2009/11/13 by Ján Mináč, Jan Minac, Minac, Jan · 1 voice
Arts and Humanities · Mathematics · Social Sciences · #11E81 #Byzantine Studies and History #Classical Antiquity Studies #FOS: Mathematics #History and Overview (math.HO) #Law in Society and Culture #Number Theory (math.NT) #math.HO #math.NT #msc:11E81
paper · pdf · doi:10.48550/arxiv.0911.2529
9 pages
arxiv created 2009/11/13 · openalex publication_date 2009/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the mid-1960s A. Pfister discovered extraordinary, strongly multiplicative forms which are now called Pfister forms. From that time on, these forms played a dominant role in the theory of quadratic forms. One of the key properties of a Pfister form q is that q extended to a suitable transcendental extension, has the polynomial q as its similarity factor. Pfister's original proof used clever matrix calculations. Here we show that the desired isometry is induced by the multiplication of a suitable field element. We further consider the surprising possibility that Pfister's forms were already known by Hamlet, Rosencrantz and Guildenstern, and that they in fact led to a terrible tragedy which is yet filled with a haunting beauty and mystery that can still inspire us to this day.