Mathematical Genius - The Story of Gauss

Gauss (C.F. Gauss, 1777.4.30-1855.2.23) was a German mathematician, physicist and astronomer who was born in Buenos Aires, Germany. A poor family in Rendswick. His father, Gerchild Didrich, worked as a berm worker, a mason, and a gardener. His first wife died of illness after living with him for more than 10 years, leaving him no children. Diedrich later married Rodea, and the following year their child Gauss was born, their only child. His father was extremely strict with Gauss, even a little excessive. He often liked to use his own experience to plan the life of young Gauss. Gauss respected his father and inherited his father's honest and cautious character. When Diederich died in 1806, Gauss had already made many epoch-making achievements.

While growing up, the young Gauss mainly relied on his mother and uncle. Gauss's maternal grandfather was a stonemason who died of tuberculosis at the age of 30. He left behind two children: Gauss's mother Rodea and uncle Friederich. Friedrich was wise, enthusiastic, smart and capable, and he devoted himself to the textile trade and made great achievements. He found that his sister's son was smart, so he spent part of his energy on this little genius and developed Gauss's intelligence in a lively way. Several years later, Gauss, who had grown up and achieved great success, recalled what his uncle had done for him, and deeply felt the importance of his success. Thinking of his uncle's prolific thoughts, he said sadly that "we have lost everything because of his uncle's death". A genius". It was precisely because Friedrich had a keen eye for talents and often persuaded his brother-in-law to let his children develop into scholars that Gauss did not become a gardener or a mason.

In the history of mathematics, few people are as lucky as Gauss to have a mother who fully supported his success. Luo Tieya did not get married until she was 34 years old, and she was already 35 years old when she gave birth to Gauss. He has a strong character, is smart and virtuous, and has a sense of humor. Since birth, Gauss has been very curious about all phenomena and things, and is determined to get to the bottom of it, which is beyond the scope of what a child can allow. When her husband reprimanded the child for this, he always supported Gauss and firmly opposed the stubborn husband who wanted to make his son as ignorant as himself.

Luo Jieya sincerely hopes that her son can do a great career and cherishes Gauss's talent very much. However, he did not dare to easily let his son invest in mathematics research that could not support his family at that time. When Gauss was 19 years old, even though he had made many great mathematical achievements, she still asked her friend W. Bolyai in the field of mathematics (W. Bolyai, one of the founders of non-Euclidean geometry). Father) asked: Will Gauss be successful in the future? W. Bolyo said that her son would be "the greatest mathematician in Europe", and she was so excited that she burst into tears.

At the age of 7, Gauss went to school for the first time. The first two years were nothing special. In 1787, when Gauss was 10 years old, he entered a class to learn mathematics. This was a class that was first established. Children had never heard of arithmetic as a subject before. The mathematics teacher was Buttner, who also played a role in Gauss's growth.

A story widely circulated around the world says that when Gauss was 10 years old, he solved the arithmetic problem Butner gave his students to add up all the integers from 1 to 100. Butner just narrated After finishing the question, Gauss calculated the correct answer. However, this is probably an untrue legend. According to the research of E.T. Bell, a famous mathematics historian who has studied Gauss, Butner gave the children a more difficult addition problem: 81297+81495+81693+…+100899.

Of course, this is also a summation problem of an arithmetic sequence (the tolerance is 198 and the number of terms is 100). As soon as Butner finished writing, Gauss also finished the calculation and handed over the small slate with the answer. E. T. Bell wrote that Gauss often liked to talk about this matter to people in his later years, saying that only the answer he wrote was correct at that time, and the other children were wrong. Gauss did not explain clearly what method he used to solve this problem so quickly. Historians of mathematics tend to believe that Gauss had mastered the method of summing arithmetic sequences at that time. It is very unusual for a child as young as 10 years old to independently discover this mathematical method. The historical facts narrated by Bell based on Gauss's own words in his later years should be relatively credible. Moreover, this better reflects the characteristic that Gauss has paid attention to grasping more essential mathematical methods since he was a child.

Butner was impressed by Gauss's calculation ability, and more importantly, Gauss's unique mathematical methods and extraordinary creativity. He specially bought the best arithmetic book from Hamburg and gave it to Gauss, saying: "You have surpassed me, and I have nothing left to teach you." Then, Gauss established an alliance with Butner's assistant J.M. Bartels. A sincere friendship existed until Bartels' death. They studied together and helped each other, and Gauss began his real mathematical research.

In 1788, the 11-year-old Gauss entered a liberal arts school. In the new school, he excelled in all his subjects, especially classical literature and mathematics. After being introduced by Bartels and others, the Duke of Brunswick summoned the 14-year-old Gauss.

This simple, smart but poor child won the sympathy of the Duke, who generously offered to be Gauss's sponsor so that he could continue his studies.

The Duke of Brunswick played a decisive role in Gauss's development. Not only that, this role actually reflects a pattern of modern scientific development in Europe, indicating that before the socialization of scientific research, private funding was one of the important driving factors for scientific development. Gauss was in a period of transition between private funding of scientific research and the socialization of scientific research.

In 1792, Gauss entered the Caroline College in Brunswick to continue his studies. In 1795, the Duke paid various fees for him and sent him to the famous G?ttingen School in Germany. This enabled Gauss to study diligently and start creative research according to his own ideals. In 1799, Gauss completed his doctoral thesis and returned to his hometown of Brunswick. Just when he fell ill worried about his future and livelihood - although his doctoral thesis was successfully passed and he had been awarded a doctorate and at the same time received Lecturership, but he failed to attract students and therefore had to return to his hometown - and it was the Duke who came to his rescue again. The Duke paid for the printing of Gauss's long doctoral thesis, gave him an apartment, and printed "Arithmetic Research" for him, so that the book could be published in 1801; he also paid for all Gauss's living expenses. All this moved Gauss very much. In his doctoral thesis and "Arithmetic Research", he wrote a sincere dedication: "To the Grand Duke", "Your kindness freed me from all worries and enabled me to engage in this unique research." .

In 1806, the Duke was unfortunately killed while resisting the French army commanded by Napoleon, which dealt a heavy blow to Gauss. He was devastated and had a deep and long-lasting hostility toward the French. The death of the Archduke brought financial constraints to Gauss, the misfortune of Germany being enslaved by the French army, and the death of his first wife made Gauss a little discouraged, but he was a strong man and never Disclose one's predicament to others, and do not allow friends to comfort one's misfortune. People only learned about his mentality at that time when his unpublished mathematical manuscripts were compiled in the 19th century. In a handwritten article discussing elliptic functions, a subtle pencil text was suddenly inserted: "For me, death is more bearable than this life."

Generous and benevolent sponsor passed away, so Gauss had to find a suitable job to maintain the family's livelihood. Due to Gauss's outstanding work in astronomy and mathematics, his reputation began to spread throughout Europe from 1802. The Petersburg Academy of Sciences kept hinting to him that since Euler's death in 1783, Euler's position in the Petersburg Academy of Sciences had been waiting for a genius like Gauss. When the Duke was still alive, he firmly discouraged Gauss from going to Russia. He was even willing to increase Gauss's salary and build an observatory for him. Now, Gauss faces new choices in his life.

In order to prevent Germany from losing its greatest genius, the famous German scholar B.A. Von Humboldt teamed up with other scholars and political figures to obtain the privileged professorship of mathematics and astronomy at the University of G?ttingen for Gauss. and the position of Director of the G?ttingen Observatory. In 1807, Gauss went to G?ttingen to take up a job, and his family moved here. From this time on, except for a trip to Berlin to attend a scientific conference, he lived in G?ttingen. The efforts of Humboldt and others not only provided a comfortable living environment for the Gauss family and allowed Gauss himself to give full play to his genius, but also created conditions for the establishment of the G?ttingen School of Mathematics and for Germany to become a world center of science and mathematics. At the same time, this also marks a good start for the socialization of scientific research.

Gauss’s academic status has always been highly respected by people. He is known as the "Prince of Mathematics" and the "King of Mathematicians" and is considered to be "one of the three (or four) greatest mathematicians" in human history (Archimedes, Newton, Gauss or more). Euler). People also praised Gauss as "the pride of mankind". Genius, precocity, high productivity, unfailing creativity..., almost all praises in the field of human intelligence are not exaggerated for Gauss.

Gauss’s research fields span all fields of pure mathematics and applied mathematics, and he has opened up many new fields of mathematics, from the most abstract algebraic number theory to intrinsic geometry, leaving his footprints. In terms of research style, methods and even specific achievements, he was a backbone figure at the turn of the 18th and 19th centuries. If we imagine the mathematicians of the 18th century as a series of mountains, then the last awe-inspiring peak is Gauss; if we imagine the mathematicians of the 19th century as a series of rivers, then their source is Gauss.

Although mathematical research and scientific work still did not become enviable professions at the end of the 18th century, Gauss was still born at the right time, because when he was about to enter his thirties, the development of European capitalism , making governments around the world begin to pay attention to scientific research. As Napoleon attached great importance to French scientists and scientific research, the Russian Tsar and many European monarchs also began to look at scientists and scientific research with admiration. The socialization process of scientific research continued to accelerate, and the status of science continued to improve. As the greatest scientist at that time, Gauss received many honors. Many world-famous scientific leaders regarded Gauss as their teacher.

In 1802, Gauss was elected as a corresponding academician by the Russian Academy of Sciences in Petersburg and a professor at Kazan University; in 1877, the Danish government appointed him as a scientific advisor. In this year, the Hannover government in Germany also hired him as a government scientist. consultant.

Gauss’s life is the life of a typical scholar. He always maintained the simplicity of a farmer, making it difficult for people to imagine that he was a great professor and the greatest mathematician in the world. He was married twice and had several children that annoyed him. However, these had little impact on his scientific creation. When it gained a high reputation and German mathematics began to dominate the world, a generation of geniuses completed their life journey.

As long as I have the chance, I will resist fate - Beethoven

Ludwig van Beethoven (1770-1827), the great German composer and Viennese classical music composer One of the representative figures. Beethoven was born on December 16, 1770 in Bonn, a small town on the Rhine River not far from France. His grandfather was the conductor of the Bonn court orchestra, and his father was a court tenor. Beethoven's musical genius has been revealed since he was a child. His father was eager to train him to become a child prodigy like Mozart. He forced him to learn piano and violin from an early age. When he was eight years old, he began to perform in concerts and try to compose music. , however, the music education he received during this period has been very fragmented and unsystematic.

At the age of twelve, he was already able to play freely and served as the assistant of the organist Nie Fei (1748-1798). It was at this time that he began to formally study music with Nie Fei. Nie Fei was a musician with many talents. He expanded Beethoven's artistic vision, made Beethoven familiar with some excellent examples of German classical art, and consolidated Beethoven's understanding of lofty purposes. Beethoven's formal learning and systematic upbringing actually began with Nie Fei's careful teaching and training: Nie Fei also guided him to Vienna to teach Mozart in 1787. After hearing his performance, Mozart predicted that one day Beethoven would shock the world. Beethoven received news of his mother's death soon after arriving in Vienna, and he had to rush back to Bonn immediately. Due to family burdens, he did not come to Vienna for the second time until the death of his father in the autumn of 1792, but by this time Mozart was no longer alive. After Beethoven came to Vienna for the second time, he quickly won the title of Vienna's most outstanding performer (especially improvisation). Later, he first studied with Haydn, and later with Schenck, Albrecht Berg and Salieri. Through his interactions with the intellectual Breining in Bonn, he came into contact with many famous professors, writers and musicians at the time, and from them he was influenced by the ideological trend of the "Turbulence Movement". His democratic ideas had reached maturity in the years before the French Revolution, but they grew particularly rapidly during the revolutionary years.

The progressive ideology of the French bourgeois revolution in 1789 inspired him a lot, thus laying the foundation for his humanistic world - a deep belief in human equality, the pursuit of justice and individual freedom, and a hatred of the oppression of feudal autocracy. . Although the three famous composers of the Vienna Classical School lived in a very close era, Beethoven's thoughts obviously did not belong to the same "era" as Haydn and Mozart. Haydn was humiliated throughout his life. Although he was occasionally provoked, he always accepted it. The progressive literary trends and revolutionary sentiments at that time rarely excited him, and his music was always insulated from struggle. Mozart suffered no less spiritually than Haydn. He was brave enough to resist and would rather be poor than endure the insult of the archbishop. However, in his music, behind the joy full of sunshine and youthful vitality, you can often still feel a trace of it. Emotions of pain, melancholy and sadness. Only Beethoven not only angrily opposed the tyranny of the feudal system, but also used his music to call on people to fight for freedom and happiness. Most of Beethoven's creations during his Bonn period (1782-1792) were small piano pieces, ensembles and songs. During this period, it can be said that he was only in the preparatory stage of creation. In the first ten years of his creation in Vienna (1792-1802), the only famous works are "Sorrow", "Moonlight", "Kreutzer" sonata and "Third Piano Concerto". But during this period, he gained a better understanding of social and political issues, and was able to realize the goals he wanted to pursue. From 1802 to 1812, his creation entered a mature period, which later became his "heroic age".

The maturation process of Beethoven's creative activities seems to be quite slow on the surface, but in fact it is very stable. He only began to write his first symphony when he was thirty years old. At this age, Mozart had already written about forty symphonies.

Beethoven had felt his hearing weakening since 1796, but it was not until 1801, when he was convinced that his ear disease was incurable, that he told his friends about it. However, his love for art and life overcame his personal pain and despair - suffering became the source of his creative power. At the height of such a spiritual crisis, he began to compose his optimistic "Eroic Symphony." "Eroica Symphony" marks a spiritual turning point for Beethoven and also marks the beginning of his "Heroic Age".

In Beethoven’s later period in Vienna, because Europe was experiencing a period of serious political reaction, that is, a period when Metternich’s reactionary rule was particularly rampant, his creations also temporarily declined (1813- 1817). From 1818 onwards, during the last ten years of Beethoven's life (1818-1827), despite being completely deaf, suffering from deteriorating health, living in poverty, and suffering mental torture, he still created """" with giant-like perseverance. "Ninth (Chorus) Symphony" summarizes his glorious and epic life and shows the best wishes of mankind.

Beethoven died in Vienna on March 26, 1827. No family member was by his side when he died, but when he was buried on the 29th of the same month, a mass wave was formed. All schools were closed to express condolences. Twenty thousand people escorted his coffin, and there was an inscription on his tombstone. With the inscription by the Austrian poet Greer Bacze (1791-1872): "When you stand in front of his coffin, what envelopes you is not dejection, but a noble emotion; we only have For a person like him, it can be said: He has accomplished a great career... \"

Beethoven is one of the great composers in the history of world art, and his creations embody his giantness. His character reflects the progressive thinking of that era, and his image of revolutionary heroism can be summarized as "through suffering - to joy; through struggle - to victory." His works are both majestic and magnificent, yet extremely simple and distinctive. His music is rich in content and at the same time easy to understand and accept for the audience. Beethoven's music embodies the pain and joy, struggle and victory of the people of his time. Therefore, it has always inspired people and inspired people's fighting spirit in the past. Even now, it makes people feel cordial and inspiring.