Some mathematical problems are easy to describe but turn out to be notoriously difficult to solve. Nonetheless, despite their reputed difficulty and repeated warnings from those who had failed to solve them in the past, these infamous problems continue to lure mathematicians into hours, days, and even years of futile labor.
In a presentation this week on "mathematical problems between order and chaos," Jeffrey C. Lagarias of AT&T Labs–Research highlighted three such notorious unsolved problems. His was a cautionary tale, aimed at an audience that included 12 high-school students who had already shown their problem-solving proficiency by topping the 2002 U.S.A. Mathematical Olympiad (USAMO).
Susceptible himself to the lure of these tantalizing conundrums, Lagarias ad