“The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. …The conic sections, invented in an attempt to solve the problem of doubling the alter of an oracle, ended by becoming the orbits followed by the planets… The imaginary magnitudes invented by Cardan and Bombelli describe… the characteristic features of alternating currents. The absolute differential calculus, which originated as a fantasy of Reimann, became the mathematical model for the theory of Relativity. And the matrices which were a complete abstraction in the days of Cayley and Sylvester appear admirably adapted to the… quantum of the atom.”

Number: The Language of Science (1930)

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Tobias Dantzig25

American mathematician 1884–1956

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“The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.”

George Dantzig (1914–2005) American mathematician

This quote is by his father Tobias Dantzig (1884-1956) Number: The Language of Science (1930) p. 240
Misattributed

“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

“It would be inconvenient to interrupt the account of Menaechmus's solution of the problem of the two mean proportionals in order to consider the way in which he may have discovered the conic sections and their fundamental properties. It seems to me much better to give the complete story of the origin and development of the geometry of the conic sections in one place, and this has been done in the chapter on conic sections associated with the name of Apollonius of Perga. Similarly a chapter has been devoted to algebra (in connexion with Diophantus) and another to trigonometry”

Thomas Little Heath (1861–1940) British civil servant and academic

under Hipparchus, Menelaus and Ptolemy
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“The problem of the biquadratic equation was laid prominently before Italian mathematicians by Zuanne de Tonini da Coi, who in 1540 proposed the problem, "Divide 10 parts into three parts such that they shall be continued in proportion and that the product of the first two shall be 6." He gave this to Cardan with the statement that it could not be solved, but Cardan denied the assertion, although himself unable to solve it. He gave it to Ferrari, his pupil, and the latter, although then a mere youth, succeeded where the master had failed. …This method soon became known to algebraists through Cardan's Ars Magna, and in 1567 we find it used by Nicolas Petri”

David Eugene Smith (1860–1944) American mathematician

of Deventer
Source: History of Mathematics (1925) Vol.2, pp.467-468

“I will prefix the motives which originally gave rise to buildings and the development of inventions in this field, following in the steps of early nature and of those writers who have devoted treatises to the origins of civilization and the investigation of inventions. My exposition will, therefore, follow the instruction which I have received from them.”

Vitruvius book De architectura

Introduction, Sec. 5
De architectura (The Ten Books On Architecture) (~ 15BC), Book II

“May the Lord array thee in the garment of salvation and surround thee with the cloak of happiness.”

Pope Alexander VI (1431–1503) pope of the Catholic Church 1492-1503

Inscribed words upon the mantle of gonfalonier given to his son Cesare Borgia (March 29, 1499), as quoted in The Life of Cesare Borgia (1912) by Rafael Sabatini, Chapter IV: Gonfalonier of the Church.