"Prime Effort," by Ivars Peterson. Science News, 25 May 2002, pages 324-5.
Peterson writes of a purported proof by Preda Mihailescu of Catalan's conjecture. Catalan's conjecture is that the only non-trivial natural number solutions to the equation xp - yq = 1 involve 3 and 2 (which give 32 - 23 = 1). The conjecture was originally formulated in 1844, and although it appears to be true and progress had been made, no proof had been found (perhaps until now). Mihailescu's prrof has been sent to several mathematicians for checking.
--- Mike Breen