Leonhard Euler

Born: 1707
Died: 1783
Title: King of Mathematics / Embodiment of Analysis

"Read Euler, read Euler, he is the master of us all." — Pierre-Simon Laplace

The Man Who Taught Humanity How to Write Mathematics

After Newton and Leibniz invented calculus—the "dragon-slaying sword"—mathematicians began using it to harvest results. Throughout the 18th century, there was almost only one protagonist whose brilliance overshadowed everyone else.

If Newton discovered the laws of nature, Euler taught humanity how to write mathematics. He was the most prolific mathematician in history. His papers continued to be published for 48 years after his death.

Core Contributions - Deep Analysis

Euler's Identity: The Most Beautiful Formula

$e^{i\pi} + 1 = 0$

This formula is universally recognized as the most beautiful in mathematics. It miraculously connects the five most important constants:

• $0$ (additive identity)
• $1$ (multiplicative identity)
• $\pi$ (the core of geometry)
• $e$ (the core of analysis)
• $i$ (imaginary unit)

Called "God's formula," this equation unifies algebra, geometry, trigonometry, and complex analysis in one elegant expression.

The Birth of Graph Theory: The Seven Bridges of Königsberg

At the time, Königsberg had seven bridges. People wondered if it was possible to cross each bridge exactly once and return to the starting point.

Euler didn't walk the bridges. Instead, he abstracted the problem into a structure of "points" and "lines" and proved it was impossible. This created graph theory and topology—entirely new branches of mathematics.

Standardization of Mathematical Notation

If you find modern mathematics textbooks readable, thank Euler. He defined the symbols we use today:

• $f(x)$ for functions
• $\pi$ for the circle constant
• $e$ for the natural logarithm base
• $i$ for the imaginary unit
• $\sum$ for summation

The Legend of Blind Calculation

Euler went blind in his later years, but his astonishing memory and mental calculation abilities allowed him to continue creating at a furious pace. It's said that his mental calculations were equivalent to an entire logarithm table. His mathematical intuition was as natural as breathing.

He published more papers through mental calculation than most mathematicians do in a lifetime. His memory was so extraordinary that he could recite the entire Aeneid from memory.

Legacy

Euler's work touched almost every branch of mathematics:

• Analysis: Advanced calculus and infinite series
• Number Theory: Euler's totient function, Euler's theorem
• Geometry: Euler's formula for polyhedra ($V - E + F = 2$)
• Physics: Fluid dynamics, mechanics, optics

He transformed calculus from a tool into a complete mathematical discipline. The 18th century is often called "Euler's century" because of his overwhelming influence. His collected works fill over 80 volumes, and he published more mathematics than any other mathematician in history—over 800 papers and books.