a problem-solver of unmatched skill. Later, invited by Frederick the Great, Euler began work at the Berlin Academy, where he spent 25 years writing and publishing a considerable number of books and articles. 

Indeed, the famous function notation “f(x)” was only one of his great innovations. Euler also revolutionized mathematical notation by using e for the natural logarithm base and choosing i to represent the square root of -1. Before him, notation was clumsy and inconsistent. Now, the concise way of communication that he has gifted us makes it easier for us to learn the same math centuries later.

Arguably, his greatest invention, Euler’s famous equation (e^(iπ) + 1 = 0), is more than a shiny exhibit. It ties together exponential functions and rotations in the complex plane, allowing us to make sense of imaginary numbers in graphed planes. Calculus, I have come to know, involves this same vein of mathematics in both power series and complex numbers later on. This type of math is not only fascinating and offers endless possibilities to explore, but it is also very practical in the real world. Engineers, physicists, and computer scientists all rely on it to describe how the world behaves.

Five of the most important numbers in mathematics: e, the base of natural logarithms; i, the unit of imaginary numbers; π, the constant of circles and trigonometry; and the two building blocks of arithmetic, 1 and 0, are all connected in this intricate equation. This very equation connects variables that predict growth in markets to ones that reveal the relationship between growth and rotation. In physics, Euler’s formula explains the behavior of waves and quantum particles. In electrical engineering, it is the reason alternating current can be modeled so precisely. In computer science, it powers algorithms that analyze sound, compress images, and transmit data. In fact, modern electromagnetic wave-dependent devices such as Wi-Fi and smartphones wouldn’t work the same way without this relationship. Hence, Euler’s formula is often called “the most beautiful equation in mathematics.”

Euler’s contributions reach so wide that it’s almost impossible to list them all. What makes him stand out is the way his discoveries continue to shape modern learning. The notation we use every day, the series we test, the functions we expand, and the methods we apply to real problems all carry his fingerprints.

So, while it’s easy to get caught up in the grind of derivatives and integrals, it’s worth remembering that the math you’re learning has a story. Leonhard Euler helped write that story, and it’s one we’re still living in today.

Leonhard Euler. Encyclopaedia Britannica, 16 July 2025, Encyclopaedia Britannica, Inc. Accessed 2 Sept. 2025.

Martin, C. Scipio. “Leonhard Euler (1707–1783) — Biography.” MacTutor History of Mathematics Archive, University of St. Andrews. Accessed 2 Sept. 2025.