Niels Henrik Abel

Niels Henrik Abel was born on August 5, 1802, on the island of Finnøy, near Stavanger, Norway. He was the second child of Søren Georg Abel, a Lutheran minister, and Anne Marie Simonsen. He showed an early interest in mathematics and was encouraged by his teacher Bernt Michael Holmboe, who introduced him to the works of Isaac Newton, Leonhard Euler, Joseph-Louis Lagrange, and Carl Friedrich Gauss. Abel entered the University of Christiania (now Oslo) in 1821 and obtained a preliminary degree in 1822. He continued his studies independently with the help of some scholarships obtained by Holmboe. He published his first papers in 1823, on functional equations and integrals. He also proved the impossibility of solving algebraically the general equation of the fifth degree, which was one of the outstanding problems of his time. He sent his proof to Gauss, who dismissed it without reading it carefully. Abel spent the winter of 1825-1826 in Berlin, where he met August Leopold Crelle, a civil engineer and a self-taught mathematician, who became his friend and mentor. Crelle founded a mathematical journal, Journal für die reine und angewandte Mathematik, also known as Crelle's Journal, and published many of Abel's papers in it. Abel also visited Paris, where he met some of the leading mathematicians of the day, such as Adrien-Marie Legendre, Augustin-Louis Cauchy, Siméon Denis Poisson, and Jean-Baptiste Fourier. He also studied elliptic functions and discovered a new class of functions, now called Abelian functions, which generalize the elliptic functions. He also made important contributions to the theory of equations, number theory, and infinite series. Abel returned to Norway in 1828, hoping to obtain a professorship at the University of Christiania, but he was disappointed by the lack of support from the Norwegian government and the academic community. He suffered from poverty and poor health, and died of tuberculosis on April 6, 1829, at the age of 26. He was buried in Froland Churchyard, near the town of Arendal. Abel's work was not fully appreciated during his lifetime, but after his death, his papers were collected and published by Crelle, Holmboe, and Peter Ludwig Mejdell Sylow, and his reputation as one of the greatest mathematicians of the 19th century was established. Many concepts and results in modern mathematics are named after him, such as Abelian groups, Abel's theorem, Abel's identity, Abel's inequality, Abel's irreducibility theorem, Abel–Jacobi map, Abel–Plana formula, Abel–Ruffini theorem, and the Abel Prize, which is awarded annually to outstanding mathematicians since 2003.