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.