„M. Desargues puts me under obligations on account of the pains that it has pleased him to have in me, in that he shows that he is sorry that I do not wish to study more in geometry, but I have resolved to quit only abstract geometry, that is to say, the consideration of questions which serve only to exercise the mind, and this, in order to study another kind of geometry, which has for its object the explanation of the phenomena of nature… You know that all my physics is nothing else than geometry.“

Letter to Marin Mersenne (July 27, 1638) as quoted by Florian Cajori, A History of Mathematics (1893) letter dated in The Philosophical Writings of Descartes Vol. 3, The Correspondence (1991) ed. John Cottingham, Robert Stoothoff, Dugald Murdoch

Adopted from Wikiquote. Last update June 3, 2021. History
René Descartes photo
René Descartes45
French philosopher, mathematician, and scientist 1596 - 1650

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„Very late in life, when he was studying geometry, some one said to Lacydes, "Is it then a time for you to be learning now?"“

—  Diogenes Laërtius biographer of ancient Greek philosophers 180 - 240

"If it is not," he replied, "when will it be?"
Lacydes, 5.
The Lives and Opinions of Eminent Philosophers (c. 200 A.D.), Book 4: The Academy

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„The main object of study in differential geometry is, at least for the moment, the differential manifolds, structures on the manifolds (Riemannian, complex, or other), and their admissible mappings. On a manifold the coordinates are valid only locally and do not have a geometric meaning themselves.“

—  Shiing-Shen Chern mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributions to differ… 1911 - 2004

[Differential geometry, its past and its future, Actes, Congrès inter. math, 1970, 41–53, http://www.math.harvard.edu/~hirolee/pdfs/2014-fall-230a-icm1970-chern-differential-geometry.pdf]

Freeman Dyson photo

„A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid.“

—  Freeman Dyson, book Infinite in All Directions

Source: Infinite in All Directions (1988), Ch. 2 : Butterflies and Superstrings, p. 17
Context: Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry?... It cannot be answered by a definition.

Robert Chambers (publisher, born 1802) photo
Thomas Jefferson photo

„Our civil rights have no dependence upon our religious opinions more than our opinions in physics or geometry.“

—  Thomas Jefferson 3rd President of the United States of America 1743 - 1826

A Bill for Establishing Religious Freedom, Chapter 82 (1779). Published in The Works of Thomas Jefferson in Twelve Volumes http://oll.libertyfund.org/ToC/0054.php, Federal Edition, Paul Leicester Ford, ed., New York: G. P. Putnam's Sons, 1904, Vol. 1 http://oll.libertyfund.org/Texts/Jefferson0136/Works/0054-01_Bk.pdf, pp. 438–441. Comparison of Jefferson's proposed draft and the bill enacted http://web.archive.org/web/19990128135214/http://www.geocities.com/Athens/7842/bill-act.htm
Variant: Our civil rights have no dependence on our religious opinions any more than our opinions in physics or geometry...
Source: The Statute Of Virginia For Religious Freedom
Context: Well aware that the opinions and belief of men depend not on their own will, but follow involuntarily the evidence proposed to their minds; that Almighty God hath created the mind free, and manifested his supreme will that free it shall remain by making it altogether insusceptible of restraint; that all attempts to influence it by temporal punishments, or burthens, or by civil incapacitations, tend only to beget habits of hypocrisy and meanness, and are a departure from the plan of the holy author of our religion, who being lord both of body and mind, yet choose not to propagate it by coercions on either, as was in his Almighty power to do, but to exalt it by its influence on reason alone; that the impious presumption of legislature and ruler, civil as well as ecclesiastical, who, being themselves but fallible and uninspired men, have assumed dominion over the faith of others, setting up their own opinions and modes of thinking as the only true and infallible, and as such endeavoring to impose them on others, hath established and maintained false religions over the greatest part of the world and through all time: That to compel a man to furnish contributions of money for the propagation of opinions which he disbelieves and abhors, is sinful and tyrannical; … that our civil rights have no dependence on our religious opinions, any more than our opinions in physics or geometry; and therefore the proscribing any citizen as unworthy the public confidence by laying upon him an incapacity of being called to offices of trust or emolument, unless he profess or renounce this or that religions opinion, is depriving him injudiciously of those privileges and advantages to which, in common with his fellow-citizens, he has a natural right; that it tends also to corrupt the principles of that very religion it is meant to encourage, by bribing with a monopoly of worldly honours and emolumerits, those who will externally profess and conform to it; that though indeed these are criminals who do not withstand such temptation, yet neither are those innocent who lay the bait in their way; that the opinions of men are not the object of civil government, nor under its jurisdiction; that to suffer the civil magistrate to intrude his powers into the field of opinion and to restrain the profession or propagation of principles on supposition of their ill tendency is a dangerous fallacy, which at once destroys all religious liberty, … and finally, that truth is great and will prevail if left to herself; that she is the proper and sufficient antagonist to error, and has nothing to fear from the conflict unless by human interposition disarmed of her natural weapons, free argument and debate; errors ceasing to be dangerous when it is permitted freely to contradict them.

Gottlob Frege photo

„A philosopher who has no connection to geometry is only half a philosopher, and a mathematician who has no philosophical vein is only half a mathematician.“

—  Gottlob Frege mathematician, logician, philosopher 1848 - 1925

Original: (de) Ein Philosoph, der keine Beziehung zur Geometrie hat, ist nur ein halber Philosoph, und ein Mathematiker, der keine philosophische Ader hat, ist nur ein halber Mathematiker.

Gottlob Frege: Erkenntnisquellen der Mathematik und der mathematischen Naturwissenschaften, 1924/1925, submitted to Wissenschaftliche Grundlagen; posthumously published in: Frege, Gottlob: Nachgelassene Schriften und Wissenschaftlicher Briefwechsel. Felix Meiner Verlag, 1990, p. 293

Benjamin Peirce photo

„Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences“

—  Benjamin Peirce American mathematician 1809 - 1880

Ben Yamen's Song of Geometry (1853)
Context: Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences; but it is the Key of an ever open door which refuses to be shut, and through which the whole world is crowding, to make free, in unrestrained license, with the precious treasures within, thoughtless both of lock and key, of the door itself, and even of Science, to which it owes such boundless possessions, the New World included. The door is wide open and all may enter, but all do not enter with equal thoughtlessness. There are a few who wonder, as they approach, at the exhaustless wealth, as the sacred shepherd wondered at the burning bush of Horeb, which was ever burning and never consumed. Casting their shoes from off their feet and the world's iron-shod doubts from their understanding, these children of the faithful take their first step upon the holy ground with reverential awe, and advance almost with timidity, fearful, as the signs of Deity break upon them, lest they be brought face to face with the Almighty.

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