From numerals to infinity, symbols have advanced mathematical thinking
Princeton Univ., $29.95
As the semanticist S.I. Hayakawa stressed in his classic book Language in Thought and Action, words are not the things they represent. Words are symbols. It’s the manipulation of those symbols that makes communication possible.
In very much the same way, it’s the manipulation of symbols of a different type that makes mathematics practical. You can describe mathematical operations using just words — in fact, in ancient times, that was the norm. But such a cumbersome approach is not conducive to anything very complicated. In large part, the advance of mathematics from simple arithmetic to the complexities of algebra and calculus was made possible by the development of effective symbols.