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

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

The most powerful influence exercised by the Arabs on general natural physics was that directed to the advances of chemistry; a science for which this race created a new era.(...) Besides making laudatory mention of that which we owe to the natural science of the Arabs in both the terrestrial and celestial spheres, we must likewise allude to their contributions in separate paths of intellectual development to the general mass of **mathematical** science.

— Alexander von Humboldt,

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,

Koyré's exaltation of the " Platonic and Pythagorean " elements of the Scientific Revolution... was based on a demonstrably false understanding of how Galileo reached his conclusions. Koyré asserted that Galileo merely used experiments as a check on the theories he devised by **mathematical** reasoning. But later research has definitively established that Galileo's experiments preceeded his attempts to give a **mathematical** account of their results.

— Clifford D. Conner,

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)

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

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

It is therefore not unreasonable to suppose that some portion of the neglect of science in England, may be attributed to the system of education we pursue. A young man passes from our public schools to the universities, ignorant of almost every branch of useful knowledge; and at these latter establishments … classical and **mathematical** pursuits are nearly the sole objects proposed to the student's ambition.

—

Too large a proportion of recent "**mathematical**" economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.

— Book 5, Chapter 21,Section 3, p. 298

Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as **mathematical** principles of philosophy; for all the difficulty of philosophy seems to consist in this from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena...

— Preface (Philosophiae Naturalis Principia Mathematica (1687))

Vacuum stands and remains a **mathematical** space. A cube placed in a vacuum would not displace anything, as it would displace air or water in a space already containing those fluids.

— Roger Bacon,

(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in **mathematical** terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not.

— Anatol Rapoport

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of **mathematical** analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

— John von Neumann, as quoted in

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.

— Simon Singh,