In mathematics after some centuries of development the semantical situation is very clean. This may not be surprising, as the subject attracts people who enjoy clarity, generality, and neatness. On the one hand we have our concepts of mathematical  objects  (numbers, relations, functions, sets), and on the other we have various formal means of  expression . The mathematical expressions are generated for the most part in a very regular manner, and every effort is made to supply all expressions with denotations. (This is not always so easy to do. The theory of distributions, for example, provided a non-obvious construction of denotations for expressions of an operational calculus. The derivative operator was well serviced, but one still cannot multiply two distributions.)
['Dana S. Scott']
Mathematical concepts in programming language semantics