I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other **mathematical** formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.

— Preface (Linear Associative Algebra (1882))

To emphasize only the beautiful seems to me to be like a **mathematical** system that only concerns itself with positive numbers.

— Diary entry (March 1906), # 759,

Conventions of generality and **mathematical** elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity and literary vagueness... It may well be that the slovenly and literary borderland between economics and sociology will be the most fruitful building ground during the years to come and that **mathematical** economics will remain too flawless in its perfection to be very fruitful.

— Boulding (1948) "Samuelson's Foundations: The Role of Mathematics in Economics," In:

There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences . Many arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called **mathematical** , unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.

— ?"The Mathematical Preface" to Henry Billingsley's English translation of Euclid's

God does not care about our **mathematical** difficulties. He integrates empirically.

— Attributed to Einstein by his colleague Léopold Infeld in his book

And last of all we have the secondary forms of crystals bursting in upon us, and sparkling in the rigidity of **mathematical** necessity and telling us, neither of harmony of design, usefulness or moral significance, nothing but spherical trigonometry and Napier's analogies. It is because we have blindly excluded the lessons of these angular bodies from the domain of human knowledge that we are still in doubt about the great doctrine that the only laws of matter are those which our minds must fabricate, and the only laws of mind are fabricated for it by matter.

— Essay "Analogies in Nature" (February 1856), reprinted in

Bacon expresses theological and moral truths in terms of **mathematical** phraseology. He compares the Trinity to an equilateral triangle, argues that the divine light of grace reaches the good in a direct perpendicular ray, the weak in a refracted ray, and the bad in a reflected ray, and compares the virtues to the rational numbers, and the passions to the irrational, etc.

— Francis Seymour Stevenson,

The obvious **mathematical** breakthrough would be development of an easy way to factor large prime numbers.

— p. 265 in hardcover edition, corrected in paperback

Remembering... that Eratosthenes of Cyrene, employing **mathematical** theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.

— Chapter VI, Sec. 9

Bacon expresses theological and moral truths in terms of **mathematical** phraseology. He compares the Trinity to an equilateral triangle, argues that the divine light of grace reaches the good in a direct perpendicular ray, the weak in a refracted ray, and the bad in a reflected ray, and compares the virtues to the rational numbers, and the passions to the irrational, etc.

— Francis Seymour Stevenson,

The subject of management science has evolved for more than 60 years and is now a mature field within the broad category of applied mathematics. This book will emphasize both the applied and **mathematical** aspects of management science.

— Wayne Winston, ?S. Albright (2011)

The spider-men came first, and presented her Majesty with a table full of **mathematical** points, lines and figures of all sorts of squares, circles, triangles, and the like; which the Empress, notwithstanding that she had a very ready wit, and quick apprehension, could not understand; but the more she endeavoured to learn, the more was she confounded

—

Grattan-Guinness has achieved a synthesis here of remarkable historical and **mathematical** scope and sensitivity. His book is a 'must read' for historians of science and mathematics, as well as mathematicians.

— From Karen Hunger Parshall's review of

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a **mathematical** construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a **mathematical** construct is solely and precisely that it is expected to work.

— "Method in the Physical Sciences", in

Numbers instill a feeling for the lie of the land, and furnish grist for the **mathematical** mill that is the physicist's principal tool.

— Chapter 6, The Book of Life, Genetic information, p. 48

The reason is not to glorify "bit chasing"; a more fundamental issue is at stake here: Numerical subroutines should deliver results that satisfy simple, useful **mathematical** laws whenever possible . [...] Without any underlying symmetry properties, the job of proving interesting results becomes extremely unpleasant. The enjoyment of one's tools is an essential ingredient of successful work .

— Vol. II,

Every attempt to refer chemical questions to **mathematical** doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena. . . . but if the employment of **mathematical** analysis should ever become so preponderant in chemistry (an aberration which is happily almost impossible) it would occasion vast and rapid retrogradation....

— Auguste Comte,

We have elected to put our money and faith in a **mathematical** framework that is free of politics and human error

— Tyler Winklevoss, in an interview with NYTimes.

We shall see that the **mathematical** treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the **mathematical** results therefore is no evidence for or against the peculiar doctrines of this theory.

— James Clerk Maxwell (1873)

Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for the **mathematical** objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer, and Sir James Jeans' belief that He is addicted to arithmetic.

— Book One, Part I, Chapter III, Pythagoras, p. 37

Archimedes will be remembered when Aeschylus is forgotten, because languages die and **mathematical** ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

— G. H. Hardy, A Mathematician's Apology (London 1941).Quotations by Hardy. Gap.dcs.st-and.ac.uk. Retrieved on 27 November 2013.