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

The original version of this story appeared in Quanta Magazine.

In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, 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

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