Niels Henrik Abel (1August 5, 802-1April 6, 829), a Norwegian mathematician, has done pioneering work in many fields of mathematics. One of his most famous achievements is the first complete proof that there is no general algebraic solution for general algebraic equations higher than quartic. This problem was one of his most famous unsolved problems at that time, and it was a suspense for more than 250 years. He is also a pioneer in the field of elliptic functions and the discoverer of Abelian functions. Although Abel's achievements were extremely high, he was not recognized before his death. He lived in poverty and died at the age of 27.
Chinese name: Niels Henrik Abel.
mbth:nielsenrikabel
Nationality: Norway
Place of birth: southern Norway
Date of birth:1August 5, 802
Date of death:1April 6, 829
Occupation: Mathematician
Graduate school: Kristiania University (Oslo University).
Main results: It is proved that the equations with quintic degree or more cannot be solved by formulas (Ruffini-Abel theorem).
Representative works: The paper "Algebraic General Solution of quintic Equation in One Yuan" (1824).
Poor boy
NielsHenrikAbel (1August 5, 802 ─1April 6, 829) was the greatest mathematician in Norway in the19th century. His father is a bishop of kristiansand (found? The priest is in a small village, and the whole family lives in poverty. 18 15 years, when he entered a Catholic school in Oslo, his talent in mathematics was revealed. After his teacher, Homebo? ), he studied the works of many famous mathematicians at that time, including Newton, Euler, Lagrange and Gauss. He not only understood their theory, but also found some tiny loopholes.
1820, Abel's father died, and the burden of taking care of a family of seven suddenly fell on his shoulders. Even so, Abel (182 1) can still enter the UniversityofChristinania, that is, UniversitetetiOslo, get the pre-university degree of 1822, and continue his studies with the support of Hombiao. At school, he almost taught himself and spent a lot of time doing research.
Hidden genius
After Abel's first paper was published in 1823, his friends urged the Norwegian government to fund him to study in Germany and France. While waiting for the government's reply, he published his paper "One-dimensional quintic equation without algebraic general solution" in 1824, hoping to bring him a positive position. He sent the paper to Gauss, a famous mathematician at that time. Unfortunately, Gauss missed the paper and didn't know that this famous algebraic problem had been solved. /kloc-in the winter of 0/825-26, he went to Berlin and got to know Creaer. Creaer is a civil engineer, and he is very enthusiastic about mathematics. He and Abel became very good friends. 1826, with Abel's encouragement, Creaer founded Journal fü rdiereineundangewantematik. In the first issue of this magazine, Abel's work on quintic equations and his papers on equation theory, functional equations and theoretical mechanics were published. In Berlin, the new math guide enabled him to continue his research independently, and Abel later went to different parts of Europe.
1in the summer of 826, he visited the top mathematicians at that time in Paris and finished a research report on transcendental functions. These works show an algebraic function theory, now called Abel theorem, which is also the theoretical basis of Abel integral and Abel function in the later period. He was snubbed in Paris. He sent his research report to the Academy of Sciences, hoping to get favorable comments, but his efforts were also in vain. Before leaving Paris, he suffered from a chronic disease. At first he thought it was just a cold, but later he knew it was tuberculosis.
He returned to Norway, but he owed a lot of money and debts. He had to make a living by teaching and receiving a meager allowance from the university. 1828, he found a substitute teacher to make a living. However, his poverty and illness did not reduce his enthusiasm for mathematics. During this period, he wrote many papers, mainly about the theory of equations and elliptic functions, that is, the theory of Abel equation and Abel group. He finished the theory of elliptic function faster than Jacoby. At this point, Abel's reputation has spread all over the Mathematics Center, and people from all walks of life also hope to find a suitable professorship for him, among which clear hopes to find a professorship for him in Berlin.
1in the winter of 828, Abel's condition became more and more serious. When he visited his fiancee, CrellyKemp, in Frohland at Christmas, his condition deteriorated. By 1829, 1 month, he knew that his days were numbered and the symptoms of bleeding could not be denied. Until1April 6, 829, Abel died, and his fiancee insisted on taking care of Abel without other people's help, "bearing this last moment alone."
After Abel died, his teacher Holmboe published a collection of works for him in 1839.
Late honor
It was not until shortly before Abel died that people realized his value. 1828, four academicians of the French Academy of Sciences wrote to the King of Norway, asking him to provide Abel with a suitable research site. Legendre also praised Abel at the meeting of the Academy of Sciences. Two days after Abel's death, Creaer wrote that Abel had successfully obtained the position of mathematics professor at FreieUniversit_tBerlin. Unfortunately, it was too late, and a generation of talented mathematicians died before they got the news. Since then, honors and awards have followed. 1830, he and Carl Jacobi won the French Academy Award.
Abel's achievements in mathematics are manifold. In addition to the quintic equation, he also studied a wider class of algebraic equations, which later generations found to be an equation with commutative Galois groups. In memory of him, later generations called it Abel Group. Abel also studied infinite series and obtained some criteria and theorems about the summation of power series. These works made him an advocate of strict analysis.
Abel and jacoby are recognized as the founders of elliptic function theory. Abel discovered the addition theorem and double periodicity of elliptic functions, and introduced the inversion of elliptic integral. He studied the form of integral (now called Abel integral), where R(x, y) is a rational function of x and y, and there is a binary polynomial _, so that _(x, y)=0. He also proved the theorem about the sum of the above integrals, which is now called Abel theorem. This theorem asserts that the sum of several such integrals can be expressed as the sum of G such integrals plus some algebraic and logarithmic terms, where G only depends on _, and it is a genus of _. Abel's series of works paved the way for the study of elliptic function theory and profoundly influenced other branches of mathematics. Hermite once said: Abel's thought can be used by mathematicians 150 years.
Fourier, secretary of the Academy of Sciences, read out the introduction of the paper, and then entrusted Le Jean de and Cauchy to take charge of the examination. Cauchy took the manuscript home and couldn't remember where it was. It was not until Abel died two years later that the lost manuscript of the paper was found again, and the official publication of the paper was delayed 12 years.