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)

[There is] a delusion that macro-economics is both viableanduseful (a
delusionencouraged by its extensive use of mathematics,
which must always impress politicians lacking
any **mathematical** education, and which is really the
nearest thing to the practice of magic that occurs among
professional economists).

— 1989 The Fatal Conceit: The Errors of Socialism, ch.6.

If the system exhibits a structure which can be represented by a **mathematical** equivalent, called a **mathematical** model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of **mathematical** models is termed **mathematical** programming.

— p.2 (Linear programming and extensions, (1963))

The fact that randomness requires a physical rather than a **mathematical** source is noted by almost everyone who writes on the subject, and yet the oddity of this situation is not much remarked.

—

It is clear that economics, if it is to be a science at all, must be a **mathematical** science.

— Chapter I, Introduction, p. 38

What seems certain is that Pythagoras developed the idea of **mathematical** logic... He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute then any previous knowledge.

—

How strange and unforeseeable! The world had been saved, not by great rulers and statesmen, not by mystics and saints and prophets and messiahs , not by any of the holy scriptures, but by an introverted eccentric writer of **mathematical** texts and children 's books and by the child who'd inspired him. The little girl become a woman , dream-ridden Alice , had inspired the nonsense not really nonsense, and this in circuitous and spiralling fashion had inspired her to do what all others had failed to do, to save eighteen billion souls and the world .

— Section 14 : "Three-Cornered Play : Caroll to Alice to Computer"

Courage is not a quality one normally associates with mathematicians. Yet it should apply to people who work in their attics in secret for seven years without cease on a problem that has eluded the greatest **mathematical** minds since first proposed in 1637.

— Column, July 5, 1993, "An Age-old Puzzle, Solved Modestly" at

Ackoff (1962)... differentiates between iconic models, which use the same materials but involve changes in scale, analogue models which also involve a change in the materials used in building the model, and symbolic models which represent reality by some symbolic system such as a system of **mathematical** equations.

— Shatrughna P. Sinha (1993)

The **mathematical** facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.

— Henri Poincare, in Analogical Reasoning in Children (23 October 2013).

The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. **mathematical** genius and artistic genius touch one another.

— Gösta Mittag-Leffler

— Quoted in N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.