Eugene Charles Catalan made his famous conjecture that 8 and 9 are the only two consecutive perfect powers of natural numbers in 1844 in a letter to the editor of Crelle s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it.

Catalan s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof...