Otto Schreier (3 March 1901 in Vienna, Austria – 2 June 1929 in Hamburg, Germany) was a Jewish-Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups. He studied mathematics at the University of Vienna and obtained his doctorate in 1923, under the supervision of Philipp Furtwängler. He then moved to the University of Hamburg.
Significance of the Artin–Schreier theorem
According to Hans Zassenhaus:
O. Schreier's and Artin's ingenious characterization of formally real fields as fields in which –1 is not the sum of squares and the ensuing deduction of the existence of an algebraic ordering of such fields started the discipline of real algebra. Really, Artin and his congenial friend and colleague Schreier set out on the daring and successful construction of a bridge between algebra and analysis. In the light of Artin-Schreier's theory the fundamental theorem of algebra truly is an algebraic theorem inasmuch as it states that irreducible polynomials over real closed fields only can be linear or quadratic.