According to I. Bernard Cohen, "it is the best account of modern mathematics that we have", and is "written in a graceful style, combining clarity of exposition with good humor".

"Apparently it has succeeded in communicating to the layman something of the pleasure experienced by the creative mathematician in difficult problem solving."

The introduction notes (p xiii) "Science, particularly mathematics, ... appears to be building the one permanent and stable edifice in an age where all others are either crumbling or being blown to bits."

The authors affirm (p xiv) "It has been our aim, ... to show by its very diversity something of the character of mathematics, of its bold, untrammelled spirit, of how, both as an art and science, it has continued to lead the creative faculties beyond even imagination and intuition."

"[e] has played an integral part in helping mathematicians describe and predict what is for man the most important of all natural phenomena – that of growth."

They address Euler's identity, i.e. the expression eπ i + 1 = 0, indicating that the venerable Benjamin Peirce called it "absolutely paradoxical".

"[I]n mathematics we have a universal language, valid, useful, intelligible everywhere in place and time ..." Finally, "Austere and imperious as logic, it is still sufficiently sensitive and flexible to meet each new need.

Yet this vast edifice rests on the simplest and most primitive foundations, is wrought by imagination and logic out of a handful of childish rules."