Twin primes, like 11 and 13, are just 2 apart, and nobody knows whether there are infinitely many. In 2013, Yitang Zhang, a little-known lecturer who had once worked as an accountant and at a sandwich shop, proved there are infinitely many pairs of primes less than 70 million apart. An international collaboration has since cut that gap to 246.
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.