Donald Knuth

Donald Knuth the American computer scientist and mathematician (born 1938) whose systematic analysis of algorithms and invention of the TeX typesetting system shaped both the theory and the practice of computing. He is the author of The Art of Computer Programming, one of the most influential works in the field, and the recipient of the 1974 Turing Award.

Early Life and Education

Donald Ervin Knuth was born on 10 January 1938 in Milwaukee, Wisconsin, where his father ran a small machine shop and taught mathematics. As a schoolboy he was exceptionally gifted and won a contest to find words beginning with the letters of the alphabet, and he later wrote for a campus humour magazine. He entered the Case Institute of Technology intending to study physics but soon turned to mathematics, graduating in 1960 and earning a master's degree from the same institution in 1961.

He completed a doctorate in mathematics at the California Institute of Technology in 1963, advised by the mathematician Marshall Hall, with a dissertation on finite projective planes. He then joined the faculty of Caltech and began to work seriously on computing, a field in which he would combine mathematical rigour with a love of programming. Colleagues recalled his extraordinary productivity and his habit of working far into the night.

The Analysis of Algorithms

Knuth argued that computer programs and the algorithms they implement could and should be studied with the same rigour as mathematical objects. His books and papers on sorting and searching established the systematic analysis of algorithms, in which the running time and memory use of a method are quantified and compared rather than judged by anecdote. He introduced widely used notations and concepts for this purpose, including the asymptotic notation now written with a large O.

His study of sorting and searching techniques, of data structures such as trees and hash tables, and of the mathematical analysis that predicts their performance, became part of the foundation of computer science. He favoured approaches that could be proved efficient, and he showed how combinatorial mathematics could settle questions about the behaviour of programs. The combination of careful theory with attention to practical implementation distinguished his work from both pure mathematics and ordinary programming.

The Art of Computer Programming

In 1962 Knuth contracted to write a book on compilers, which grew into a far larger project. The first volume of The Art of Computer Programming appeared in 1968, and further volumes followed over the ensuing decades. The work presents the fundamental algorithms of computing with exhaustive analysis and exercises of great difficulty, and many consider it the definitive reference in the field and a monument of technical exposition.

While preparing later volumes he became dissatisfied with the typesetting of his mathematics and with the changing technology of printing. This frustration led him to design a new typesetting system, TeX, and a companion font design system, Metafont, released in the late 1970s and made freely available. TeX produced beautifully composed mathematical text and became the standard tool for scientific publishing, especially in mathematics and physics.

Literate Programming and Further Contributions

Knuth introduced the idea of literate programming, in which a program is written to be read by human beings, with the code interspersed with explanatory prose in an order that suits the human understanding; the computer then extracts the machine-executable form. The concept invited programmers to regard their work as literature as well as engineering, and it influenced the development of documentation practices and of programming tools.

He has also worked on the theory of context-free languages, on attribute grammars, and on the analysis of ancient texts. A long-running project examined the problem of reconstructing the original text of the Bible from ancient sources, applying combinatorial methods to the classification of manuscript variants. His breadth across mathematics, computing and scholarship is unusual even among the leaders of the field.

Influence and Legacy

Knuth received the Turing Award in 1974 for his contributions to the analysis of algorithms and the design of programming languages, and he later received the National Medal of Science and many honours besides. His name is attached to the Surreal Numbers, to the MIX and MMIX model computers used in his books, to Knuth's up-arrow notation, and to a celebrated reward for finding errors in his work. The TeX system he created still typesets most of the world's mathematics.

He is remembered as the scholar who gave computer programming an intellectual foundation and a literature. Through The Art of Computer Programming he taught generations to think rigorously about efficiency, and through TeX he gave scientists a tool that improved the communication of their ideas. He has said that he retired early to devote himself to his books, and his long dedication to that project exemplifies his ideal of careful, lasting work.

See also

• The Art of Computer Programming
• TeX
• Analysis of algorithms
• Literate programming