Talking of mathematics as a bondage-and-discipline precise science always seemed to me as misleading. This is not how mathematics is <i>done</i>, even if the <i>result</i> looks so.<p>As to PG's definition of mathematics as <i>study of terms that have a precise meaning</i>, this is wrong too, as exemplified by problems of set theory and its logic, from which mathematicians escaped into more loosy setting of category theory and categorical logic.<p>I think article "When is one thing equal to another" by Barry Mazur somewhat fits into the theme of this blog note <a href="http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf" rel="nofollow">http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf</a>