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

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)

I was at first almost frightened when I saw such **mathematical** force made to bear upon the subject, and then wondered to see that the subject stood it so well.

— Letter to James Clerk Maxwell (25 March 1857), commenting on Maxwell's paper titled "On Faraday's Lines of Force"; letter published in

Now, the velocity of wave propagation can be seen, without the aid of any **mathematical** analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed.

—

The nude gains its enduring value from the fact that it reconciles several contrary states. It takes the most sensual and immediately interesting object, the human body, and puts it out of reach of time and desire; it takes the most purely rational concept of which mankind is capable, **mathematical** order, and makes it a delight to the senses; and it takes the vague fears of the unknown and sweetens them by showing that the gods are like men and may be worshiped for their life-giving beauty rather than their death-dealing powers.

— Ch. I: The Naked and the Nude

"He was a man of immense intellectual capabilities and most of us were marvelling at his doctorate thesis which focused on the **mathematical** solutions using digit zero. As a politician he was a man who choose his words carefully.As a personal and trusted friend whom I had assigned key responsibilities, the loss of Saitoti has been a painful experience to me,"

— Speaking at the George Saitoti burial (16 June 2012) at

Grosseteste was deeply concerned with the detailed investigation of natural phenomena. It was the inspiration of this attitude of mind, together with Grosseteste's emphasis on the importance of mathematics, that was perhaps his chief legacy to thinkers in fourteenth-century Oxford who were developing the beginnings of a **mathematical** physics.

— Neil Lewis, "Robert Grosseteste" Stanford Encyclopedia of Philosophy (2007, 2013)

If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The **mathematical** axioms are therefore neither synthetic nor analytic, but definitions. ...Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.

— Hans Reichenbach, in 'The Philosophy of Space and Time (1928), as translated by Maria Reichenbach (1957), § 14