Quanta Magazine reported that mathematicians have proven the lonely runner conjecture for up to ten runners, a milestone that extends the reach of a problem that has long intrigued mathematicians. The lonely runner problem, first framed in the 1960s by Jörg M. Wills, has been shown to be equivalent to questions about clear line of sight in a field of obstacles, billiard ball trajectories, and network organization. In the 1970s, the conjecture was proved for four runners, and by 2007 it had been extended to seven runners. Last year, Matthieu Rosenfeld of the Laboratory of Computer Science, Robotics, and Microelectronics of Montpellier settled the case for eight runners. 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 ten runners. Matthias Beck of San Francisco State University said the progress was a "quantum leap," noting that adding just one runner makes the task of proving the conjecture "exponentially harder." Beck added, "Going from seven runners to now 10 runners is amazing." When Wills saw the lonely runner paper, he emailed one of the authors, Luis Goddyn of Simon Fraser University , to congratulate him on "this wonderful and poetic name." (Goddyn's reply: "Oh, you are still alive.") The new proofs open the door to exploring the conjecture for larger numbers of runners.