An elementary proof of Hilbert's theorem on ternary quartics: Some complements

2024/11/13 by Albrecht Pfister, Pfister, Albrecht, Claus Scheiderer +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2411.08479

openalex publication_date 2024/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1888, Hilbert proved that every nonnegative quartic form f=f(x,y,z) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry. In a 2012 paper we presented a new approach that used only elementary techniques. In this note we add some further simplifications to this proof.

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