Summary
- In the 1970s, Douglas Hofstadter was part of a group of physicists trying to understand electron behavior in a magnetic field.
- They were trying to mathematically determine the energy levels of an electron in such a situation and struggled to make headway with the problem.
- Hofstadter took a different approach, crunching numbers with a calculator to diagnose the situation.
- He came to suspect that when alpha was irrational, energy levels would form a fractal known as a Cantor set, but he couldn’t prove it.
- That problem eventually became known as the 10 martini problem, as mathematician Mark Kac offered 10 martinis to anyone who could solve it.
- After decades of work, mathematicians finally proved the 10 martini problem, but the proof had limitations.
- Yet after that problem was proven, physicists created experiments that showed the emergence of the Cantor set in a lab.
- That result unsettled mathematicians, who wanted to explain it using pure mathematics.
- A new proof, published in the Annals of Mathematics, has since resolved that discomfort.
- It also relies on a new way of thinking about a geometric object that may have future applications.
By Lyndie Chiou and Joseph Howlett
Original Article