These ideas lead to more advanced topics including Pascal's triangle, the Seven Bridges of Königsberg, the prime number theorem and the sieve of Eratosthenes, and the beginnings of algebra and its use in proving the impossibility of certain straightedge and compass constructions.
Later topics in this part include the countability of the rationals, the irrationality of the square root of 2, exponentiation and logarithms, graphs of functions, slopes and areas of curves, and complex numbers.
[5] Topics in the third part include non-Euclidean geometry, higher dimensions, mathematical logic, the failings of naive set theory, and Gödel's incompleteness theorems.
[1][4] Reviewer Philip Peak writes that the book succeeds in showing readers the joy of mathematics without getting them bogged down in calculations and formulas.
[2] And similarly, although W. W. Sawyer in reviewing the original 1955 publication calls its inclusion of topics from graph theory and topology "truly modern", Harkleroad points out that more recent works in this genre have included other topics in their own quest for modernity such as "fractals, public-key cryptography, and internet search engines", which for obvious reasons Péter omits.