UPDATE: This talk has been rescheduled to the following Thursday, the 8th of May.

On August 8th 1900, in what was possibly the most famous lecture in the history of mathematics, the great David Hilbert set a list of 23 open problems that he deemed important enough to set the direction for mathematical research in the 20th century. These problems have all gained a special status in mathematical lore and have gained a great deal of attention during the past 100 years, leading to the resolution of many (though not all) of them.

A problem which is particularly elementary and interesting was the third on his list. The question is that of knowning if two polyhedra of the same volume can be cut into congruent pieces (equidecomposed) or made congruent by sticking other polyhedra onto them (equicomplemented). This is a more important problem than it seems: if the answer is yes, we can prove familiar expressions for the volumes of polyhedra through elementary means and without resorting to calculus, as is possible for plane geometry (where this does indeed hold and is known as the Bolyai-Gerwien theorem). Hilbert himself believed it to be false, which is clear by his own wording of the problem: "specifying two tetrahedra of equal bases and equal altitudes which can in no way be split up into congruent tetrahedra, and which cannot be combined with congruent tetrahedra to form two polyhedra which themselves could be split up into congruent tetrahedra".

The negative answer was indeed provided later that year by his own student Max Dehn, whose work, though initially quite complicated, can be simplified to the point of needing only basic geometry and 1st year linear algebra. The problem has in fact still been studied since and sparked much discussion: one of the approaches we present dates from 2007! Join us at 7:30 PM this Thursday in MS.03 as we take you through a proof of this fascinating theorem, followed by equicomplementation with drinks at the pub.