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A new section about Pythagoras number for fields? The Pythagoras number is not only defined for fields, but also for general rings (at least for commutative ones). For example, in the book Pfister: Quadratic Forms with Applications in Geometry and Topology, Chapter 7 is about the Pythagoras number, with §1 being called "Results for fields" and §2 "Results for rings". And it contains quite a few interesting results. I suggest to create a new, quite short section about this more general definition and some results (e.g. that the Pythagoras number of an order in a number field K is at most 5 unless K is totally real [Example 2.4 b) in Pfister's book], Rudolf Scharlau's construction of orders in totally real number fields with arbitrary large Pythagoras number [Example 2.4 c)], or the quite recent proof that the Pythagoras number of an order is bounded by a constant depending only on the degree of the field which contains it [Kala, Yatsyna, Lifting problem for universal quadratic forms]. I'd write such a section myself, but 1) I'm not a native speaker and I don't know whether Wikipedia appreciates texts with my level of English, 2) I plan to do research in exactly this area of number theory, and while my motivation is not self-promotion, it still doesn't seem quite fair. Thanks for any reaction, I'm quite inexperienced as a Wikipedist. Cheeseruch (talk) 13:54, 3 July 2021 (UTC)