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

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George Forsythe5

Stanford University computer scientist 1917–1972

Ivars Peterson (1948) Canadian mathematician

Source: The Mathematical Tourist: New and Updated Snapshots of Modern Mathematics (1998), Chapter 1, “Explorations” (p. 10)

“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

“Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology.”

Doron Zeilberger (1950) Israeli mathematician

“If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.”

George Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. 2

“It’s time to let the secret out: mathematics is not primarily a matter of plugging numbers into formulas and performing rote computations. It is a way of thinking and questioning that may be unfamiliar to many of us, but is available to almost all of us.”

John Allen Paulos book A Mathematician Reads the Newspaper

Introduction (p. 3)
A Mathematician Reads the Newspaper (1995)

“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

“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