# The Niels Henrik Abel Award

The Danish prime minister proposed in August 2001 the creation of the $27 million Niels Henrik Abel memorial fund to create an international prize for outstanding scientific work in mathematics. In January 2002 the fund was set up and administered by the Norwegian Academy of Science and Letters. This award is intended to perform the same function as the Nobel Prize, as it does not exist for work in mathematics. The Fields Medal used to be considered the equivalent of the Nobel Prize, but the Fields Medal only awards mathematicians under the age of forty. The Abel Prize will have no age limit or limits on the area of ​​mathematics to be awarded. The fundamental criterion that guides the award is the quality of the work and the acceptance by the mathematical community. The prize will be awarded annually and the first prize took place in 2003 worth US$ 825,000 to the French mathematician Jean Pierre Serre.

The name of the award is a tribute to the Norwegian mathematician Niels Henrik Abel (1802-1829) who died at the age of twenty-six leaving an exceptional scientific legacy. The idea of ​​an international award honoring Abel was first suggested by the Norwegian mathematician Sophus Lie in the late 19th century. In 1902 King Oscar II of Sweden and Norway proposed the creation of the award, but the proposal died when the union of the two nations was dissolved in 1905. The current initiative of the award came from the Department of Mathematics of the University of Oslo which hosted the Abel Bicentennial Conference in June 2002 to commemorate the 200thO. Abel's birthday and was enthusiastically supported by the International Mathematical Union (IMU) and the European Mathematical Society (EMS).

The Abel Prize aims to contribute to the growing status of mathematics in society, to strengthen research in the field of mathematics and thus to stimulate the interest of children and young people in science. The Award Selection Committee consists of five exceptional mathematicians, one nominated by the EMS, three nominated by the IMU, and one Norwegian mathematician. The 2003 Abel Award Selection Committee had the following mathematicians: “Erling Stormer (University of Oslo - Chairman of the Committee), John M. Ball (University of Oxford), Friedrich Hirzebruch (Max Planck Institute for Mathematics), David Mumford (Brown University) and Jacob Palis (IMPA-Brazil) ”.

French mathematician Jean Pierre Serre, emeritus professor at the Collège de France, received the first Abel Prize from the Norwegian Academy of Sciences. Serre was born in 1926 in the French city of Bages, studied at the École Normale Supérieure and received his doctorate in 1951 at the Sorbonne in Paris under the direction of French topologist H. Cartan. In 1956 he assumed a position at the Collège de France. Serre's work is of extraordinary breadth, depth, and influence in contemporary mathematics. Serre has received numerous awards during his brilliant career, including the Fields Medal in 1954, where he applied the spectral sequence method, created by French topologist J. Leray, to calculate the sphere homotopy group. sno (a particular case, in dimension 2, is the surface s2of a ball). Serre has received numerous honorary titles from many universities and awards during his career: Prix Gaston Julia in 1970, Balzan Prize in 1985, Steele Prize in 1995, Wolf Prize in 2000, becoming Commander Légion D'Honneur and High Officer Ordre National du Mérite. .

He developed revolutionary algebraic methods for studying topology. In particular, he studied the cohomology of complex spaces with coefficients in sheaves of holomorphic functions. Theorems about the structure of certain classes of cohomology of analytic spaces are currently mentioned in the literature by the name of: “Kodaira-Serre Duality Theorems" All these results developed by Serre were fundamental in the development of Algebraic Topology and Geometry. After this period, Serre turned to Algebraic Geometry and Number Theory. It ushered in a golden age in Algebraic Geometry where it introduced and developed algebraic concepts that dramatically determined when the constructions of 19th century algebraic geometers worked, thus clarifying Classical Algebraic Geometry. Serre's magnificent vision of arithmetic questions has led the number theory to its glory days. His view of Number Theory is so vast and original that we find it impossible to give a glimpse of his work here. However, we recall that Serre has achieved significant results in p-Adic Group Representation Theory, and in modular functions, work that has been vital in many of the celebrated recent developments such as, for example, Andrew Wiles's demonstration of Fermat's Last Theorem.

Serre's work extends in many ways and connects with the ideas Abel introduced, in particular, Abel's demonstration of the impossibility of radicals solving the fifth degree equation and his analytical techniques in the study of polynomial equations in two variables. Modern Algebra begins with the work of the French mathematician Evariste Galois. Galois lived in the nineteenth century and, during his short existence of about twenty years, radically changed the character of algebra. Previously to Galois one of the great goals of the algebrists was the solution of algebraic equations. Gauss demonstrated that every equation of the form xno-1 = 0, can be solved completely by radicals, and that any algebraic equation can be solved in the set of complex numbers. Scipione del Ferro, Tartaglia and Cardano showed how to solve grade 3 equations, and Ferrari the grade 4 equations. Ingeniously, Galois was the first to investigate the structures of bodies and groups, and showed how these two structures are closely linked. Thus, to know if an equation can be solved by radicals, the structure of its equation is analyzed. Galois group. After Galois, algebraists began to concentrate their efforts on investigating algebraic structures such as groups, rings, bodies, and algebras. Algebraic structures, in general, are sets equipped with operations that satisfy certain properties. The most important predecessors of Galois were Lagrange, Gauss and Abel.

Abel was one of the most talented mathematicians on record. As a teenager, Abel thought he could solve the general fifth degree equation by radicals, but soon realized a mistake. During the spring of 1824 he demonstrated that it was impossible to give radical solutions to general equations of the fifth degree. With his own resources, he published a booklet in French entitled “Memoires sur les algebraic equations”In which he presented a very clear demonstration of this impossibility. Two months before his death in 1829, Abel published another article in which he investigated a particular type of arbitrary degree equations that are soluble by radicals. To this class of equations belongs the equation xno-1 = 0. One of the results established by Abel in this article is a special case of a larger Galois theory theorem. This result was presented by Galois to the Paris Academy in 1829, the same year Abel's paper was published. Currently the algebraic structures that satisfy the commutative property are called Abelianas.

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