The '10 Martini' Proof Connects Quantum Mechanics With Infinitely Intricate Mathematical Structures

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, uses number theory to explain quantum fractals. In 1974, five years before he wrote his Pulitzer Prize-winning book, Douglas Hofstadter was a graduate student in physics at the University of Oregon. When his doctoral adviser went on sabbatical to Regensburg, Germany, Hofstadter tagged along, hoping to practice his German. The pair joined a group of brilliant theoretical physicists who were agonizing over a particular problem in quantum theory. They wanted to determine the energy levels of an electron in a crystal grid placed near a magnet. Hofstadter was the odd one out, unable to follow the others' line of thought. "Part of my luck was that I couldn't keep up with them," he said.