“Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer.”

— John D. Barrow

Introduction
Cosmic Imagery: Key Images in the History of Science (2008)
Context: Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer.... The PC revolution has made science more visual and more immediate.... by creating films of imaginary experiences of mathematical worlds.... Words are no longer enough.

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John D. Barrow58

British scientist 1952–2020

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“The major cause [of the software crisis] is that the machines have become several orders of magnitude more powerful! To put it quite bluntly: as long as there were no machines, programming was no problem at all; when we had a few weak computers, programming became a mild problem, and now we have gigantic computers, programming has become an equally gigantic problem. In this sense the electronic industry has not solved a single problem, it has only created them, it has created the problem of using its products.”

Edsger W. Dijkstra (1930–2002) Dutch computer scientist

1970s, The Humble Programmer (1972)

“When we had no computers, we had no programming problem either. When we had a few computers, we had a mild programming problem. Confronted with machines a million times as powerful, we are faced with a gigantic programming problem.”

Edsger W. Dijkstra (1930–2002) Dutch computer scientist

Dijkstra (1986) Visuals for BP's Venture Research Conference http://www.cs.utexas.edu/users/EWD/transcriptions/EWD09xx/EWD963.html (EWD 963). <br class="br">1980s

“Computer science is still a young field. The first computers were built in the mid 1940s, since when the field has developed tremendously. Applications from the early years of computerization can be characterized as follows: the programs were quite small, certainly when compared to those that are currently being constructed; they were written by one person; they were written and used by experts in the application area concerned. The problems to be solved were mostly of a technical nature, and the emphasis was on expressing known algorithms efficiently in some programming language. Input typically consisted of numerical data, read from such media as punched tape or punched cards. The output, also numeric, was printed on paper. Programs were run off-line. If the program contained errors, the programmer studied an octal or hexadecimal dump of memory. Sometimes, the execution of the program would be followed by binary reading machine registers at the console.”

Hans van Vliet (1949) Dutch computer scientist

Source: Software Engineering: Principles and Practice, 2007, p. 2

“It soon became clear that the only real long-term solution to the problems that I encountered is to start using computers in the verification of mathematical reasoning.”

Vladimir Voevodsky (1966–2017) Russian mathematician

Univalent Foundations, Vladimir Voevodsky, IAS, March 26, 2014 http://www.math.ias.edu/vladimir/files/2014_IAS.pdf p. 13

“Computer science research is different from these more traditional disciplines. Philosophically it differs from the physical sciences because it seeks not to discover, explain, or exploit the natural world, but instead to study the properties of machines of human creation. In this it as analogous to mathematics, and indeed the "science" part of computer science is, for the most part mathematical in spirit. But an inevitable aspect of computer science is the creation of computer programs: objects that, though intangible, are subject to commercial exchange.”

Dennis M. Ritchie (1941–2011) American computer scientist

Reflections on Software Research (1984)

“Computers, it seemed, could be programmed to do almost anything but sense when someone was up to no good.”

Daniel Abraham (1969) speculative fiction writer from the United States

Source: Nemesis Games (2015), Chapter 7 (p. 76)

“With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation.”

Kenneth E. Iverson (1920–2004) Canadian computer scientist

Source: Math for the Layman (1999), Ch. 10, §D

“Are there mathematical propositions for which there is a considerable amount of computational evidence, evidence that is so persuasive that a physicist would regard them as experimentally verified?”

Gregory Chaitin (1947) Argentinian mathematician and computer scientist

Thoughts on the Riemann hypothesis http://link.springer.com/article/10.1007/BF02985392 The Mathematical Intelligencer (December 2004) vol. 26, issue 1, pp. 4–7, quote on p. 4

“A source of strength in the early days was that groups in various parts of the world were prepared to construct experimental computers without necessarily intending them to be the prototype for serial production. As a result, there became available a body of knowledge about what would work and what would not work.”

Maurice Wilkes (1913–2010) British computer scientist

Sect. 1: Pioneering Days
"Computers Then and Now" (1968)

“The use of practically any computing technique itself raises a number of mathematical problems. There is thus a very considerable impact of computation on mathematics itself, and this may be expected to influence mathematical research to an increasing degree.”

George Forsythe (1917–1972) Stanford University computer scientist

George Forsythe (1958) cited in: Computers and people Vol 23. (1974). p. 11 Pagina 11

“Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer.”

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John D. Barrow58

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