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

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

— p. 265 in hardcover edition, corrected in paperback

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,

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)

As any reader of Eisenstein must realise, he felt hard pressed for time during the whole of his short **mathematical** career... His papers, although brilliantly conceived, must have been written by fits and starts, with the details worked out only as the occasion arose; sometimes a development is cut short, only to be taken up again at a later stage.

— André Weil in

I was appalled to find that the **mathematical** notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations.

— "Kenneth E. Iverson", autobiographical sketch from an unfinished work (ca. 2004), on his experience at Harvard with "a Masters program in Automatic Data Processing in 1955; in effect, the first computer science program."

A good **mathematical** joke is better, and better mathematics, than a dozen mediocre papers.

— "Introduction to A Mathematician's Miscellany", p. 24.

[Oddly enough, Putnam believes part of the attraction of some of these formalisms is their obscurity]. "I think part of the appeal of **mathematical** logic is that the formulas look mysterious - you write backward Es!"

— Putnam as quoted in: Julian Baggini, Jeremy Stangroom (2005)

The rest of Sitka’s homicides are so-called crimes of passion, which is a shorthand way of expressing the **mathematical** product of alcohol and firearms.

— Chapter 1 (The Yiddish Policemen’s Union (2007))

This essential coalition between royal military power and often dubious supernatural authority anticipated a similar alliance between the scientists and **mathematical** games theorists with the higher agents of government today, and was subject to similar corruptions, miscalculations, and hallucinations.

— pg 176 (Technics and Human Development (1967))

Music, also, the architect ought to understand so that he may have knowledge of the canonical and **mathematical** theory, and besides be able to tune ballistae , catapultae, and scorpiones to the proper key. For to the right and left in the beams are the holes in the frames through which the strings of twisted sinew are stretched by means of windlasses and bars, and these strings must not be clamped and made fast until they give the same correct note to the ear of the skilled workman.

— Chapter I, Sec. 8

Game theory can be defined as the study of **mathematical** models of conflict and cooperation between intelligent rational decision-makers.

— Roger B. Myerson (1991).

When we went to school we were told that we were governed by laws, not men. As a result of that, many people think there is no need to pay any attention to judicial candidates because judges merely apply the law by some **mathematical** formula and a good judge and a bad judge all apply the same kind of law. The fact is that the most important part of a judge's work is the exercise of judgment and that the law in a court is never better than the common sense judgment of the judge that is presiding.

— Robert H. Jackson, reported in Eugene Gerhart,

The effects of heat are subject to constant laws which cannot be discovered without the aid of **mathematical** analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.

— Joseph Fourier,

In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite... Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a **mathematical** teaser, and yet its consequences lead straight to Goya's Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.

— Arthur Koestler,

**mathematical** Reasoning is not only exact; it has its own criteria of reality

— pg52 (Science in a Free Society (1978))