Solving a 60-Year-Old Math Mystery with a Single Unifying Formula
When picturing a person who solves a legendary math problem, one might imagine an elderly professor with a head full of gray hair. But Jineon Baek, the mathematician who recently cracked the infamous “moving sofa problem,” doesn’t quite fit the stereotype. Freshly minted with a Ph.D., Baek arrived at the interview in a black jacket, radiating the calm focus and quiet energy more typical of a university student than of a celebrated mathematician. His humble demeanor stood in contrast to the feat he had just accomplished—solving a puzzle that had confounded mathematicians for more than six decades.
The “moving sofa problem” poses a deceptively simple question: What is the largest shape of a sofa that can be maneuvered around a right-angled hallway corner? While it may sound like a quirky geometry riddle, it is actually an immensely complex optimization problem involving infinite-dimensional variables and elusive geometric calculations. The problem has long frustrated mathematicians due to its blend of geometric intuition and analytical intractability.
Baek’s breakthrough has made ripples through the global math community, catapulting him into the spotlight as a rising figure in the field. We sat down with him to hear how he approached the challenge, and what it took to bring this decades-old conundrum to a close.
Q: Can you introduce yourself to our readers?
I’m currently a postdoctoral researcher at Yonsei University under Professor Junkyung Lee. I completed my Ph.D. at the University of Michigan and my undergraduate studies at POSTECH in South Korea.
Q: How did you first come across the sofa problem?
During my mandatory military service, which I fulfilled as an alternative research program, I stumbled upon a Korean math blog during some downtime. It featured a variety of intriguing puzzles, and one of them happened to be the moving sofa problem. The blog has since been taken down, but at the time, it was a treasure trove of curious mathematical problems—and that’s where I first encountered this one.
Q: Did you begin with the intent of solving a famous open problem?
I’ve always had the desire to solve at least one difficult problem in my life. Back in school, I dreamed of making the national math Olympiad team, though I never quite made it. But I did spend long periods grappling with hard problems, and that helped build the endurance I needed for this. Over the years, I attempted dozens of unsolved problems—mostly without success. But the sofa problem somehow felt “doable,” and I trusted that feeling.
Q: It seems so simple on the surface. Why is it so difficult?
There are several structural reasons. First, to describe a sofa shape precisely, you need infinitely many variables. Every curve, every corner requires its own definition—so you end up with an infinite-dimensional optimization problem. Second, unlike other problems where you can write down a neat formula, this one doesn’t allow for that. Each shape would need its own custom equation, and it wasn’t clear which shapes or which formulas were even appropriate.
Q: What was your approach?
Traditionally, people tried to tackle each possible sofa shape individually. I took a different approach—I tried to create one overarching formula that could apply to all shapes. Instead of calculating the exact area of the sofa, I defined a formula that gives an upper bound—a value slightly larger than the actual area—but which equals the true area when applied to the optimal shape. That way, I could turn the problem into a single coherent optimization challenge, rather than dealing with countless separate cases.
Q: Were there moments when you hit a wall?
Absolutely. I had a strong sense that the problem was solvable, but the first three years yielded no concrete progress. I didn’t even know how to start. I simply had to keep going on faith. Only after three years did I find a framework that seemed promising. Even then, executing that plan was grueling. The final proof ran nearly 400 pages. There were days when I could barely write a single page. It felt like walking through a tunnel with no end in sight.
Q: Seven years on one problem is hard to imagine. How did you stay motivated?
I had to learn to be comfortable with uncertainty. In high school, I would sometimes wrestle with Olympiad problems for weeks or even months. Those early experiences taught me how to endure long periods of mental fog. If I had an unproductive day, I’d simply say, “Well, not today,” and keep going. I also developed a sort of intuitive faith—an internal compass that told me the solution might be waiting around the corner.
Q: What drew you to mathematics in the first place?
As a child, I remember getting a stack of textbooks at the start of the school year. This was before I had access to a computer, so out of boredom, I started reading them all. Math just grabbed me more than any other subject. It wasn’t some grand epiphany—just a natural pull that’s stayed with me ever since.
Q: Did you ever look at sofas differently during this process?
The “sofa” in the problem isn’t really a sofa in the everyday sense, so I don’t feel sentimental when I see one. But friends do like to joke, “Bet you can’t look at that without thinking about your problem!”
Q: Did you ever physically push a sofa through a hallway to test things out?
I didn’t, personally. But I know that Professor Ben Romik at UC Davis 3D-printed models of sofa shapes and conducted some real-life tests. I think it’d be fun to make a model someday and display it in my office.
Q: Did you have a classic “Eureka!” moment?
Yes—ironically, in the shower. I had designed a formula to estimate sofa area from above, but in order to optimize it, I needed it to have a mathematical property called convexity. One day, while showering in my small basement apartment in the U.S., the key idea just flashed into my head. I rushed out to write it down before the thought slipped away.
Q: What is the broader mathematical significance of solving the sofa problem?
It sits at the intersection of two fields: motion planning, which deals with how robots or self-driving cars navigate around obstacles, and volume optimization, which is about maximizing area or volume under constraints. Both are well-studied individually, but combining them—especially under such a simple premise—was a rarity. I think this work provides a useful case study for tackling other hybrid problems and contributes meaningfully to theoretical math.
Q: What are you working on now?
I’m currently looking at how to pack four-dimensional spheres as densely as possible. This has been solved in 3D with computer assistance, but 4D remains open. I’m also interested in whether machine learning can assist with solving hard math problems. And I still enjoy tackling pure theoretical questions, like the so-called “happy ending problem,” which has a sort of elegant beauty to it.
Q: Any words for young people interested in math?
Honestly, I think it’s worth seriously considering not doing math. The world is vast and full of fascinating fields. Explore broadly, and only pursue math if, after all that, you find yourself thinking, “I can’t not do this.” If that happens, go for it with everything you’ve got.
Rather than chasing quick answers, Jineon Baek carved his own path through years of uncertainty. What guided him was a quiet confidence, a relentless focus on the problem, and an unwavering belief that persistence could reveal the solution, even in the murkiest of unknowns. In solving the moving sofa problem, Baek displayed not just intellectual rigor, but a calm, unshakable resolve. That same steady determination now fuels his journey into the next great mathematical frontiers. Unbound by convention and driven by purpose, Baek’s steadfast approach invites anticipation: what new possibilities might he unlock in the vast, unfolding universe of mathematics?
