Donald E. Knuth lived two separate lives in the late 1950s. During daylight he ran down the visible and respectable lane of mathematics. During nighttime, he trod the unpaved road of computer programming and compiler writing. Both roads intersected -- as Knuth discovered while reading Noam Chomsky's book Syntactic Structures on his honeymoon in 1961. "Chomsky's theories fascinated me, because they were mathematical yet they could also be understood with my programmer's intuition. It was very curious because otherwise, as a mathematician, I was doing integrals or maybe was learning about Fermat's number theory, but I wasn't manipulating symbols the way I did when I was writing a compiler. With Chomsky, wow, I was actually doing mathematics and computer science simultaneously." How, when, and why did mathematics and computing converge for Knuth? To what extent did logic and Turing machines appear on his radar screen? The early years of convergence ended with the advent of Structured Programming in the late 1960s. How did that affect his later work on TeX? And what did "structure" come to mean to Knuth? Shedding light on where computer science stands today by investigating Knuth's past -- that's what this booklet is about.

"What an absolutely cool guy " --- Dennis Shasha, NYU "Fascinating... very worthwhile" --- Robert Harper, CMU What mathematical rigor has and has not to offer to software engineers. Peter Naur wrote his first research paper at the age of 16. Soon an internationally acclaimed astronomer, Naur's expertise in numerical analysis gave him access to computers from 1950. He helped design and implement the influential ALGOL programming language. During the 1960s, Naur was in sync with the research agendas of McCarthy, Dijkstra, and others. By 1970, however, he had distanced himself from them. Instead of joining Dijkstra's structured programming movement, he made abundantly clear why he disapproved of it. Underlying Naur's criticism is his plea for pluralism: a computer professional should not dogmatically advocate a method and require others to use it in their own work. Instead, he should respect the multitude of personal styles in solving problems. What philosophy has to do with software engineering. Though Peter Naur definitely does not want to be called a philosopher, he acknowledges having been influenced by Popper, Quine, Russell, and others. Naur's writings of the 1970s and 1980s show how he borrowed concepts from philosophy to further his understanding of software engineering. In later years, he mainly scrutinized the work in philosophy and mathematical logic & rules in particular. By penetrating deeply into the 1890 research of William James, Naur gradually developed his own theory of how mental life is like at the neural level of the nervous system. This development, in turn, helps explain why he always opposed the Turing Test and Artificial Intelligence, why he had strong misgivings about the Formal Methods movement and Dijkstra's research in particular.

Contrary to what many believe, Alan Turing is not the father of the all-purpose computer. Engineers were, independently of Turing, already building such machines during World War II. Turing's influence was felt more in programming after his death than in computer building during his lifetime. The first person to receive a Turing award was a programmer, not a computer builder. Logicians and programmers recast Turing's notions of machine and universality. Gradually, these recast notions helped programmers to see the bigger picture of what they were accomplishing. Later, problems unsolvable with a computer influenced experienced programmers, including Edsger W. Dijkstra. Dijkstra's pioneering work shows that both unsolvability and aesthetics have practical relevance in software engineering. But to what extent did Dijkstra and others depend on Turing's accomplishments? This book presents a revealing synthesis for the modern software engineer and, by doing so, deromanticizes Turing's role in the history of computing.