Algebra

"[…] algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world." (Alfred North Whitehead, “The Organization of Thought”, 1974)

 "The symbolism of algebra is its glory. But it also is its curse." (William Betz) "Algebra begins with the unknown and ends with the unknowable." (Anonymous)

“Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.” (Alfred North Whitehead)

“We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.”  (William K Clifford, “Common Sense of the Exact Sciences”, 1885)

“The word is of Arabic origin. "Al" is the Arabic article the, and "gebar" is the verb to set, to restitute.” (Tobias Dantzig & Joseph Mazur, “Number: The Language of Science”, 1930)

”Nothing proves more clearly that the mind seeks truth, and nothing reflects more glory upon it, than the delight it takes, sometimes in spite of itself, in the driest and thorniest researches of algebra.” (Bernard de Fontenelle, “Histoire du Renouvellement de l'Académie des Sciences”, 1708)

”The first thing to be attended to in reading any algebraical treatise, is the gaining a perfect understanding of the different processes there exhibited, and of their connection with one another. This cannot be attained by a mere reading of the book, however great the attention which may be given. It is impossible, in a mathematical work, to fill up every process in the manner in which it must be filled up in the mind of the student before he can be said to have completely mastered it. Many results must be given of which the details are suppressed, such are the additions, multiplications, extractions of the square root, etc., with which the investigations abound. These must not be taken on trust by the student, but must be worked by his own pen, which must never be out of his hand, while engaged in any algebraical process.” (Augustus de Morgan, “On the Study and Difficulties of Mathematics”, 1830)

“The science of algebra, independently of any of its uses, has all the advantages which belong to mathematics in general as an object of study, and which it is not necessary to enumerate. Viewed either as a science of quantity, or as a language of symbols, it may be made of the greatest service to those who are sufficiently acquainted with arithmetic, and who have sufficient power of comprehension to enter fairly upon its difficulties.” (Augustus de Morgan, “Elements of Algebra”, 1837)

“They that are ignorant of Algebra cannot imagine the wonders in this kind are to be done by it: and what further improvements and helps advantageous to other parts of knowledge the sagacious mind of man may yet find out, it is not easy to determine. This at least I believe, that the ideas of quantity are not those alone that are capable of demonstration and knowledge; and that other, and perhaps more useful, parts of contemplation, would afford us certainty, if vices, passions, and domineering interest did not oppose and menace such endeavors.” (John Locke, “An Essay Concerning Human Understanding”, 1689)

”Behind these symbols lie the boldest, purest, coolest abstractions mankind has ever made. No schoolman speculating on essences and attributes ever approached anything like the abstractness of algebra.” (Susanne K Langer, “Philosophy in a New Key”, 1957)

“Every moment of time dictated and determined the following moment, and was itself dictated and determined by the moment that came before it. Everything was calculable: everything happened because it must; the commandments were erased from the tables of the law; and in their place came the cosmic algebra: the equations of the mathematicians.” (George B Shaw, “Too True to Be Good”, 1934)

“Algebra is applied to the clouds, the irradiation of the planet benefits the rose, and no thinker would dare to say that the perfume of the hawthorn is useless to the constellation.” (Victor Hugo, “Les Miserables”, 1938)

“In mathematics itself abstract algebra plays a dual role: that of a unifying link between disparate parts of mathematics  and that of a research subject with a highly active life of its own.” (Israel N Herstein, ”Abstract Algebra”, 1986)