Mathematics as Language II

"The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language." (Herbert G Wells, “Mankind in the Making”, 1904)

”Mathematics is the language of definiteness, the necessary vocabulary of those who know. Hence the intimate connection between mathematics and science.” (William F White, “A Scrap-book of Elementary Mathematics”, 1908)

“[…] one does not know a foreign language unless on is able to think in that language; one does not know mathematics unless one is able to think mathematically.” (John A L Waddell, 1908)

”One of the difficulties which a mathematician has in describing his work to non-mathematicians is that the present day language of mathematics has become so esoteric that a well educated layman, or even a group of scientists, can comprehend essentially nothing of the discourse which mathematicians hold with each other, or of the accounts of their latest researches which are published in their professional journals.” (Angus E Taylor, “Some Aspects of Mathematical Research”, American Scientist , Vol. 35, No. 2, 1947)

“The study of mathematics cultivates the reason; that of the languages, at the same time, the reason and the taste. The former gives the grasp and power to the mind; the latter both power and flexibility. The former by itself, would prepare us for a state of certainties, which nowhere exists; the later, for a state of probabilities which is that of common life. Each, by itself, does but an imperfect work: in the union of both, is the best discipline for the mind, and the best mental training for the world as it is.” (Tyron Edwards, “The New Dictionary of Thoughts”, 1948)

”[…] the merit of mathematics, in all its forms, consists in its truth; truth conveyed to the understanding, not directly by words but by symbols which serve as the world’s only universal written language.” (David Eugene Smith, “The Poetry of Mathematics and Other Essays”,  1934)

”Mathematics is infinitely wide, while the language that describes it is finite. It follows from the pigeonhole principle that there exist distinct concepts that are referred to by the same name. Mathematics is also infinitely deep and sometimes entirely different concepts turn out to be intimately and profoundly related.” (Doron Zeilberger, 1988)

”Mathematics […] is mired in a language of symbols foreign to most of us, [it] explores regions of the infinitesimally small and the infinitely large that elude words, much less understanding.” (Robert Kanigel, “The Man Who Knew Infinity”, 1991)

”Mathematics is not a way of hanging numbers on things so that quantitative answers to ordinary questions can be obtained. It is a language that allows one to think about extraordinary questions.” (James O Bullock, “Literacy in the Language of Mathematics”, The American Mathematical Monthly, Vol. 101, No. 8, October, 1994)

"When you get to know them, equations are actually rather friendly. They are clear, concise, sometimes even beautiful. The secret truth about equations is that they are a simple, clear language for describing certain "recipes" for calculating things." (Ian Stewart, “Why Beauty Is Truth”, 2007)

"Mathematics is not a language, it's an adventure." (Paul Lockhart, “A Mathematician's Lament", 2009)