J. Ernest Wilkins has worked on a wide variety of mathematical problems throughout his distinguished career. A member of the National Academy of Engineering who received his doctorate in mathematics from the University of Chicago at the age of nineteen, Wilkins has worked in academia, industry, and government. This videotape combines an interview with Wilkins and his Invited Address. In the interview, Wilkins describes some of the mathematical problems he has worked on and discusses some of the difficulties in trying to improve the participation of members of underrepresented groups in science and mathematics. His lecture explores a fascinating problem about heat transfer that arises in a variety of settings. With any heat engine, it is necessary to expel heat to the surroundings. One way to do this is to attach "fins" to the outer wall of the engine. The shape of the fins has a large impact on how efficiently they are able to expel heat. Wilkins examines the mathematical aspects of determining the optimal shape of such fins. The lecture is accessible to undergraduates with background in differential equations.