The formulas and theorems in the book are regarded as correct mathematics but the claims about practical or pedagogical superiority are primarily promoted by Wildberger himself and have received mixed reviews.
[3][5] Finally, Part IV considers practical applications in physics and surveying, and develops extensions to higher-dimensional Euclidean space and to polar coordinates.
[1][6] The feature of the book that was most positively received by reviewers was its work extending results in distance and angle geometry to finite fields.
Reviewer Laura Wiswell found this work impressive, and was charmed by the result that the smallest finite field containing a regular pentagon is
James Franklin points out that for spaces of three or more dimensions, modelled conventionally using linear algebra, the use of spread by Divine Proportions is not very different from standard methods involving dot products in place of trigonometric functions.
[6] Although multiple reviewers felt that a reduction in the amount of time needed to teach students trigonometry would be very welcome,[3][5][7] Paul Campbell is skeptical that these methods would actually speed learning.
[7] Gerry Leversha keeps an open mind, writing that "It will be interesting to see some of the textbooks aimed at school pupils [that Wildberger] has promised to produce, and ... controlled experiments involving student guinea pigs.
[1] While agreeing with Wiswell, Barker points out that there may be other mathematicians who share Wildberger's philosophical suspicions of the infinite, and that this work should be of great interest to them.
Henle, Barker, and Leversha conclude that the book has not made its case for this,[3][4][6] but Sandra Arlinghaus sees this work as an opportunity for fields such as her mathematical geography "that have relatively little invested in traditional institutional rigidity" to demonstrate the promise of such a replacement.