“Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?”

Source: Adventures of a Mathematician - Third Edition (1991), Chapter 11, The 'Super', p. 222

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Stanislaw Ulam33

Polish-American mathematician 1909–1984

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“Isaac Newton’s Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.”

Nick Land (1962) British philosopher

"Time in Transition" https://web.archive.org/web/20121113235339/http://www.thatsmags.com/shanghai/article/777/time-in-transition (2011) (original emphasis)

“In general the position as regards all such new calculi is this - That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able - without the unconscious inspiration of genius which no one can command - to solve the respective problems, yea to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange's calculus of variations, with my calculus of congruences, and with Mobius's calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

As quoted in Gauss, Werke, Bd. 8, page 298
As quoted in Memorabilia Mathematica (or The Philomath's Quotation-Book) (1914) by Robert Edouard Moritz, quotation #1215
As quoted in The First Systems of Weighted Differential and Integral Calculus (1980) by Jane Grossman, Michael Grossman, and Robert Katz, page ii

“Calculus systematically evades a great deal of numerical calculation.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“Calculus is the mathematics of change. …Change is characteristic of the world.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.”

Giuseppe Peano (1858–1932) Italian mathematician

Geometric Calculus (1895) as translated by Lloyd C. Kannenberg (2000) "The Operations of Deductive Logic'" Ch. 1 "Geometric Formations"

“Understanding the methods of calculus is vital to the creative use of mathematics… Without this mastery the average scientist or engineer, or any other user of mathematics, will be perpetually stunted in development, and will at best be able to follow only what the textbooks say; with mastery, new things can be done, even in old, well-established fields.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“As a public teacher of mere striplings, I am often amazed by the facility and absence of resistance with which the principles of the infinitesimal calculus are accepted and assimilated by the present race of learners. When I was young, a boy of sixteen or seventeen who knew his infinitesimal calculus would have been almost pointed at in the streets as a prodigy, like Dante, as a man who had seen hell. Now-a-days, our Woolwich cadets at the same age, talk with glee of tangents and asymptotes and points of contrary flexure and discuss questions of double maxima and minima, or ballistic pendulums, or motion in a resisting medium, under the familiar and ignoble name of sums.”

James Joseph Sylvester (1814–1897) English mathematician

J. J. Sylvester. "Additional Notes to Prof. Sylvester's Exeter British Association Address", Collected Mathematical Papers, Vol. 2 (1908), pp. 717–718 https://babel.hathitrust.org/cgi/pt?id=miun.aas8085.0002.001;view=1up;seq=732

“I have completely forgotten the symbolic calculus.”

Emmy Noether (1882–1935) German mathematician

Original: (de) Ich habe das symbolische Rechnen mit Stumpf und Stil verlernt.

Habilitation curriculum vitae (1919) submitted to the Göttingen Faculty, as quoted by Peter Roquette, "Emmy Noether and Hermann Weyl" (Jan. 28, 2008) extended manuscript of a talk presented at the Hermann Weyl conference in Bielefeld, September 10, 2006.

“I have completely forgotten the symbolic calculus.”

Emmy Noether (1882–1935) German mathematician

Letter to , "Emmy Noether and Hermann Weyl" (Jan. 28, 2008) extended manuscript of a talk presented at the Hermann Weyl conference in Bielefeld, September 10, 2006.

“Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?”

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Stanislaw Ulam33

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