Knuth Mathematics

[Paciente Flynn]

DonaldErvin Knuth (/kəˈnuːθ/[3] kə-NOOTH; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science.[4] Knuth has been called the "father of the analysis of algorithms".[5]

Knuth is the author of the multi-volume work The Art of Computer Programming. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces.

As a writer and scholar, Knuth created the WEB and CWEB computer programming systems designed to encourage and facilitate literate programming, and designed the MIX/MMIX instruction set architectures. He strongly opposes the granting of software patents, and has expressed his opinion to the United States Patent and Trademark Office and European Patent Organisation.

Knuth received a scholarship in physics to the Case Institute of Technology (now part of Case Western Reserve University) in Cleveland, Ohio, enrolling in 1956.[11] He also joined the Beta Nu Chapter of the Theta Chi fraternity. While studying physics at Case, Knuth was introduced to the IBM 650, an early commercial computer. After reading the computer's manual, Knuth decided to rewrite the assembly and compiler code for the machine used in his school because he believed he could do it better.[12]

In 1958, Knuth created a program to help his school's basketball team win its games.[13] He assigned "values" to players in order to gauge their probability of scoring points, a novel approach that Newsweek and CBS Evening News later reported on.[12]

Knuth was one of the founding editors of the Case Institute's Engineering and Science Review, which won a national award as best technical magazine in 1959.[14][15] He then switched from physics to mathematics, and received two degrees from Case in 1960:[11] his Bachelor of Science, and simultaneously a master of science by a special award of the faculty, who considered his work exceptionally outstanding.[4][12]

In 1963, with mathematician Marshall Hall as his adviser,[2] he earned a PhD in mathematics from the California Institute of Technology, with a thesis titled Finite Semifields and Projective Planes.[16]

Knuth accepted a commission to write a book on computer programming language compilers. While working on this project, he decided that he could not adequately treat the topic without first developing a fundamental theory of computer programming, which became The Art of Computer Programming. He originally planned to publish this as a single book, but as he developed his outline for the book, he concluded that he required six volumes, and then seven, to thoroughly cover the subject. He published the first volume in 1968.[18]

Just before publishing the first volume of The Art of Computer Programming, Knuth left Caltech to accept employment with the Institute for Defense Analyses' Communications Research Division,[19] then situated on the Princeton campus, which was performing mathematical research in cryptography to support the National Security Agency.

In 1967, Knuth attended a Society for Industrial and Applied Mathematics conference and someone asked what he did. At the time, computer science was partitioned into numerical analysis, artificial intelligence, and programming languages. Based on his study and The Art of Computer Programming book, Knuth decided the next time someone asked he would say, "Analysis of algorithms".[20]

In 1969, Knuth left his position at Princeton to join the Stanford University faculty,[21] where he became Fletcher Jones Professor of Computer Science in 1977. He became Professor of The Art of Computer Programming in 1990, and has been emeritus since 1993.[22][23]

In the 1970s, Knuth called computer science "a totally new field with no real identity. And the standard of available publications was not that high. A lot of the papers coming out were quite simply wrong. ... So one of my motivations was to put straight a story that had been very badly told."[24]

From 1972 to 1973, Knuth spent a year at the University of Oslo among people such as Ole-Johan Dahl. This is where he had originally intended to write the seventh volume in his book series, which was to deal with programming languages. But Knuth had finished only the first two volumes when he came to Oslo, and thus spent the year on the third volume, next to teaching. The third volume came out just after Knuth returned to Stanford in 1973.[25]

By 2011, Volume 4A had been published.[18] Concrete Mathematics: A Foundation for Computer Science 2nd ed., which originated with an expansion of the mathematical preliminaries section of Volume 1 of TAoCP, was published in 1994. In April 2020, Knuth said he anticipated that Volume 4 will have at least parts A through F.[20] Volume 4B was published in October 2022.

Knuth is also the author of Surreal Numbers,[26] a mathematical novelette on John Conway's set theory construction of an alternate system of numbers. Instead of simply explaining the subject, the book seeks to show the development of the mathematics. Knuth wanted the book to prepare students for doing original, creative research.

In 1995, Knuth wrote the foreword to the book A=B by Marko Petkovšek, Herbert Wilf and Doron Zeilberger.[27] He also occasionally contributes language puzzles to Word Ways: The Journal of Recreational Linguistics.[28]

Knuth has delved into recreational mathematics. He contributed articles to the Journal of Recreational Mathematics beginning in the 1960s, and was acknowledged as a major contributor in Joseph Madachy's Mathematics on Vacation.[29]

In addition to his writings on computer science, Knuth, a Lutheran,[33] is also the author of 3:16 Bible Texts Illuminated,[34] in which he examines the Bible by a process of systematic sampling, namely an analysis of chapter 3, verse 16 of each book. Each verse is accompanied by a rendering in calligraphic art, contributed by a group of calligraphers led by Hermann Zapf. Knuth was invited to give a set of lectures at MIT on the views on religion and computer science behind his 3:16 project, resulting in another book, Things a Computer Scientist Rarely Talks About, where he published the lectures God and Computer Science.[35]

Knuth strongly opposes granting software patents to trivial solutions that should be obvious, but has expressed more nuanced views for nontrivial solutions such as the interior-point method of linear programming.[36] He has expressed his disagreement directly to both the United States Patent and Trademark Office and European Patent Organisation.[37]

In the 1970s, the publishers of TAOCP abandoned Monotype in favor of phototypesetting. Knuth became so frustrated with the inability of the latter system to approach the quality of the previous volumes, which were typeset using the older system, that he took time out to work on digital typesetting and created TeX and Metafont.[38]

Knuth embodied the idea of literate programming in the WEB system. The same WEB source is used to weave a TeX file, and to tangle a Pascal source file. These in their turn produce a readable description of the program and an executable binary respectively. A later iteration of the system, CWEB, replaces Pascal with C, C++, and Java.[40]

Knuth used WEB to program TeX and METAFONT, and published both programs as books, both originally published the same year: TeX: The Program (1986); and METAFONT: The Program (1986).[41] Around the same time, LaTeX, the now-widely adopted macro package based on TeX, was first developed by Leslie Lamport, who later published its first user manual in 1986.[42]

Donald Knuth married Nancy Jill Carter on 24 June 1961, while he was a graduate student at the California Institute of Technology. They have two children: John Martin Knuth and Jennifer Sierra Knuth.[43]

Knuth gives informal lectures a few times a year at Stanford University, which he calls "Computer Musings". He was a visiting professor at the Oxford University Department of Computer Science in the United Kingdom until 2017 and an Honorary Fellow of Magdalen College.[44][45]

Knuth is an organist and a composer. He and his father served as organists for Lutheran congregations. Knuth and his wife have a 16-rank organ in their home.[46] In 2016 he completed a piece for organ, Fantasia Apocalyptica, which he calls a "translation of the Greek text of the Revelation of Saint John the Divine into music". It was premired in Sweden on January 10, 2018.[47]

In 2006, Knuth was diagnosed with prostate cancer. He underwent surgery in December that year and said, "a little bit of radiation therapy ... as a precaution but the prognosis looks pretty good" in his video autobiography.[50]

Knuth used to pay a finder's fee of $2.56 for any typographical errors or mistakes discovered in his books, because "256 pennies is one hexadecimal dollar", and $0.32 for "valuable suggestions". According to an article in the Massachusetts Institute of Technology's Technology Review, these Knuth reward checks are "among computerdom's most prized trophies". Knuth had to stop sending real checks in 2008 due to bank fraud, and now gives each error finder a "certificate of deposit" from a publicly listed balance in his fictitious "Bank of San Serriffe".[51]

Knuth published his first "scientific" article in a school magazine in 1957 under the title "The Potrzebie System of Weights and Measures". In it, he defined the fundamental unit of length as the thickness of Mad No. 26, and named the fundamental unit of force "whatmeworry". Mad published the article in issue No. 33 (June 1957).[52][53]

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