On Inequalities I

"The worst form of inequality is to try to make unequal things equal." (Aristotle)

"Among simple even numbers, some are superabundant, others are deficient: these two classes are as two extremes opposed to one another; as for those that occupy the middle position between the two, they are said to be perfect. And those which are said to be opposite to each other, the superabundant and the deficient, are divided in their condition, which is inequality, into the too much and the too little." (Nicomachus of Gerasa,"Introductio Arithmetica", cca. 100 AD)

"Inequality is the cause of all local movements. There is no rest without equality." (Leonardo da Vinci, Codex Atlanticus, 1478)

"It is from this absolute indifference and tranquility of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality. (Edmund Burke, "On the Sublime and Beautiful", 1757)

"Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom." (Francis Picabia, "Comoedia", 1922)

"The fundamental results of mathematics are often inequalities rather than equalities." Edwin Beckenbach & Richard Bellman, "An Introduction to Inequalities", 1961)

"There are three reasons for the study of inequalities: practical, theoretical and aesthetic. On the aesthetic aspects, as has been pointed out, beauty is in the eyes of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive." (Richard E Bellman, 1978)

"Linear programming is concerned with the maximization or minimization of a linear objective function in many variables subject to linear equality and inequality constraints."  (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)

"From the historical point of view, since inequalities are associated with order, they arose as soon as people started using numbers, making measurements, and later, finding approximations and bounds. Thus inequalities have a long and distinguished role in the evolution of mathematics." (Claudi Alsina & Roger B Nelsen, "When Less is More: Visualizing Basic Inequalities", 2009)

"Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often. especially in secondary and collegiate mathematics. the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubti mportant, they do not possess the richness and variety that one finds with inequalities." (Claudi Alsina & Roger B Nelsen, "When Less is More: Visualizing Basic Inequalities", 2009)