5 quotes
Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.
Notation as a Tool of Thought (1979)
The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation which make it such an effective tool of thought.
Notation as a Tool of Thought (1979)
The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the amount of vocabulary and the complexity of grammatical rules which the user must keep in mind. Economy of notation is therefore important.
Notation as a Tool of Thought (1979)
If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from a problem, but also of those arising in subsequent analysis, generalization, and specialization.
Notation as a Tool of Thought (1979)
The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide and a test in exploring equivalent processes possessing other characteristics, such as greater efficiency, is very common in mathematics. It is a very fruitful practice which should not be blighted by premature emphasis on efficiency in computer execution.
Notation as a Tool of Thought (1979)