In regarding mathematics literally as language one can draw parallels between sentences and mathematical expressions, the linguistic roles played by nouns and terms, adjectives and coefficients, verbs and operators. As in ordinary language much is left understood and is a major source of ambiguity. There are implicit assumptions that one writer may treat as shared among all practitioners but are not. There may be deliberate omissions and ambiguities for moral or political purposes. Careers and reputations depend on the judgments of other mathematicians with known preferences and prejudices. Lacuna or obscurity may also hide difficulties, or spring from not understanding the significance of aspects of the problem under discussion, or from implicit assumptions of a deeper kind that make discussions of certain issues impossible as they may destroy the foundations of the discourse. This of course is true of eighteenth-century calculus.I've frequently claimed (without any real knowledge to back it up) that our understanding of the world is entirely based on stories, and that the descriptions of the world found in science are stories written in the language of mathematics.
Serendipity while sort-of on strike this afternoon led me to this book on the shelves of the OU library, with the quote here taken from a section entitled 'Mathematics as Language'.
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