Remembering the Mathematics of Robert Brown Gardner

Robby Gardner, one of the organizers of this Summer Research Institute, passed away on May 5, 19981. Robby led an extremely active mathematical life producing more than fifty papers, three books, eighteen masters students and thirteen Ph.D students. He seemed to spend a sizeable fraction of every year traveling to conferences and meetings around the world. I was continually amazed by the number of mathematicians who had met Robby. He was one of those personalities that everyone, regardless of field, knew. Robby was part of a long heritage of great differential geometers, tracing a direct line from Élie Cartan, through S.S. Chern, to himself. Robby’s own mathematical interests clearly reflect this lineage. Even a casual observer of Robby’s work could not help noticing the central role of exterior differential systems. Nor could anyone fail to notice Robby’s enthusiasm for Cartan’s work and his vigorous efforts to bring this work to a much larger audience. Robby certainly succeeded. Numerous “heirs to Cartan” dot the current mathematical landscape, and many of them have Robby as an ancestor on their family tree. Robby’s mathematical interests covered a number of areas. A list of these areas includes the following: • geometric partial differential equations • Cartan’s equivalence method • Cartan’s method of moving frames • exterior differential systems