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Preface

Published online by Cambridge University Press:  11 January 2010

Francis Borceux
Affiliation:
Université Catholique de Louvain, Belgium
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Summary

E. Galois (1811–1832) would certainly be surprised to see how often his name is mentioned in the mathematical books and articles of the twentieth century, in topics which are so far from his original work.

Since antiquity, mathematicians have been able to solve polynomial equations of degree 1 or 2. Formulæ for solving the equations of degree 3 or 4 were found during the sixteenth century. But it was only during the nineteenth century that the problem of equations of higher degree reached a final answer: the impossibility of solving by radicals a general equation of degree at least 5, and some methods for finding some solutions by radicals when these exist. Galois and Abel certainly played a key role in the development of this theory. All these results can be found in almost every book on Galois theory … and that's the reason why we considered it useless to present them once more in the present book.

A strong peculiarity of those developments about solving equations is that the methods used to reach the final goal proved to be much more interesting than the problem to be solved. Nobody uses the formulæ for solving cubic or quartic equations … but their consideration forced the discovery of complex numbers. And the impossibility proof for equations of higher degree led to specifying the notion of group, on the interest of which it is unnecessary to comment.

Let us now sketch, in modern language, the central result used by Galois to prove his celebrated theorem.

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Galois Theories , pp. vii - xiv
Publisher: Cambridge University Press
Print publication year: 2001

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  • Preface
  • Francis Borceux, Université Catholique de Louvain, Belgium, George Janelidze
  • Book: Galois Theories
  • Online publication: 11 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511619939.001
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  • Preface
  • Francis Borceux, Université Catholique de Louvain, Belgium, George Janelidze
  • Book: Galois Theories
  • Online publication: 11 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511619939.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preface
  • Francis Borceux, Université Catholique de Louvain, Belgium, George Janelidze
  • Book: Galois Theories
  • Online publication: 11 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511619939.001
Available formats
×