Early Computer Science Adventures of a Mathematician

Abstract

I had several experiences involving computer science before I knew that it was what I was doing. The first of these took place when I was visiting the Institute for Advanced Study during the two years 1957–59. Larry Wilets, a professor of physics at the University of Washington, asked me to help him with the many calculations he needed to make in order to find the eigenvalues of a sparse binary matrix which arose from his observed data in experimental physics. He challenged me to find a graph theoretic method which would save him enormous amounts of time. I was pleasantly surprised when I solved this problem with a matrix algorithm for finding the strongly connected components of a digraph. Later I learned that in 1962 a paper was published which presented “Warshall’s Algorithm”. He had published his paper in a computer journal whereas mine appeared in the Journal of Mathematical Physics [4]. That is why the determination of the transitive closure of a binary relation is attributed to him. In 1962, I applied this method to the inversion of a sparse matrix [8]. Gabriel Kron visited me at University of Michigan to tell me about his “method of tearing” which utilizes the same method for matrix inversion. His work preceded mine.