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,

Einsteins relativity work is a magnificent **mathematical** garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king... its exponents are brilliant men but they are metaphysicists rather than scientists.

—

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

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

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,

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)

Economics, if it is to be a science at all, must be a **mathematical**
science.

— 1871The Theory of Political Economy.

I don't suppose that applies so much to other physicists; I think it’s a peculiarity of myself that I like to play about with equations, just looking for beautiful **mathematical** relations which maybe don’t have any physical meaning at all. Sometimes they do.

— Interview with Dr. P. A. M. Dirac by Thomas S. Kuhn at Dirac's home, Cambridge, England, May 7, 1963

It is not particularly satisfactory to see equations set forth as direct results of observation and experiment, where we used to get long **mathematical** deductions as apparent proofs of them. Nevertheless, I believe that we cannot, without deceiving ourselves, extract much more from known facts than is asserted in the papers referred to. If we wish to lend more color to the theory, there is nothing to prevent us from supplementing all this and aiding our powers of imagination by concrete representations of the various conceptions as to the nature of electric polarisation, the electric current, etc.

—

For reasons **mathematical**, psychological, and sociological, it is a good idea to use a money management system that is relatively forgiving of estimation errors.

— Part Six, Blowing Up, Survival Motive, p. 296-297

Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all **mathematical** ideas admit of being referred.

— Sylvester's

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.

— Brian Hayes (scientist),

If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago. [...] This time, however, it is not only based on intuition, but also on experiments of great precision and sophistication, and on a rigorous and consistent **mathematical** formalism.

— Ch. 1, Modern Physics, p. 19

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.

— Reported in Eugene Gerhart,

I think visual literacy and media literacy is not without value, but I think plain old-fashioned text literacy and **mathematical** literacy are much more powerful and flexible ways to organize your mind.

— Neal Stephenson coins the term "text literacy" during interview for the article "Pushing the Edge With 'Diamond Age' Nano-Machines," Associated Press, May 10, 1995

The possibility of a stable economic life with full utilization of our resources is still not sufficiently assured, and it is extremely important that it should be so assured, and that the whole world should accept this as a fact. The work that is being done in econometrics is massive, and undaunted by **mathematical** difficulties, but it appears, at any rate as viewed from outside, to be unclear as to its aim.

— Arnold Tustin

The Society for General Systems Theory and its publication General Systems was a mixed bag. Few authors were actually doing research -they philosophized, and many prematurely resolved dilemmas by **mathematical** equations in a language poorly understood by the empirical investigator.

— Roy R. Grinker, Sr. (1976) in

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,

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of **mathematical** science.

— Richard Courant in:

**mathematical** physics is in the first place physics and it could not exist without experimental investigations.

— Inaugural lecture for his professorship of mathematical physics at the University of Utrecht (1913), as quoted by Davies, Mansel.

**mathematical** physics represents the purest image that the view of nature may generate in the human mind; this image presents all the character of the product of art; it begets some unity, it is true and has the quality of sublimity; this image is to physical nature what music is to the thousand noises of which the air is full...

— Théophile de Donder as quoted by Ilya Prigogine in his

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