Carl Gauss: Prince of mathematics solved an ancient problem with a history of more than 2,000 years in just one night

Surely when we were in school, at least once we heard the name Gauss and were told about the anecdotes or theorems that this prodigy left behind. Indeed, it is considered that, except for the name Newton, there is rarely a mathematician who has left as much influence on modern mathematics as Carl Gauss; His name is also ranked on par with other prominent mathematicians such as Euler, Archimedes, etc. Some people say Gauss was willing to publish all of his research, perhaps mathematics developed earlier than it does today. at up to 50 years. And, like Newton, Gauss not only shined in the field of mathematics, but also researched and contributed a lot to other fields such as geodesy, astronomy, physics, electrostatics and optics,.

'Learn to count before learning to speak'

Johann Carl Friedrich Gauss (April 30, 1777 - February 23, 1855).

The correct spelling of his name is Johann Carl Friedrich Gauß , he was born on April 30, 1777 and died on February 23, 1855. Gauß was praised by people as the ' Prince of Mathematicians' , but his title This is not entirely due to his contributions to mathematics, but also because since childhood, he was a prodigy with superior computational ability. Gauß's family belonged to the poor working class in German society, his mother was not even literate and had very little knowledge. Because she was illiterate, she could not record Gauß's birth date but only remembered that he was born in April, 8 days before Ascension and 39 days after Easter. As a child, thanks to the data his mother gave him, Gauß was able to calculate his date of birth and discovered many methods of calculating calendar dates.

Many anecdotes say that Gauß has been extremely sharp in calculations since he was 3 years old, an age when children still cry and fight over lollipops. One day he accidentally met his father calculating sales records, he suddenly noticed a small mistake and told him. The father at that time was half convinced and half doubted because his son was only 3 years old so how could he know whether it was right or wrong, however he still carefully checked and recalculated. It was surprising to see that he had miscalculated right where Gauß told him.

When Gauß was 7 years old, another anecdote about his calculating ability continued to appear. Gauß went to class and the teacher gave him a math problem: calculate the sum of numbers from 1 to 100. This is a simple arithmetic problem for us today, but for a 7 year old child, this is is a relatively complicated question. Thinking for a few seconds, Gauß announced that he had solved it, but the teacher said that he could not solve it that quickly, so he told Gauß to look carefully, maybe the calculation was wrong. But Gauß was not wrong, he came up with an extremely good and simple solution that surprised both teachers and friends. Here's how:

• Gauß noticed that if you gradually add pairs of numbers at the beginning and end of the number sequence, they always have the same total, for example 100+1, 99+2, 98+3,. all have a total of 101. There are 100 numbers in total. , meaning there will be 50 pairs with a total of 101 like that, so he just needs to multiply 101 by 50, the result is 5050. Extremely fast and compact. Historians believe that this is a true story, although the details may vary from reality.

Impressed by Gauß's superior intelligence, Duke Karl Wilhelm Ferdinand granted him a scholarship to attend Collegium Carolinum. Gauß then attended university at Gottingen. During his time in school, Gauß continuously discovered many important mathematical theorems, for example proving that every polygon has a number of sides equal to a good Fermat integer that can be constructed with just a compass and a ruler. Fermat prime numbers are prime numbers of the form 2^2^n + 1, for example 3, 5, 17, 257,. And mentioning the story of constructing pictures with compass and ruler, we have an extremely interesting story. interesting about Gauß.

A 19-year-old student successfully solved a 2,000-year-old math problem

About 300 years BC, mathematicians from Euklid's time were always trying to solve a problem that sounded simple but no one had ever been able to do it thoroughly. That is finding a way to construct regular polygons using only a ruler and compass. At that time, people could only find ways to construct squares, equilateral triangles, regular pentagons, and closer to Gauß's time, they could only construct 15 equilateral sides.

Returning to Gauß, he was now a young man less than 19 years old and studying at University. Every day, your instructor will give you 2 math problems to do each day as homework. As usual, the two problems the teacher gave were not enough to hold Gauß off and it only took him a few short hours to solve them. But, unlike usual, one day Gauß accidentally found another math problem stuck in his problem book. He was a bit surprised because the teacher gave him 3 problems today, but he still started solving them without complaining. The problem is as follows: 'Using a compass and a straightedge ruler, draw a figure with exactly 17 equal sides'

Obviously, this is a case of a problem that has existed for more than 2,000 years and that no one has been able to solve in a general way, or at least in the case of 17 edges. This question is too difficult, unlike the previous two questions. Gauß spent a lot of time, every hour passed in the night and he had to exhaust all his knowledge and mind to find a way to create the image. Gauß worked hard with pen, paper, compass and ruler until morning. Now it seemed like Gauß had completed the problem.

Even though he solved it, Gauß still felt ashamed because he thought he had solved this problem for too long. He met the instructor and said 'I'm sorry for disappointing your efforts, it took me all night to complete the third problem.' . The teacher was surprised by the words, quickly picked up Gauß's notebook to examine it and stood still because he was so frightened. The teacher asked again:

Did you really do this yourself?

Yes, of course, but it took me all night to complete this article. You are so incompetent - Gauß replied.

The teacher asked his student to sit down and asked Gauß to personally draw in front of him a regular 17-sided polygon. Gauß drew again in the teacher's admiration. After finishing, the teacher said: 'Do you know that this is a problem that no one has been able to solve before, not even Archimedes or Isaac Newton? This problem is more than 2000 years old, and you just solved it in one night, you really are a genius!' .

Many people believe that this math problem was intentionally given to Gauß by the teacher to challenge the student, but some also think that the teacher himself was also stuck in solving the difficult problem and unintentionally. to get the problem into Gauß's problem set. But no matter what, that moment marked a major milestone in the legend of mathematics.

Gauß was surprised by what his teacher told him. From disappointment, he turned into joy and happiness. The 17-sided regular polygon and its construction problem became one of the works that Gauß was most interested in in his life. He even requested that when he died, this image be engraved on his stele. But interestingly, it was too difficult to erect this image on the stone stele, so the stele maker rejected Gauß's wish and his wish could not come true.

Gauß's tombstone now.

Later, Gauß shared and said again that 'If someone had told me that it was a difficult problem, with 2000 years of history and no one had solved it, I would probably have given up and not been able to complete it. that city' . This quote is also a lesson that, perhaps if we don't know how difficult the problem we are facing is, perhaps we will do it better than if we outline many challenges already. give up.

Research comes first

Gauß has many famous and important works for science, but in the framework of this article I want to present to readers interesting and fun anecdotes rather than delving deeply into professional knowledge. He is always a perfectionist at work, putting research first, regardless of family. It is said that when Gauß was doing research, he received news that his wife was about to die from a messenger. He said: 'Ask her to wait for me a moment, so I can finish my work'.

Gauß is also a very individualistic person and likes to decide his own direction.

Gauß is also a very individualistic person and likes to decide his own direction. Although he researched a lot, he rarely published his works to the world. Not because he wanted to keep this knowledge to himself, but because he basically thought that these studies were not yet complete or perfect. This move is quite similar to the way he felt guilty when it took him all night to complete his teacher's homework that he mentioned above. He always follows the pauca sed matura doctrine, which means little but sure. Because it is rare to publish research works, in many cases it is discovered that works that other mathematicians published independently had appeared in Gauß's notes decades earlier. For example, it was discovered that Gauß had discovered non-Euklid geometry, but he did not publish it, so later, this work was registered by Janos Bolyai. This proves that he was a man whose brain was ahead of his time, and that is also the reason why posterity respect him so much.

There is also a funny anecdote between Gauß and Bolyai. Bolyai's father, Farkas Bolyai, was a friend of Gauß and tried to discover Euklid's geometry based on the axioms but failed. When Janos Bolyai announced the discovery of non-Euklid geometry, Gauß wrote to Farkas and said 'To praise this work is to praise myself, because it coincides with what I have thought and researched. over the past 30 years' . It was this statement that created tension in the relationship between Gauß and the Bolyai family.

The Twitter page of the Fields Mathematics Prize also posts congratulations and celebrations on Gauß's birthday every time it is his birthday.

Contemporaries also commented that Gauß was an extremely strict and conservative person. He rarely collaborated on research with anyone and often separated himself from the crowd. During the event where mathematicians raced to solve Fermat's great theorem, Gauß also stood on the sidelines, refusing to participate. The rare time Gauß collaborated on research with another scientist was with Wilhelm Weber and produced many results in the field of magnetism (this will be learned by anyone who studies physics in college).

End of life

For his contributions Gauß was honored worldwide, and especially in his native Germany. From 1989 to 2001, Germany printed his image and the Gauß distribution he discovered on the 10-mark banknote. At the same time, the country also printed stamps commemorating the 100th and 200th anniversary of his birth. A longtime student of his also wrote a lot about his teacher, and considered him a giant of science.

From 1989 to 2001, Germany printed his image and the Gauß distribution he discovered on the 10-mark banknote.

Thanks to his contributions to astronomy, a crater on the Moon and the asteroid 1001 Gaussia were also named after him. Gauß died on February 23, 1855 of a heart attack. When buried, people kept his genius brain for preservation and research to determine how this man was so incredibly intelligent.