Albrecht Pfister (mathematician)
Albrecht Pfister (born November 30, 1934) is a German mathematician known for his significant contributions to quadratic form theory.
Pfister studied mathematics at the University of Göttingen, where he obtained his doctorate in 1961 under the supervision of Martin Kneser. He then became a professor at the University of Mainz, where he remained for the rest of his career.
Pfister is best known for his discovery of Pfister forms. These are certain multiplicative quadratic forms over fields, which have deep connections to the theory of valuations and orderings. Specifically, a Pfister form is a quadratic form of the type <1, a1>⊗<1, a2>⊗...⊗<1, an>, where ai are elements of the field. Pfister forms and their associated Pfister quadrics have become fundamental objects in the study of quadratic forms and algebraic geometry.
His work on Pfister forms and related topics led to important advances in understanding the structure of Witt rings of fields, the theory of formally real fields, and the algebraic theory of quadratic forms. He has authored numerous research papers and books on these subjects, and his work has had a lasting influence on the field of algebra.
Pfister received the Cantor Medal of the German Mathematical Society in 2012 for his outstanding contributions to mathematics.