Remembering George Forsythe

January 8, 1998

George Forsythe (third from left) at the 1964 Gatlinburg Conference on Numerical Algebra with (from left) James H. Wilkinson, Wallace Givens, Alston Householder, Peter Henrici, and Fritz Bauer.

Paul Davis

The time before computer science was a discipline is not yet the distant past. Most of the early visionaries are gone. But many remember them and the direction they provided at a time when today's certainties were only possibilities faintly seen. George Forsythe, founding head of Stanford University's Computer Science Department from 1965 until his death in 1972, was one of the most influential of those early leaders, shaping both the discipline itself and the careers of colleagues and students, many of whom are active members of SIAM. Appropriately, a minisymposium at SIAM's 45th Anniversary Meeting at Stanford commemorated the 25th anniversary of Forsythe's death.

Rather than a formal review of Forsythe's accomplishments, the memorial minisymposium, organized by Cleve Moler, chief scientist at The MathWorks and Forsythe's eighth doctoral student, was a sort of Irish wake that celebrated the man as much as his science. Lacking a formal program or a list of speakers, the conversation among the friends and colleagues assembled in the room ranged over his time at Stanford with a mixture of anecdotes, apocryphal stories, and reminiscences of personal encounters, many of which defined the speakers' lives for decades afterward.

Cleve Moler, who organized the memorial minisymposium, credits Forsythe with the idea of incorporating working code into numreical analysis texts.

To begin the conversation, Moler drew on a presentation about Forsythe given several months earlier by James Varah of the University of British Columbia, Forsythe's 12th student. Varah had spent considerable time in Stanford's Forsythe archives gathering material about Forsythe's life and work.

A Very Personal Influence
The bare facts of Forsythe's life are impressive: co-author of four seminal books in scientific computing (and a fifth on meteorology), editor of a series of more than 75 influential books in computer science, president of the Association for Computing Machinery, scientific progenitor of many of today's leaders in scientific computation, among the first to envision computer science as a distinct discipline, and the one who gave shape to that vision in the form of Stanford's Computer Science Department.

But for those who had gathered to remember Forsythe, especially his former students, the strongest memories were not of those accomplishments but of his very personal influence on them. "Professionally," Moler said, "Forsythe was the most important man in my life. He got me to my first Gatlinburg meeting [the prestigious series on numerical linear algebra] even though the committee at that time didn't want students."

Alan George, a professor of computer science at the University of Waterloo and Forsythe number 14, had the same memory of his first Gatlinburg meeting, in 1972. He too sensed the resistance to students, but "students were way up on Forsythe's agenda."

It was Forsythe's intervention, recalls Alan George, that got him and other students to some of the early (by-invitation-only) Gatlinburg meetings: "Students were way up on Forsythe's agenda."

Forsythe arrived at Stanford in 1957, Molers freshman year at Caltech. "A bit later," Moler said, "after earning a C- at Caltech in the Apostol analysis course---not taught by Apostol!---and an A+ in John Todd's numerical analysis course, I asked Todd for advice on graduate school. He steered me to Stanford to work with Forsythe." Moler arrived in the fall of 1961, just as Beresford Parlett (Forsythe number 4) and James Ortega (Forsythe number 2) were leaving. "My first job for Forsythe," he recalls, "was fixing a bug in a program of Ortega's that accumulated inner products!"

In spite of the time Forsythe devoted to working with his 17 graduate students, once they began their own work, it always belonged to them. The papers his students drew from their theses never carried his name. Rather than dictate a beginning and an end, he would ask at some point, "When do you think you will be done?"

Correcting and Challenging
Alan George recalled going to Forsythe's office the day after giving him his very first piece of technical writing. "The manuscript was covered with blue pencil. It was completely rearranged. Arrows pointed everywhere. It made a lasting impression to see how much time this busy man had spent untangling my convoluted prose."

The urge to correct and improve wasn't limited to his students' prose. Peter Henrici had dedicated his Elements of Numerical Analysis to Forsythe. "I have Forsythe's copy of that book," Moler announced, with his characteristic laugh; "he had even corrected a typo in Henrici's dedication to him!"

George reminded the Stanford alums of the problem seminar Forsythe had run for computer science graduate students, an idea borrowed from George Pólya's seminar in Stanford's Mathematics Department. (Coincidentally, Stanford has honored both Forsythe and Pólya by naming campus buildings for them.) One of the seminar questions concerned a lattice model of a porous material: Would its center become wet when it was immersed in water? George had found a computational answer to the problem. (His insight lay in writing a program that used recursion and started computing from the center, not from the (wet) outside.)

At the seminar's next meeting, he presented his results, including his heavily commented ALGOL code. "But I hadn't indented it very well. It was ugly! Forsythe chastised me mildly after the presentation: You must never forget that programs will be read by people as well as machines. Write them carefully.'"

Forsythe challenged his department's graduate students right up to the end of their student days. While Joseph Traub was visiting Stanford, Michael Jenkins, now at Queens University, began his thesis with him, work that would culminate in the well-known Jenkins-Traub algorithm for finding roots of polynomials.

Moler recalled Jenkins's thesis presentation, at the heart of which was the proof of the algorithm's ability to find all the roots of a polynomial. At the conclusion of Jenkins's presentation, Forsythe had asked him, "If getting your PhD depended on finding an example where your method didn't work, what would you do?" Happily, Jenkins knew that overflow could be his algorithm's undoing, thereby making the connection with practical computing that Forsythe was seeking.

Establishing Computer Science As an Academic Discipline
Forsythe's profound influence on the discipline of computer science goes far beyond his founding of one of its first departments. "More than any other person," said Donald Knuth, Emeritus Professor of The Art of Computer Programming at Stanford, "he is the one responsible for establishing computer science as an academic discipline. Knuth had dressed for the occasion of the memorial symposium in a t-shirt commemorating the 32nd anniversary of the department's founding, "a much more significant number than 25!"

Forsythe's vision, says Donald Knuth, was that "computer science was something that could be taught. It wasn't just a bag of tricks."

Knuth cited Forsythe's "vision that computer science was something that could be taught. It wasn't just a bag of tricks." As a young scientist, Knuth continued, he had "enjoyed programming but didn't think of it as science in the sense of proving that a program is correct. It had never occurred to me that you could have students majoring in this subject."

Beresford Parlett interjected, "Have your views changed?"

As the laughter died away, Knuth offered an affirmative smile, and then elaborated on the impact of Forsythe's view of computer science as a discipline:

"By the time Stanford's Computer Science Department came into existence, people all over the world who we now know were born to be computer scientists were beginning to find one another. People who were good at programming, who had a certain mental outlook, could share ideas with one another. He gave a home to those people, and the result was high-bandwidth communication.

"You know every field draws people with different profiles of abilities, and every field can feel that no one appreciates how hard it is."

On a humorous note of his own, Knuth added, "But I think numerical analysis is too hard. I can't imagine debugging a program when the answer isn't an integer like 2 or 3. Those fractions [from floating-point computations] are very terrifying!"

Forsythe himself had once expressed his view of the relation between numerical analysis and computer science, in a comment symposium participants struggled in vain to recall exactly. Knuth, in a memorial article, has quoted Forsythe's quip as "Many numerical analysts have progressed from being queer people in mathematics departments to queer people in computer science departments."

The Stanford archives contain 20 boxes of Forsythe's working papers, including the meticulous notes he took at every colloquium. Since almost everyone who was anyone passed through Stanford at that time, Knuth suggested that Forsythe's notes could form the core of an intellectual history of computer science through 1972.

Moler pointed to yet another characteristic the discipline had inherited from Forsythe: "Maybe it is not as fiercely competitive as some other fields. If so, that's a legacy of Forsythe and of Gene Golub."

Building Computer Science At Stanford
Forsythe hired many now-famous computational scientists early in their careers, among them John McCarthy, the founder of artificial intelligence, Gene Golub, developer of the singular value decomposition and a former SIAM president, and Knuth himself.

Knuth described Forsythe's first efforts to recruit him from Caltech, in 1963, and his initially negative response: "No, no. Not now. Let me first finish my book on the art of computer programming. It's half done already!" The audience knew that joke: Knuth's "half-done" 1963 book now consists of three volumes in multiple editions, with four more volumes still in preparation! Happily, Forsythe persisted and Knuth moved to Stanford, where "just like Cleve, Forsythe was the most influential person in my professional life.

"I've dedicated my book Selected Papers on Computer Science to him," Knuth said. "It's a collection of general papers, many of them the result of some of his advice. He had warned me that I would be called upon to lecture to people who weren't computer scientists. 'It's hard when you don't know the audience,' he said, 'but it's a responsibility you will have.'

"He was a total role model for everyone. His sense of responsibility was contagious. He would even remind faculty to bring extra chalk when they went to certain lecture rooms!"

Sudden Loss
Even after 25 years, the shock of Forsythe's sudden illness and death seemed fresh to many of his friends. Moler somberly recalled Forsythe "telling me one day in his office that he had a doctor's appointment that afternoon for a possible ulcer. Two weeks later he was dead."

Knuth described writing a memorial article for him in the short week between Forsythe's death and Knuth's departure for a sabbatical in Norway. "His briefcase was still on top of his desk. In a drawer I found life expectancy rates for skin cancer, a disease he had in the 1960s. He knew he was ill."

Parlett concurred: "He knew he was dying. He came to Berkeley to see me in 1971, the summer before he died. The visit wasn't really needed. It was his way of saying goodbye."

A Sea Change In Numerical Analysis Texts
Forsythe's name remains important to recent generations of computational scientists because of his books, the four that carry his name as co-author and the long series in automatic computation that he edited for Prentice Hall. (Forsythe once told Moler that he earned more money from Prentice Hall royalties than from his Stanford salary!) Perhaps the most widely read of all the books is Computer Methods for Mathematical Computations, completed by Moler and Michael Malcolm after Forsythe's death.

Forsythe had originally asked Malcolm to start the book from his notes. He enlisted Moler as well when he knew he was dying. "Reviews from Pete Stewart and others made it clear that the first draft had been written by three different guys!" Moler said. "But we fixed that."

Michael Heath of the Department of Computer Science at the University of Illinois suggested that the incorporation of working Fortran code into Forsythe, Malcolm, and Moler represented a "sea change from proofs and theorems in numerical analysis texts." Moler credited Forsythe for the idea of including working code, an approach that appears as well in Bill Gear's Numerical Initial Value Problems in Ordinary Differential Equations and Alan George and Joseph Liu's Computer Solution of Large Sparse Positive Definite Systems.

"All the code for Forsythe, Malcolm, and Moler, less a few examples, fit onto 2000 IBM cards---one box full," Moler recalled. "At least you could flip through the box and read that code. When was the last time you read a disk that way?"

From boxes of punch cards and programming as a bag of tricks to Netlib's library of algorithms and theories of correctness and computability, computing has probably outstripped even Forsythe's penetrating vision. But it hasn't left behind the fruits of his friendship, teaching, and scientific leadership. Few individuals have left such a legacy: a new discipline, a world-renowned department, an ever-growing tree of influential intellectual descendants, seminal books, and personal memories that are warm and vibrant even after 25 years.

Paul Davis is a professor in the Department of Mathematical Sciences at Worcester Polytechnic Institute.

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