Gerald Goertzel (1920-2002), As I Knew Him

Herbert S. Wilf

October 25, 2004

In 1951 I was a junior at MIT, and one weekend I was in New York City and I wanted to play some duplicate bridge. I went to the headquarters of the American Contract Bridge League, in the west 50’s in Manhattan, to find a list of tournaments that I might play in. It was a Saturday, though, and their office was closed. Next door I saw an office marked “Nuclear Development Associates” (NDA), a name that intrigued me because I was then interested in nuclear physics, so I walked in and was very cordially received. In fact I was offered a summer job on the spot. My association with them continued through 1959, that is, through my graduate education at Columbia University.

NDA was composed of a large number of very bright and creative and young scientists of all sorts, headed by John Menke, and including J. Ernest Wilkins Jr. as the head of the mathematics department, and Gerald Goertzel as a consulting physicist. They were trying to develop the first nuclear reactors for electric power generation. My job with them paid for my graduate education, and more importantly brought me into contact with all of the bright people who worked there, and whose ideas and thought processes have left their marks on me to this day. For example my interest in random generation of combinatorial objects is a direct outgrowth of my work at NDA on Monte Carlo methods for simulating the operation of nuclear power plants.

Among all of the scientific staff, I remember Gerald Goertzel as one who influenced me very profoundly. He was at the time a Professor of Physics at NYU. In 1952, when I met him, it was, for me anyway, the dawn of the computer era, and I was doing as much programming as I could because I enjoyed it. Jerry taught me about programming and about computers. His world view was modular. I hadn’t ever heard of modularity before and I found it very impressive. It meant that the way to create a complex system was to break it down into small subsystems, and to describe the desired input and output of each subsystem totally independently of all of the others. If that were done diligently then one could parcel out the various subsystems to different people or groups and ask each of them to create their assigned subsystem independently. Then all of them would be collected, wired together, and would work perfectly the first time, or so the scenario went.

This philosophy of wiring together little black boxes with specified inputs and outputs in order to make a complex system was very profound and very effective, and Jerry Goertzel instructed me in that thought process quite thoroughly. I remember well the patience and the good humor and the joy of discovery that he brought to his work and to his mentoring of me. The combination of his personality and his forceful ideas was very potent medicine for me.

Later he became essentially my thesis advisor at Columbia, for my PhD thesis. I say “essentially” because the late Herbert Robbins was my nominal advisor, for the record, but in fact my technical work for the thesis was done with the inspiration and guidance of Gerald Goertzel. The title of the thesis was “The transmission of neutrons in multilayered slab geometry.” It solved the transport equation in multilayered geometry by regarding each homogeneous layer as a little black box with prescribed inputs and outputs (which point of view was Jerry’s hallmark), and it wired them together by representing each by a matrix. Then to get through the various different layers, one simply multiplied the matrices together. My name was on the thesis, but it was Jerry’s philosophy that made it happen, along with his specific advice on numerous technical problems. He was quite definitely my mentor, though that word never occurred to me.

At about the same time Jerry instructed me in the view that the roots of orthogonal polynomials are the eigenvalues of tridiagonal matrices associated with those polynomials, and that the eigenvectors of those matrices gave the weights for the corresponding Gauss quadrature. I wrote all of this up in my book Mathematics for the Physical Sciences,” published by Wiley in 1952. My name was on the book, but Jerry’s ideas and inspiration were the core of the presentation of orthogonal polynomials and Gauss Quadrature via tridiagonal matrices and their spectra..

After getting my PhD from Columbia in 1958, I left to join the faculty of the University of Illinois, and lost contact with Jerry, and saw him only a very few times before his death in 2002.