Is the Quintic Unsolvable?

  • Jeremy Gray
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


In this chapter, we turn to what today is regarded as a different branch of algebra, the solution of polynomial equations, although Gauss’s work on the ‘higher arithmetic’ was not automatically regarded as being part of algebra. We shall find that polynomial algebra also evolved in the direction of deepening conceptual insight, so here we witness again one of the origins of the transformation from school algebra to modern algebra.


  1. Gauss, C.F.: Demonstratio nova altera theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse. Comm. Recentiores (Gottingae) 3, 107–142 (1816). In Werke, vol. 3, pp. 31–56Google Scholar
  2. Lagrange, J.-L.: Réflexions sur la résolution algébrique des équations. Nouv. Mém de l’Académie des Sciences, Berlin, pp. 222–259 (1770/71); in Oeuvres de Lagrange 3, 205–404, J.-A. Serret (ed.) ParisGoogle Scholar
  3. Lagrange, J.-L.: Traité de la résolution des équations numériques de tous les degrés, Paris (1st ed. 1798, 3rd ed. 1826) (1808); in Oeuvres de Lagrange 8, J.-A. Serret (ed.) ParisGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jeremy Gray
    • 1
    • 2
  1. 1.School of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

Personalised recommendations