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In the 30’s, Witt initiated the study of quadratic forms over a general
field by introducing the Witt group of a field. This study gained great momentum
in the 60’s by Pfister’s theory of multiplicative forms, now called Pfister forms.
Pfister’s theory led to the solution of several longstanding problems on quadratic
forms and several new quesions and conjectures were thrown open. One such is the
Milnor conjecture on the classification of quadratic forms via Galois cohomological
invariants. The first few of these invariants, the so-called classical invariants, can
be explained in terms of the Clifford algebra of the quadratic form. In this talk, we
shall describe some major developments in this direction.
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