Niels Henrik Abel (1August 5, 802-1April 6, 829)

Norwegian mathematician who 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.

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 a mathematical magazine. 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.

Extended data

Abel's main achievements:

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? , manufacturing? (x，y)=0 .

He also proved the theorem about the above-mentioned integral sum, which is now called Abel theorem. It asserts that the sum of several such integrals can be expressed as the sum of integrals such as g plus some algebraic and logarithmic terms, where g depends only on? , that is? The 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.

Baidu Encyclopedia-Niels Henrik Abel