# Karen Uhlenbeck

Karen Uhlenbeck (1942-) was born in Cleveland, Ohio and is the daughter on an engineer and an artist. O’Connor and Robertson note that she is an expert in the field of partial differential equations and has served on the editorial boards of many professional journals. She has been active in promoting the careers of women in mathematics and has lamented that so few women enter the field.

Ms. Uhlenbeck initially wished to be a physicist, but she switched to mathematics while an undergraduate at the University of Michigan. She gained a B.S. in math from Michigan in 1964, received a master’s from Brandeis, and then her Ph.D from that same school in 1968. She had several non-tenure track appointments—at M.I.T. and U.C. Berkeley—and had trouble in finding a permanent position at a top flight school, trouble she believes had to do with the fact that she was female. She finally did get a tenure track job at the University of Illinois, Urbana, and was prompted to full professor at the University of Illinois at Chicago in 1983. In 1988 she was given the Sid W. Richardson Foundation Regents chair at the University of Texas.

A derivative of a function is the “infinitesimal change in the function with respect to whatever parameters it may have”. An ordinary differential equation is one in which an equality involving a function and its derivatives are expressed. A partial derivative is a derivative of a function with multiple variables in which all the variables save the variable of interest are held constant. A partial differential equation is therefore the expression of an equality in which partial derivatives and their functions appear as terms. As students of calculus know, a partial derivative of a function representing a figure in space will be the instantaneous rate of change of the function with respect to a unit of change along one axis. Weisstein notes that partial differential equations are very difficult to solve (2154) and the field is considered to be one of the more difficult branches of mathematics. Because they are very useful for the analysis of geometric objects, Uhlenbeck states, “they are used…in a technical fashion to look at shapes in space”. It is in this topological application of partial differential equations that Uhlenbeck is an acknowledged expert.