Professor Hawkins is examining the origins and development of the theory of the structure and representation of semisimple Lie algebras. This theory is an important component of contemporary mathematics, with many applications to other areas of mathematics and physics. The historical roots of Lie algebras are entwined with many strands of 19th and early 20th century mathematics, involving the leading mathematical schools of the period. By considering together and in some detail the complex web of mathematicians and mathematical ideas that combined to produce the theory, a more realistic portrait of the development of mathematics will emerge. That is, one that does justice to the fact that mathematics grows in large part through the cross fertilization of diverse mathematical ideas, theories and perspectives originating from many sources and that the significance of a mathematical problem or theory often changes with time and circumstances. Professor Hawkins studies will also provide a broad-based case study of the growth of mathematical knowledge that will benefit philosophers of mathematics who utilize history in their philosophical studies of the nature of mathematics.
