Business · Wired
The ‘Lonely Runner’ Problem Only Appears Simple
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The original version of this story appeared in Quanta Magazine.
Key facts
- It touches so many different mathematical fields,” said Matthias Beck of San Francisco State University
- Mathematicians proved it for four runners in the 1970s, and by 2007, they’d gotten as far as seven
- Then last year, Matthieu Rosenfeld, a mathematician at the Laboratory of Computer Science, Robotics, and Microelectronics of Montpellier, settled the conjecture for eight runners
- Going from seven runners to now 10 runners is amazing
Summary
Picture a bizarre training exercise: A group of runners starts jogging around a circular track, with each runner maintaining a unique, constant pace. It touches so many different mathematical fields,” said Matthias Beck of San Francisco State University. Mathematicians proved it for four runners in the 1970s, and by 2007, they’d gotten as far as seven. And within a few weeks, a second-year undergraduate at the University of Oxford named Tanupat (Paul) Trakulthongchai built on Rosenfeld’s ideas to prove it for nine and 10 runners. “It’s a quantum leap,” said Beck, who was not involved in the work. Dash At first, the lonely runner problem had nothing to do with running. Instead, mathematicians were interested in a seemingly unrelated problem: how to use fractions to approximate irrational numbers such as pi, a task that has a vast number of applications.