Dijkstra presents mathematics as the art and science of effective reasoning rather than simply the study of number, quantity and space. He defends formal methods against objections from industry, programmers and mathematicians, arguing that resistance often reflects established habits rather than defects in formal reasoning.

He identifies notation as central to mathematical economy. Good notation should capture what is essential, support a small repertoire of reliable manipulations and make formulae easy to work with. He favours calculational reasoning over repeated appeals to intuition, arguing that formal manipulation can reduce ambiguity and remove unnecessary dependence on particular models.

Dijkstra develops this principle through what he calls “domain removal”: eliminating references to individual values when they are irrelevant to an argument. He connects the same approach to program correctness, where reasoning can replace exhaustive testing. Throughout, elegance is treated as evidence of effective reasoning and the removal of what is inessential.