[4] In modern times, the impossibility of solving the three classical problems by straightedge and compass, finally proven in the 19th century,[5] has often been viewed as analogous to the foundational crisis of mathematics of the early 20th century, in which David Hilbert's program of reducing mathematics to a system of axioms and calculational rules struggled against logical inconsistencies in its axiom systems, intuitionist rejection of formalism and dualism, and Gödel's incompleteness theorems showing that no such axiom system could formalize all mathematical truths and remain consistent.

[5] Some specific theories on the authorship of Greek mathematics, put forward by the book, include the legitimacy of a letter on square-doubling from Eratosthenes to Ptolemy III Euergetes,[6] a distinction between Socratic-era sophist Hippias and the Hippias who invented the quadratrix, and a similar distinction between Aristaeus the Elder, a mathematician of the time of Euclid, and the Aristaeus who authored a book on solids (mentioned by Pappus of Alexandria), and whom Knorr places at the time of Apollonius.

[7] The book is written for a general audience, unlike a follow-up work published by Knorr, Textual Studies in Ancient and Medieval Geometry (1989), which is aimed at other experts in the close reading of Greek mathematical texts.

[7] Reviewer Colin R. Fletcher calls it "essential reading" for understanding the background and content of the Greek mathematical problem-solving tradition.

[2] In its historical scholarship, historian of mathematics Tom Whiteside writes that the book's occasionally speculative nature is justified by its fresh interpretations, well-founded conjectures, and deep knowledge of the subject.