Here's a problem anyone can understand: you're moving a sofa around an L-shaped corridor. What's the largest sofa that can make the turn? Simple to ask. Apparently, impossibly hard to prove.

The moving sofa problem was first posed in 1966 by mathematician Leo Moser — an apparently innocent question about the largest rigid flat shape that can be manoeuvred around a right-angled corridor exactly one metre wide. What looked like a fun geometry puzzle became one of mathematics' most stubborn open problems for nearly six decades.

In 1992, mathematician Joseph Gerver designed a complex curved shape with an area of roughly 2.2195 square metres that stood as the best known candidate for decades — but nobody could actually prove it was the definitive answer. 

Enter Baek Jin-eon. The South Korean mathematician first encountered the puzzle during his military service, was struck by the absence of a clear theoretical framework, and spent the next seven years building a rigorous proof entirely through formal reasoning — no algorithms, no simulations, no geometry software.

The result was a 119-page demonstration published in late 2024, showing that Gerver's shape is indeed the absolute limit — no larger rigid figure can navigate the corridor. He is 31 years old.

The proof is currently under review at the Annals of Mathematics — often regarded as the ultimate stamp of approval for major mathematical breakthroughs.