The Art of Computer Programming (TAOCP) is a comprehensive multi-volume monograph (Volumes 1–7) written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. As of 2026 it consists of published volumes 1, 2, 3, 4A, and 4B, with more expected to be released in the future. The Volumes 1–5 are intended to represent the central core of computer programming for sequential machines; the subjects of Volumes 6 and 7 are important but more specialized. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment of Volume 4 appeared in paperback as Fascicle 2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was released in December 2015; Volume 4, Fascicle 5 ("Mathematical Preliminaries Redux; Backtracking; Dancing Links") was released in November 2019. Volume 4B consists of material evolved from Fascicles 5 and 6. The manuscript was sent to the publisher on August 1, 2022, and the volume was published in September 2022. Fascicle 7 ("Constraint Satisfaction"), planned for Volume 4C, was the subject of Knuth's talk on August 3, 2022 and was published on February 5, 2025.
History
After winning a Westinghouse Talent Search scholarship, Knuth enrolled at the Case Institute of Technology (now Case Western Reserve University), where his performance was so outstanding that the faculty voted to award him a master of science upon his completion of the bachelor's degree. During his summer vacations, Knuth was hired by the Burroughs Corporation to write compilers, earning more in his summer months than full professors did for an entire year. Such exploits made Knuth a topic of discussion among the mathematics department, which included Richard S. Varga. In January 1962, when he was a graduate student in the mathematics department at Caltech, Knuth was approached by Addison-Wesley to write a book about compiler design, and he proposed a larger scope. He came up with a list of twelve chapter titles the same day. In the summer of 1962 he worked on a FORTRAN compiler for UNIVAC, considering that he had "sold my soul to the devil" to develop a FORTRAN compiler after ALGOL developments with Burroughs. He remained as a consultant to Burroughs over the period 1960 to 1968 while writing Volume 1 "Fundamental Algorithms". During this time, he also developed a mathematical analysis of linear probing, which convinced him to present the material with a quantitative approach. After receiving his Ph.D. in June 1963, he began working on his manuscript, of which he finished his first draft in June 1965, at 3000 hand-written pages. He had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about 1+1⁄2 hand-written pages translated to one printed page. This meant he had approximately 2000 printed pages of material, which closely matches the size of the first three published volumes. The first volume of "The Art of Computer Programming", "Fundamental Algorithms", took five years to complete between 1963 and 1968 while working at both Caltech and Burroughs. Knuth's dedication in Volume 1 reads:
This series of books is affectionately dedicatedto the Type 650 computer once installed atCase Institute of Technology,in remembrance of many pleasant evenings. In the preface, he thanks first his wife Jill, then Burroughs for the use of B220 and B5500 computers in testing most of the programs, and Caltech, the National Science Foundation, and the Office of Naval Research. Section 2.5 of "Fundamental Algorithms" is on Dynamic Storage Allocation. Parts of this are used in the Burroughs approach to memory management. Knuth claims credit for: “the “boundary-tag” method, introduced in Section 2.5, was designed by the author in 1962 for use in a control program for the B5000 computer.” Knuth received support from Richard S. Varga, who was the scientific adviser to the publisher. Varga was visiting Olga Taussky-Todd and John Todd at Caltech. With Varga's enthusiastic endorsement, the publisher accepted Knuth's expanded plans. In its expanded version, the book would be published in seven volumes, each with just one or two chapters. Due to the growth in Chapter 7, which was fewer than 100 pages of the 1965 manuscript, per Vol. 4A p. vi, the plan for Volume 4 has since expanded to include Volumes 4A, 4B, 4C, 4D, and possibly more. In 1976, Knuth prepared a second edition of Volume 2, requiring it to be typeset again, but the style of type used in the first edition (called hot type) was no longer readily available. In 1977, he decided to spend some time creating something more suitable. Eight years later, he returned with TEX, which is currently used for all volumes. Another characteristic of the volumes is the variation in the difficulty of the exercises including a numerical rating varying from 0 to 50, where 0 is trivial, and 50 is an open question in contemporary research.
Bounty for finding errors The offer of a so-called Knuth reward check worth "one hexadecimal dollar" (100HEX base 16 cents, in decimal, is $2.56) for any errors found, and the correction of these errors in subsequent printings, has contributed to the highly polished and still-authoritative nature of the work, long after its first publication.
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