Niels Henrik Abel

Niels Henrik Abel
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Name	Niels Henrik Abel
Caption	Portrait of Niels Henrik Abel
Birth date	5 August 1802
Birth place	Nedstrand, Denmark–Norway
Death date	6 April 1829 (aged 26)
Death place	Froland, United Kingdoms of Sweden and Norway
Fields	Mathematics
Alma mater	Royal Frederick University
Known for	Abel's theorem, Abelian group, Abel's identity, Abel's inequality, Abel's summation formula, Abel equation, Abel transform, Abelian variety, Proof of the Abel–Ruffini theorem
Influences	Bernt Michael Holmboe
Influenced	Évariste Galois, Carl Gustav Jacob Jacobi
Prizes	Grand prix des sciences mathématiques (1830, posthumous)

Niels Henrik Abel was a pioneering Norwegian mathematician who made profound contributions to several fields despite his tragically short life. His work laid essential foundations for group theory, elliptic functions, and the theory of algebraic equations. He is best known for proving the impossibility of solving the general quintic equation by radicals, a problem that had confounded mathematicians for centuries, and for his deep investigations into Abelian integrals.

Early life and education

Born in Nedstrand and raised in Gjerstad, his early education was overseen by his father, Søren Georg Abel, a theologian and politician. After his father's death, the family faced significant poverty, but his mathematical talent was recognized and nurtured by his teacher Bernt Michael Holmboe at the Cathedral School of Christiania. With financial support from professors at the Royal Frederick University, including Christopher Hansteen, he was able to attend university. A grant from the Norwegian government later allowed him to travel to Berlin and Paris to further his studies, where he interacted with leading mathematicians like August Leopold Crelle and Adrien-Marie Legendre.

Mathematical contributions

His most famous achievement was the first complete proof of the Abel–Ruffini theorem, demonstrating that a general solution by radicals for equations of degree five or higher is impossible. This work indirectly paved the way for the development of modern Galois theory by Évariste Galois. In the field of analysis, he rigorously investigated the convergence of binomial series and established foundational results in the theory of elliptic functions, working concurrently with Carl Gustav Jacob Jacobi. He also developed what are now called Abelian integrals and Abelian functions, and his name is attached to numerous concepts including Abel's theorem, Abelian groups, and the Abel transform.

The Abel Prize

In 2002, on the bicentennial of his birth, the Norwegian government established the Abel Prize, an annual international award for outstanding scientific work in the field of mathematics. Administered by the Norwegian Academy of Science and Letters, the prize is widely considered the mathematician's equivalent of the Nobel Prize. The award ceremony is held in Oslo, and the prize money is awarded by His Majesty The King of Norway, cementing his legacy as a national icon of scientific achievement.

Legacy and recognition

His work fundamentally transformed algebra and analysis, influencing generations of mathematicians including Bernhard Riemann and Karl Weierstrass. Many fundamental mathematical objects bear his name, such as abelian varieties, abelian categories, and abelian sandpile models. The term "abelian" has become a standard descriptor in group theory and other areas. Despite initial neglect by the French Academy of Sciences, his collected works, the *Oeuvres Complètes*, were later published through the efforts of August Leopold Crelle and Carl Gustav Jacob Jacobi, securing his posthumous fame.

Personal life and death

He was engaged to Christine Kemp, a governess he met while tutoring in Froland. Throughout his travels, he suffered from chronic financial difficulties and poor health. In 1829, while traveling to visit his fiancée, he contracted tuberculosis. He died at Froland Ironworks at the age of twenty-six, just two days before a letter arrived from Augustin-Louis Cauchy announcing a professorship for him in Berlin. He was buried first at Froland and later reinterred in the cemetery of Our Saviour's Cemetery in Oslo.

Category:Norwegian mathematicians Category:1802 births Category:1829 deaths