Lagrange’s Theory of Quadratic Forms

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


It was Lagrange who sought to produce a general theory of quadratic forms, after Euler had published a number of deep and provocative studies of many examples—what would today be called ‘experimental mathematics’. In this chapter we look at one key idea in his treatment: the reduction of forms to simpler but equivalent ones. We are led to one of the great theorems in mathematics: quadratic reciprocity. It was conjectured well before it was proved for the first time, as we shall see later.


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© 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

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