Bill Gear Honored for Three Decades of Achievements at Illinois

April 3, 2002

Bill Gear is the first computer scientist whose portrait appears in the "alumni hall of the fame" at the University of Illinois, Urbana-Champaign.

Paul Saylor, Ryan Szypowski, and Judy Tolliver

Gaining eminence and renown by writing a technical book is asking a lot, but it can happen. Publication of the book Numerical Initial Value Problems in Ordinary Differential Equations (1971) had precisely that effect for Bill Gear. "Almost overnight, a set of previously intractable equations could be dealt with on a routine basis," wrote Kahaner, Moler, and Nash in their book Numerical Methods and Software. Gear's name was heard about as often among computational scientists as the word "gear" among designers of racing bicycles. Gear did this influential work at the University of Illinois, Urbana-Champaign, with which he was closely associated for three decades, starting as a graduate student (in 1956) and ultimately serving as head of the department (1985-90) before moving on to another stage of his career. In recognition of his achievements, the Alumni Association made Gear the first computer scientist whose portrait would hang in a corridor of the campus student union in what can be called an "alumni hall of fame."

Gear's English accent reveals his origins to his American listeners and, to the more astute among them, his London background. For Gear, the World War II years and the danger to Londoners meant long periods of time spent away from his home in the London suburbs. His childhood fascination with electrical and mechanical devices went beyond the play of a clever child, a distraction from the siege atmosphere, to an intellectual interest and ultimately to enrollment at Cambridge University as a scholarship student in mathematics.

Getting to elite American research universities was a common goal among English graduates in the "Brain Drain" era, 1950-1960. Gear's teachers encouraged him to apply for a fellowship, advising him to avoid MIT, Harvard, and other usual institutional choices and consider places off the beaten path. It was David Wheeler, a Cambridge mathematician and member of the EDSAC (Electronic Delay Storage Automatic Calculator) project in the early fifties, who suggested Illinois.

Go to the edge of the agricultural region bordering Chicago, and imagine the reaction of a student from another part of the world seeing it for the first time. It is vast, distinctive, exotic, and obviously manmade on an immense scale. Gear paused in Chicago before completing his journey through stretches of the flat prairie that had been converted to huge, uniform croplands. The university campus and the community containing it form an island in the surrounding sea of corn and soybeans. Classes, assistantship duties, and adjustments to a new setting soon establish a routine for students, leaving the prairie milieu forgotten. The agreeable campus life, punctuated by occasional trips to Chicago, led Gear to stay on for four years rather than the one-year commitment typical of other British students.

Growth in education and research in the Digital Computer Lab, the precursor of the Department of Computer Science, meant classes, exams, research projects, thesis approvals and, most of all, finding and working with an adviser. For Gear this was Abe Taub, head of the Computer Lab, an applied mathematician who had made contributions to relativity theory and hydrodynamics. Exactly two computer classes were offered: a programming class taught by Dave Muller and a class in logic design taught by Jim Robertson (the "R" in the SRA division algorithm). As Muller's research assistant, Gear wrote library routines in machine language for the ILLIAC and later switched to work on computer architecture and the ILLIAC II with Don Gillies. Rules requiring that thesis topics be in a different area from assistantship duties resulted in Gear's working on a topic in numerical analysis, with Taub as adviser. He worked hard, went to movies occasionally, enjoyed the sociability of life in the computer lab, married and became a father, bought a fifteen-dollar TV, and earned a PhD, all by 1960.

Gear exchanged a research position at Illinois---half-time in architecture---for a full-time job at IBM British Laboratories. On a salary that amounted to half his Illinois stipend, the new IBM architect helped design the company's first microprogrammed computer, with many fun hours using an oscilloscope for debugging. The project finally lost out in internal competition against the 7044. Gear spent his last few months at IBM on the System/360 design team, which got him back to the U.S. several times for meetings in Poughkeepsie with IBM researchers, including Gene Amdahl and Fred Brooks. Only weeks before the family's return to the U.S., Gear became a father for the second time; much later, he admitted to concealing some heavy items under his new son on the flight back in order to avoid weight restrictions on luggage.

Gear's employment in the academic ranks resulted from an offer to join an Illinois "predepartment" as an assistant professor. The group he was joining consisted of fewer than ten faculty in computer science. Even with the usual demands on a new faculty member, he found the time to write an assembler for the ILLIAC II plus an operating system, which made it possible for the university to actually use the machine. Never mind that software and programming counted little toward getting tenure. And he wrote a compiler.

Great error analysis runs deep inside quality system software, as it does in quality numerical software, only it shows up in the form of help messages. One of the system software error messages in Gear's Fortran compiler resulted in an amusing incident. The compiler for the ILLIAC II was based on the IBM 7094's, so that users could run the same job on both machines. One day, Gear recalls, a physicist was running a large program on ILLIAC II, and the compiler complained about it. "It was one of those strange errors," Gear says. "It was deep in the guts of the program and I couldn't figure out how it would ever get to that point, but I put a message in that said 'If you see this message, please see Gear.' It was an option on a branch that I didn't think could happen. The physicist came running over, complaining that his program ran on the 7094 and not on the ILLIAC. It turned out that the input contained an error. A plus sign was missing, and the 7094 assumed multiplication. So the program ran on the 7094, but the answer it got was wrong."

Gear's elegant and rich results in stiff equations are the contributions for which he is best known. He got his start in numerical ordinary differential equations as a graduate student of Taub. Further encouragement came from Leslie Fox, during a visit to Illinois from Oxford.

Gear's extracurricular activities in research at Argonne National Laboratory presented him with a challenge that led to his great work in stiff methods. In what amounted to a dare, a chemist at the lab declared that his group was using an analog computer to solve problems that Gear and his digital computers couldn't even touch. At the time, in fact, solving stiff equations on a digital computer was time consuming and not practical. Taking up the challenge, Gear thought about better ways to solve such equations digitally.

The great English astronomers rarely did astronomy and nothing else. Newton was a prime example, John Couch Adams another. Adams was a computational mathematician of a high order, as seen in his development of a family of methods for solving differential equations. Nearly a century later, the Adams methods were ready when Gear needed to draw on them for his work on stiff equations. He took advantage of a variety of other techniques as well, such as automatic error control, to produce the end result, a Fortran routine known as DIFSUB. He described the overall effort in a recent conversation: "I rediscovered methods that already existed, but I put them together in a different way and coded them to get the characteristics needed. I found that people had already used these methods, but not as effectively, probably because they didn't fully understand them. So I popularized them and put them into automatic code, which is what got them into big use."

A good educator, active in research, Gear was prominent in the computer science department, becoming its chair in 1985. By that time the department had grown to about thirty people. Gear's research, which began with a PhD thesis in applied mathematics and numerical methods, had expanded to include software, computer architectures, and computer graphics. Later on at Illinois, he moved more and more to mathematical software and computational science, which were his main interests by 1990, when he was recruited to head the newly formed computer science division of the NEC Research Institute in Princeton, New Jersey.

Gear edged into another realm of computer science in his work at NEC. The Research Institute is a collaborative facility focused on long-term, fundamental research in computer and physical science. Only two years after his arrival, the president of the lab died, and Gear was appointed to succeed him.

Gear experienced the age-determined retirement customary for employees of his Japanese company when he had his sixty-fifth birthday in February 2000. In the course of his long career, he wrote fourteen books and more than sixty papers. He was named a fellow of ACM, IEEE, and AAAS, and a member of the National Academy of Engineering. Along the way, he served a term as president of SIAM (1987-88) and received a Fulbright fellowship.

A good eye for attractive research opportunities has served Gear well. In his retirement, he continues to conduct research on his own. "I'm doing work in computer vision and a few other things-whatever takes my fancy," he says. "And I don't have to keep a sponsor satisfied with the results."

Gear enjoys a reputation as a man who knows how to pilot a sailboat, but his modest enjoyment of his achievements in computer science and mathematics does not allow acknowledgment of eminence or renown. Let others say that his first book bestowed eminence and renown. Eminence and Renown? Suitable as names for a boat, perhaps, though not one of Gear's. To own Eminence would mean that someone would hear "his Eminence" but think it was "His Eminence." As for names, perhaps Discovery, a virtual ship that he has always been sailing on. In fact, sailing has become more virtual than real for Gear since he sold the boat that had been moored in his garage. He is looking forward to other pleasures, including travel and visits with his grandchildren. His passion for the theater takes him and his wife Ann to London each year to see Shakespeare performed at the National Theatre. And he is a fan of the opera.

Note to readers: The lead author points out that Gear's name has been woven into the text at the beginning of each paragraph, as an acronym. Thus, for example, "Gear Enjoys A Reputation."

Paul Saylor is a program director in the Division of Mathematical Sciences at the National Science Foundation. He was formerly a professor of computer science at the University of Illinois, Urbana. Ryan Szypowski is a graduate student in computer science at the University of Illinois, Urbana. Judy Tolliver is coordinator of alumni relations and development at the University of Illinois, Urbana.

The opinions, findings, conclusions, or recommendations expressed in this article are those of the authors and do not reflect the views of the National Science Foundation.

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