The bottom part is a graph of the equation, which, as you can see, is exactly the same. To be fair, this equation cheats a little bit. You may notice that the y-axis of that graph begins at ‘k’.

Do the math and the chess reward would have amounted to about 18.5 quintillion grains, which is 52,000 times the rice reserves in all of the Food Corporation of India’s warehouses. How can that be?

After more than 70 years of intransigence, one of the most stubborn numbers in math has finally budged. In a four-page proof posted in late September, David Conlon and Asaf Ferber provided the most ...