The Predecessors of Galois

Bartel Leenert van der Waerden
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Bartel Leenert van der Waerden: Universität Zürich, Mathematisches Institut

Chapter Chapter 4 in A History of Algebra, 1985, pp 76-88 from Springer

Abstract: Abstract Modern algebra begins with Evariste Galois. With Galois, the character of algebra changed radically. Before Galois, the efforts of algebrists were mainly directed towards the solution of algebraic equations. Scipione dal Ferro, Tartaglia, and Cardano showed how to solve cubic equations, and Ferrari succeeded in solving equations of degree 4. Gauss proved that the cyclotomic equation $$ {x^n} - 1 = 0 $$ can be completely solved by radicals, and that every algebraic equation can be solved by complex numbers a + bi. Galois, on the other hand, was the first to investigate the structure of fields and groups, and he showed that these two structures are closely connected. If one wants to know whether an equation can be solved by radicals, one has to analyse the structure of its Galois group. After Galois, the efforts of the leading algebrists were mainly directed towards the investigation of the structure of rings, fields, algebras, and the like.

Keywords: Rational Function; Galois Group; Galois Theory; Primitive Root; Hypo Thesis (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-3-642-51599-6_4

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