He can sum the integers from 1 to 100 when he was nine, and show a high talent at a young age. Sometimes referred to as the “Princeps mathematicorum”, “Gauss” can be seen everywhere. How glorious his past is?


Info of Gauss

Johann Carl Friedrich Gauss

Euler’s portrait
(Image Source:Wikipedia

1+…+100 = ?

Imagine that you were taught by a teacher who lost his enthusiasm for teaching when you were nine, and he was trying to fool around in every class. Today he ask you to sum integers from 1 to 100. The question is too difficult for kids who has just learned the concept of addition. So your classmates start working hard to solve the problem. It seems that the teach could slack off at class. At this moment, someone stands up, and hands in his answer – it is correct! This imagination happened before, and this clever classmate’s name is Gauss.

Talent in mathematics

It is not exaggerated to refer Gauss as the prince of mathematics. He showed a great talent for mathematics at his young age. When Gauss was three, he can find out the mistakes on his father’s accounts. The authenticiy of this story is unidentifiable, but Gauss’ achievement in the future also made this anecdote widely circulated. He started to doubt the proof in geometry at the age of 12. When he was 15, he entered a college and began to do research on advanced mathematics. Then he predicted that there will be a totally different geometry  beyond Euclidean geometry. The geometry is called  non-Euclidean geometries nowaday.

Have you learned how to draw only by ruler and compass (also called “straightedge and compass construction”)? Now imagine that you have to draw a regular Heptadecagon by straightedge and compass construction. Do you have any thoughts about the way to draw Heptadecagon? Gauss did it at the age of 19. He was proud of this achievement. He even hoped that Hepadecagon could be engraved on his tombstone to memorize this important mathematical discovery.

Gauss is everywhere

Not just mathematics, Gauss is also knowledgeable in other fields, such as statistics, analysis, geodesy, astronomy, mechanics, optics, etc. It is said that there are 110 research results named after “Gauss”! Even if you only look at achievements in one fields, Gauss is an authority. There are lots of things appear to memorize Gauss, like stamp, paper money, etc.


Gauss is not a productive mathematician. He attached importance to the strictness of theory and proof. He would not publish things that are not fully certain and immature. So when his colleague published their research, Gauss often said: I have already proved it. There are three people worked on non-Euclidean geometry: Gauss,  János Bolyai (1802-1860), and Nikolai Lobachevsky (1792-1856). Farkas Bolyai is  János Bolyai’s father, also a friend of Gauss. One day Farkas sent to Gauss his son János’ work on the subject. Gauss replied: to praise it would mean to praise myself. That is, he had already prooved this work thirty years before János did it. These are all certified in Gauss’ notes after his death.

Again, you can see him EVERYWHERE

In mathematics, he derived the general form of the binomial theorem and developed the prime number distribution theorem, the least square method, and arithmetic–geometric mean.

In the field of statistics, the standard normal distribution curve that you will frequently see at the beginning is Gaussian distribution, which is obtained when Gauss focused on studying curve surfaces and curve calculations. 

In astronomy, an astronomer in Italy who discovered Ceres delayed the observation due to illness and lost the trajectory of the asteroid. Gauss used the data he observed before to calculate the trajectory of Ceres, and then astronomers followed this trajectory to find the asteroid successfully. It also made Gauss famous in the astronomical field, and wrote this method in his work “Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections”.

In the field of geodesy, he used the least square method he invented to improve the accuracy of measurement.Then he invented the heliostat and continuously improved the design, and developed it into a sextant. In the calculation of the observation results, Gauss wrote nearly 20 papers on geodesy. During the time, he wrote the theory of curve surfaces and projection, which became the important basis of differential geometry.

In physics research, he and a German physicist, Wilhelm Weber, drew the world’s first map of the Earth magnetic field, and determined the locations of the magnetic south pole and magnetic pole, which was confirmed by American scientists next year.

He is involved in number theory, algebra, function theory, differential geometry, probability theory, mechanics, hydraulics, electrical engineering, optics, etc. I believes that Gauss’ contributions to the modern world are undoubtedly deduced by dozens of forwards year.

There are so many untelled stories

Compared to Gauss’s achievements, this article is very short and not enough. Of course, I will continue to update it.

Add some ingredient

Wikipedia – Carl Friedrich Gauss

Seasoned with Chinese

◊ least squares method – 最小平方法
◊ normal distribution、Gaussian distribution – 常態分布

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