"The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics. (Galileo Galilei, "The Assayer", 1623)
"It is impossible to disassociate language from science or science from language, because every natural science always involves three things: the sequence of phenomena on which the science is based; the abstract concepts which call these phenomena to mind; and the words in which the concepts are expressed. To call forth a concept a word is needed; to portray a phenomenon a concept is needed. All three mirror one and the same reality." (Antoine-Laurent Lavoisier, "Traite Elementaire de Chimie", 1789)
"There cannot be a language more universal and more simple, more free from errors and obscurities [...] more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes." (Joseph Fourier, "The Analytical Theory of Heat", 1822)
"In treating of the practical application of scientific principles, an algebraical formula should only be employed when its shortness and simplicity are such as to render it a clearer expression of a proposition or rule than common language would be, and when there is no difficulty in keeping the thing represented by each symbol constantly before the mind." (William J M Rankine, "On the Harmony of Theory and Practice in Mechanics", 1856)
"The language of mathematics, permitting great sharpness and accuracy of definition, conduces largely to their power of drawing necessary conclusions. Language is not only a means of recording the results of our thinking; it is an instrument of thought, and that of the highest value." (Thomas Hill, "The Imagination in Mathematics", The North American Review Vol. 85 (176), 1857)
"Every science aims to become a popular science. A science can only reach this goal if it also uses a popular language." (Hermann G Grassmann, 1870)
"No one for a moment can pretend that printing is so great a discovery as writing, or algebra as a language." (Benjamin Disraeli, "Lothair", 1870)
"The laws of nature are drawn from experience, but to express them one needs a special language: for, ordinary language is too poor and too vague to express relations so subtle, so rich, so precise. Here then is the first reason why a physicist cannot dispense with mathematics: it provides him with the one language he can speak […]. Who has taught us the true analogies, the profound analogies which the eyes do not see, but which reason can divine? It is the mathematical mind, which scorns content and clings to pure form." (Henri Poincare, "The Value of Science", 1905)
"Numbers constitute the only universal language." (Nathanael West, "Miss Lonelyhearts", 1933)
"We can now return to the distinction between language and symbolism. A symbol is language and yet not language. A mathematical or logical or any other kind of symbol is invented to serve a purpose purely scientific; it is supposed to have no emotional expressiveness whatever. But when once a particular symbolism has been taken into use and mastered, it reacquires the emotional expressiveness of language proper. Every mathematician knows this. At the same time, the emotions which mathematicians find expressed in their symbols are not emotions in general, they are the peculiar emotions belonging to mathematical thinking." (Robin G Collingwood, "The Principles of Art", 1938)
"Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone." (Albert Einstein & Leopold Infeld, "The Evolution of Physics", 1938)
"It will probably be the new mathematical discoveries which are suggested through physics that will always be the most important, for, from the beginning Nature has led the way and established the pattern which mathematics, the Language of Nature, must follow." (George D Birkhoff, "Mathematical Nature of Physical Theories" American Scientific Vol. 31 (4), 1943)
"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)
"What distinguishes the language of science from language as we ordinarily understand the word? […] What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data." (Albert Einstein, "Ideas and Opinions", 1954)
"Scientists whose work has no clear, practical implications would want to make their decisions considering such things as: the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment." (C West Churchman, "Costs, Utilities, and Values", 1956)
"Both science and art form in the course of the centuries a human language by which we can speak about the more remote parts of reality, and the coherent sets of concepts as well as the different styles of art are different words or groups of words in this language." (Werner K Heisenberg, "Physics and Philosophy", 1958)
"The simplicities of natural laws arise through the complexities of the languages we use for their expression." (Eugene P Wigner, 1959)
"Numbers are the landmarks which enable us to speak in a language common to all men, of successive moments of duration." (Félix E Borel, "Space and Time", 1960)
"By taking the word as an absolute, never investigating its personal significance, the word acquires a life of its own. Reifying the word in this way removes it from its practical function as a more or less efficient way of referring to a process which remains alive and has continually changing referents. Enactment is one way of keeping alive the words a person uses to characterize himself or someone else. Keeping his language connected to action permits feelings of change and growth." (Erving Polster & Miriam Polster, "Gestalt Therapy Integrated", 1973)
"The use of metaphor is one of many devices available to the scientific community to accomplish the task of accommodation of language to the causal structure of the world." (Richard Boyd, "Metaphor and theory change: what is ‘metaphor’ a metaphor for?", 1979)
"Metaphor plays an essential role in establishing a link between scientific language and the world. Those links are not, however, given once and for all. Theory change, in particular, is accompanied by a change in some of the relevant metaphors and in the corresponding parts of the network of similarities through which terms attach to nature." (Thomas S Kuhn, "Metaphor in science", 1993)
"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 2002)
"The claim that scientific models are metaphors is tied to the fact that often an analogy is exploited to construct a model about a phenomenon. [...] Scientific models appear to be, contrary to past research traditions, as central in scientific practice for describing and communicating aspects of the empirical world as metaphors are in ordinary language." (Daniela M Bailer-Jones," Models, Metaphors and Analogies", 2002)
"Science does not speak of the world in the language of words alone, and in many cases it simply cannot do so. The natural language of science is a synergistic integration of words, diagrams, pictures, graphs, maps, equations, tables, charts, and other forms of visual and mathematical expression. [… Science thus consists of] the languages of visual representation, the languages of mathematical symbolism, and the languages of experimental operations." (Jay Lemke, "Teaching all the languages of science: Words, symbols, images and actions", 2003)
"Mathematics is more than a tool and language for science. It is also an end in itself, and as such, it has, over the centuries, affected our worldview in its own right." (Stephen Hawking,"God Created the Integers", 2007)
"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 the means by which we deduce the consequences of physical principles. More than that, it is the indispensable language in which the principles of physical science are expressed." (Steven Weinberg, "To Explain the World: The Discovery of Modern Science", 2015)
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