A decades-old geometry puzzle, famously referenced in the classic sitcom Friends, has finally been solved by a mathematician from South Korea.
The 'Pivot!' Problem Finally Put to Rest
Dr Baek Jin Eon, a 31-year-old research fellow at the Korea Institute for Advanced Study, has provided a definitive answer to the 'moving sofa problem'. This conundrum, which has intrigued mathematicians for nearly 60 years, asks a seemingly simple question: what is the largest possible two-dimensional shape that can be manoeuvred around a right-angled corner in a corridor of width one?
The problem gained pop culture fame in Friends season five, episode 16, where Ross Geller's infamous struggle to move a sofa upstairs while yelling 'Pivot!' became an iconic moment. Dr Baek's work proves mathematically that no shape larger than a specific, previously proposed design can make the turn.
A Monumental Proof Without Computer Aid
The solution centres on a shape known as Gerver's sofa, proposed by mathematician Joseph Gerver. Dr Baek's monumental achievement was to prove, through pure logical reasoning, that this is indeed the largest possible sofa that can navigate the L-shaped hallway.
His 119-page proof, published in late 2024, is notable for being achieved entirely through analytical methods, a deliberate departure from the computer simulations used in many earlier attempts. This rigorous approach has earned the work significant recognition, including a place in Scientific American's 'Top 10 Math Discoveries of 2025'.
The proof is currently undergoing the rigorous peer review process at the prestigious Annals of Mathematics, a journal considered one of the most authoritative in the field.
Why This Mathematical Milestone Matters
While on the surface a quirky puzzle about moving furniture, the solution has deeper implications for the field of computational geometry and optimisation. Problems like this explore the fundamental limits of shape and space, with potential applications in robotics, logistics, and urban design where navigating tight constraints is crucial.
Dr Baek's success in solving a problem that has stumped experts since the 1960s marks a significant milestone in pure mathematics. It demonstrates how persistent logical inquiry can crack even the most stubborn and entertaining of intellectual challenges, one that will now forever be linked to a beloved Friends gag.
