About 500 years ago, there lived in Nuremberg—the world’s bratwurst capital—a painter named Albrecht Dürer. True to his Renaissance roots, he was also an ace mathematician.
His famous engraving, “Melencolia I,” no bigger than nine inches long and seven inches wide, is a portrait of melancholy. To the philosophers of that day, “melancholy” had a vastly different connotation. It wasn’t interpreted as a feeling of gloom and funk as it’s today, but as creative genius.
The trait is personified by a winged woman, seated dejectedly, with her head resting on her hand, which holds a caliper. Scattered around her is a jumble of geometry tools. There’s a putto sitting on a grindstone.
Its most striking element is on the wall behind her: an “order-4 magic square,” seen for the first time in European art.
It features a mathematical puzzle—an arrangement of numbers in a square grid, in which each number appears only once, and where the numbers in each row (horizontal), each column (vertical), and the two diagonals, all add up to the same total. Its size is described as being “of order ‘n,’” where “n” denotes the number of rows.
Whichever way you go—along the rows or columns or diagonals—the numbers all add up to 34. Those in any of the four quadrants or the interior four cells also lead to the same result.
The title and the date of the artwork come from the plate itself. The two numbers in the middle of the bottom row supply the date: 1514. 1 and 4, on either side of it, correspond to the letters “A” and “D,” which are the artist’s initials.