The field of operator algebras was begun by von Neumann early in the last century, shortly after the discovery of quantum mechanics, with two important papers around 1930, one of them the bicommutant theorem for weak operator closed *-algebras of bounded operators, the beginning of what is now von Neumann algebra theory, and the other the uniqueness (up to multiplicity) of a representation of the Heisenberg commutation relations, for finitely many degrees of freedom. The latter theorem, and its proof, presaged the abstract theory of C*-algebras developed by Gelfand and Naimark over ten years later. It also raised the challenge, met by Gaarding and Wightman over twenty years later, followed up by Mackey, Glimm, Effros, and others, of refuting this uniqueness in the case of infinitely many degrees of freedom.

At the same time, building on the monumental edifice created by Murray and von Neumann during the thirties, a world-wide community of operator algebraists gradually grew up, encompassing schools in a number of countries, including France, the U.K., the Soviet Union, Scandinavia, and Japan, as well as the U.S. and also Canada. More recently, Germany and several other European countries, India, Australia and New Zealand, China, and, notably, several countries in South America, have developed strong centres.

This community, bolstered by the early meetings in Baton Rouge, Kingston, and Rumania, not to mention the very early annual meeting in Canada, followed by GPOTS, developed more and more rapidly, with essential contributions to all of mathematics ranging from Connes's non-commutative Chern character to the Jones knot polynomial and Voiculescu's free probability. It is now a rare person, or meeting, that can hope to cover the field as a whole, but at least a modest attempt will be made towards that on the present occasion.

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