Around 1637, Pierre de Fermat wrote in a book's margin that he had found a “truly marvellous proof” of a statement about whole numbers, but that the margin was too narrow to contain it. For more than three centuries, the greatest minds failed. Andrew Wiles, fascinated by the problem since age 10, announced a solution in 1993; after fixing an error, his proof was published in 1995.
How many different structures can you build with six classic 2-by-4 Lego bricks of the same colour? The company used to quote just over 102 million. In 2005, Danish mathematician Søren Eilers recounted everything by computer: 915,103,765 combinations. The official estimate had been too low by a factor of about nine.
Fold an A4 sheet in half and you get an A5 with the same proportions. That only works for one ratio between length and width: about 1.414, the square root of 2. The A0 format measures exactly one square metre, and A4 is a sixteenth of it. With standard 80-gram-per-square-metre paper, an A4 sheet therefore weighs exactly 5 grams.