George Forsythe and the Development of Computer Science by Donald E. Knuth The sudden death of George Forsythe this spring was considered such combinatorial algorithms to be a part of a serious loss to everyone associated with computing. numerical analysis [46, p. 7], and he regarded automatic When we recall the many things he contributed to the programming as another branch [49, p. 655]. He began field during his lifetime, we consider ourselves fortunate to foresee the less obvious implications of programming: that computer science has had such an able leader. The use of practically any computing technique itself raises a My purpose in this article is to review George For- number of mathematical problems. There is thus a very con- sythe's contributions to the establishment of Computer siderable impact of computation on mathematics itself, and this may be expected to influence mathematical research to an in- Science as a recognized discipline. It is generally agreed creasing degree. [46, p. 5] that he, more than any other man, is responsible for the The automatic computer really forces that precision of thinking rapid development of computer science in the world's which is alleged to be a product of any study of mathematics. colleges and universities. His foresight, combined with his [49, p. 655l untiring efforts to spread the gospel of computing, have He also noticed that the rise of computers was being had a significant and lasting impact; one might almost accompanied by an unprecedented demand for young regard him as the Martin Luther of the Computer Re- mathematicians: formation! The majority of our undergraduate mathematics majors are lured Since George's publications express these ideas so at once into the marketplace, where they are greatly in demand well, I believe the best way to summarize his work is to as servants of the fast-multiplying family of fast-multiplying com- puters. [49, p. 651] repeat many of the things he said, in his own words. This article consists mainly of the quotations that particularly Therefore he began to argue th,at computers should struck me as I reread his papers recently. Indeed, much of play a prominent role in undergraduate mathematics edu- what follows belongs in a computer-science supplement cation. At this time he felt that only one new course was to Bartlett's Familiar Quotations. needed for undergraduates, namely an introduction to programming; he stressed that the best way to teach it From Numerical Analysis to Computer Science would be to combine computer programming with the George's early training and research in numerical traditional courses, instead of having separate training in analysis was a good blend of theory and practice: numerical analysis. His paper "The Role of Numerical The fact that the CPC was generally wrong when I knew the Analysis in an Undergraduate Program" [49] suggests answer made me wonder what it was like for someone who didn't over 50 good ways to mix computing into other courses; know what to expect. [76, p. 5] these suggestions ought to be required reading for all Starting in 1948 he worked for the National Bureau of teachers today, since they are now perhaps even more Standards' Institute for Numerical Analysis in Los Ange- relevant than they were in 1959. Indeed, the ad'aptation les, California, where he did extensive programming for of traditional courses has been painfully slow (probably the SWAC computer. In 1954 this Institute became part of because professors of the older generation have not U.C.L.A., and he put a great deal of energy into the teach- wanted to dirty their hands with the newfangled ma- ing of mathematics and numerical analysis. He also worked chines) ; in 1970 Forsythe was still strongly urging math- on nonnumerical problems, such as the tabulation of all ematics teachers to bend a little: possible semigroups on four elements; at this time, he Compared with most undergraduate subjects, mathematics courses 721 Communications August 1972 of Volume 15 the ACM Number 8 are very easy to prepare for, because they change so slowly. The gradually been working its way into the English language, computing part of it is probably the only part that changes much. but his influence was an important factor in the present Why not devote time to learning that? [80, p. 23] widespread acceptance of the term. In 1961 we find him using the term "computer sci- A brief digression into the history of computer sci- ence" for the first time in his writing: ence education seems appropriate at this point. Appar- [Computers] are developing so rapidly that even computer scien- ently computing courses got started in universities largely tists cannot keep up with them. It must be bewildering to most mathematicians and engineers...In spite of the diversity of the because IBM donated about 100 "free" computers dur- applications, the methods of attacking the difficult problems with ing the 1950s, with the stipulation that programming computers show a great unity, and the name of Computer Sciences is being attached to the discipline as it emerges. It must be under- courses must be taught. This strategy made it possible stood, however, that this is still a young field whose structure is for computing to get its foot in the academic door. Natur- still nebulous. The student will find a great many more problems ally there were many students and a few members of the than answers. [59, p. 177] faculty who were intrigued and became involved. Engi- He identified the "computer sciences" as the theory of neering departments, especially at schools like M.I.T., programming, numerical analysis, data processing, and Pennsylvania, and Illinois, where computers were being the design of computer systems, and observed that the built, also had a head start. Many ideas were exchanged latter three were better understood than the theory of during special summer school sessions at the University programming, and more available in courses. of Michigan, and later the Ford Foundation sponsored a project there on the use of computers in engineering The Establishment of Computer Science education. A good survey of these developments has By that time Forsythe knew that numerical analysis been given by Howard E. Tompkins in Advances in Com- was destined to be only a part of the computing milieu; a puters Vol. 4, Academic Press, New York, 1963, pp. new discipline was crystallizing which cried out to be 135-168. taught. He had come to Stanford as a professor of math- But these early stages hardly represented computer ematics in 1957, but now he and Professor John Herriot science as it is understood today, nor did many people wanted to hire colleagues interested in programming, regard it as the germ of a genuine discipline worthy of artificial intelligence, and such topics, which are not con- study on a par with other subjects. I myself was a gradu- sidered mathematics. Stanford's administration, espe- ate student in mathematics who enjoyed programming cially Dean Bowker (who is now Chancellor at Berkeley), as a hobby; I had written two compilers, but I had no idea also became convinced that computing is important; so that I would someday be teaching about data structures George was able to found the Division of Computer and relating all this to mathematics. A few people, like Science within the Mathematics Department in 1961. George Forsythe and Alan Perlis and Richard Hamming, During that academic year he lectured on "Edu- had no such mental blocks. Louis Fein had also perceived cational Implications of the Computer Revolution" at the eventual rise of computer science; he had recom- Brown University: mended in 1957 that Stanford establish a Graduate "Machine-held strings of binary digits can simulate a great many School of Computer Science, analogous to the Harvard kinds of things, of which numbers are just one kind. For example, they can simulate automobiles on a freeway, chess pieces, elec- Business School. (cf. reference [B] below.) trons in a box, musical notes, Russian words, patterns on a paper, George argued the case for computer science long human cells, colors, electrical circuits, and so on. To think of a and loud, and he won; at Stanford he was in fact "the computer as made up essentially of numbers is simply a carry- over from the successful use of mathematical analysis in studying producer and director, author, scene designer, and cast- models...Enough is known already of the diverse applications ing manager of this hit show." [A] Several more faGulty of computing for us to recognize the birth of a coherent body of members were carefully selected, and the Division be- technique, which I call computer science...Whether computers are used for engineering design, medical data processing, com- came a separate academic department in January 1965. posing music, or other purposes, the structure of computing is Since this was one of the first such departments, it much the same. We are extremely short of talented people in this naturally came under very close scrutiny. Now we realize field, and so we need departments, curricula, and research and degree programs in computer science...I think of the Computer that eventually every university will have such a depart- Science Department as eventually including experts in Program- ment. Although this development is inevitable in the long ming, Numerical Analysis, Automata Theory, Data Processing, run, it will happen sooner than might be expected largely Business Games, Adaptive Systems, Information Theory, Infor- mation Retrieval, Recursive Function Theory, Computer Linguis- because George was such an effective spokesman, espe- tics, etc., as these fields emerge in structure...Universities must cially to mathematicians and to people in the government.