*Notices Amer. Math. Soc.*

**46**(4) (1999), 461-462:

It is a great honour to receive the Steele Prize for Lifetime Achievement. I am very happy to accept it. This award is given occasionally, I'm sure, to people who can say that they did it all alone. That is certainly not the present case. I collaborated during much of my career with people who are splendid mathematicians as well as dear friends. My students, both graduate and postdoctoral, taught me much of what I know. My teachers during my graduate student days were a constant source of inspiration and support. To all of these people I owe a great debt of gratitude for whatever success I may have had.

The field in which I have worked for a large part of my life is the theory of operator algebras. I have had the good fortune to watch it flourish and make contact with most of mathematics and physics and a good many other subjects as well. Heisenberg and Schrödinger taught us that the analysis that goes with quantum physics is of a very special sort. Dirac and von Neumann formulated that *noncommutative *analysis in terms of operators on a Hilbert space and the algebraic interrelations among those operators. The physical observables of a quantum system are modelled by self-adjoint operators on such a space. With that as one of the principal grounds for Dirac and von Neumann's study, it was clear that the algebras of such operators are important mathematical constructs. It rapidly became clear as well that their structure was complicated and rich enough to keep an army of research mathematicians occupied for quite some time. The few of us at work on the subject fifty years ago knew that we would not be short of fascinating mysteries to occupy our thoughts.

It wasn't certain, however, that we would have much company on that journey of discovery. As it turned out, a formidable force of remarkably talented and dedicated researchers gathered and joined us. As with all the great fields of mathematics, this group included a small number of brilliant practitioners. They give the field much of its lustre and direction. We are lucky to have our supply of such people. There are an encouraging number of very talented young mathematicians able and willing to join the ranks of serious researchers in all the great fields. They aren't expecting (nor will they find!) an easy life. A wise society would care for and make the best use of this precious resource.

It has been my privilege and joy to be among the workers in my field throughout most of my career. I'm hoping to continue working with them for some years to come.