Newton has a story about being hit by an apple (though he said wasn’t);
Archimedes has a saying, “Give me a place to stand on, and I will move the Earth.”;
The story that Gauss sum the integers from 1 to 100 has been told to this day;
However there is a great mathematician that has no amazing story like above on him.
The man is Leonhard Euler.
Info of Euler

Leonhard Euler

Euler’s portrait
(Image Source:Wikipedia

The school time of Euler

There is another genius story.

Euler was born in a priest’s family in Switzerland. He entered Basel University at the age of 13 and majored in philosophy and laws. On weekends, Euler learned math with a famous mathematicians, Johann Bernoulli. Euler got the master’s degree when he was seventeen years old. After that, he started to studied theology for the sake of his father’s expectation. However, Johann Bernoulli admired Euler at that time and tried hard to convince Euler’s father to allow Euler to continue studying mathematics. Euler then get PhD in the study of sound communication at the age of 19.

Prolific and high quality

Do you remember Gauss? He is famous for not prolific but high quality. In the last era, Euelr was the mathematician with the second most publiched papers in history. There is a hug gap in the number of papers between Gauss and Euler. Though Euler is prolific, the quality of each paper didn’t decline. It was all from his own hand.

Memory point everywhere

It’s exaggerated that to say Euler didn’t have any story on him. Actually, Euler is everywhere. You can find Euler in many flied. Now, let me briefly inroduce some of his contribution.


Euler introduce the concept of a “function”, and was the first to write ” \(f(x)\) ” to denote the function \(f\) applied to the argument x. \(e\), Euler’s number( \(\approx 2.71828\)). \(\pi\), a letter to denote the ratio of a circle’s circumference to its diameter, etc. Although these notations wasn’t originated with Euler, the use of them was popularized by him. His name also appears in calculus, differential equation (Euler method is the famous one), number theory, etc.

If you are not a math guy, maybe you have seen this equation printed on T-shirt or mugs: 

\(e^{i \pi} + 1 = 0\)

This equation is mixed by five important constants, called ‘the most remarkable formula in mathematics” by Richard P.Feynman.

Have you heard about the problem known as  Seven Bridges of Königsberg? There is a mathematician whose name is Carl Gottlieb Ehler lived in Königsberg. The city of Königsberg was set on the Pregel River, and included two large islands that were connected to each other and the mainland by seven bridges. Carl was confused by a problem: Is it possible to follow a path that crosses each bridge exactly once and returns to the starting point? You can try it by yourself! Euler figured out at that time and published papers. It is the origin of topology.


Euler developed Euler equations in fluid dynamics, and applied it to the blood flow in the body. We use it on shark wave research nowadays. Euler’s law of motion in rigid body mechanics is the extension of Newton’s laws of motion. Euler also develop Euler-Lagrange function in analytical mechanics.

Not only these, Euler also made great contributions to Optics and Astronomy.

The master of us all

Unlike some geniuses who have a weird temper, Euler was said to be very generous and kind. He also loved children. Euler exchanged letters with many scholars. He always told his findings and details unreservedly in the letters, and also loved to help others. Everyone knew that Euler won’t possess the results of others. He was an enthusiastic educator.

In addition to the academic achievements mentioned above, Euler also involved in literature, theology, laws, music, and so on. Mathematicians in Europe regarded Euler as their teacher. Laplace even made a famous saying:

Read Euler, read Euler, he is the master of us all.

Eye disease

Euler suffered a serious illness, and the fever was almost fatal at the age of 28. His right eye continued to deteriorate. Coupled with the work of cartography at the St. Petersburg Academy of Sciences, his right eye was almost blind three years later. When he was 59, he was diagnosed with a cataract by a doctor and nearly complete blind a few weeks later. (There is other saying that the eye got worse due to Euler watched the sun directly.)

Although his eyes were blind, Euler was not discouraged. With his excellent mental arithmetic and the ability to memory, he continued his research and even increase the output of papers.

“He ceased to calculate and to live”

After dinner on September 18, 1783, Euler was drinking tea while playing with his granddaughter. Suddenly, the pipe fell from his hand. He said, “My pipe…”, and bent over trying to pick it up, but he didn’t. He held his head and said, “I’m dead.” Then he passed away. I couldn’t help thinking that did he calculate this? When Marquis de Condorcet, a French philosopher and mathematician heard this news, he said, “…il cessa de calculer et de vivre (Euler ceased to calculate and life)”, which is often quoted by historians of mathematics.

Add some ingredient

Wikipedia – Leonhard Euler
MacTutor – Leonhard Euler

Seasoned with Chinese

◊ Euler’s formula – 歐拉公式
◊ Euler’s number – 歐拉數
◊ differential equation – 微分方程
◊ 變分法 – Variational Calculus

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