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Six-decade math puzzle solved by Korean mathematician
- brewcejener 10mo ago[dead]
- gnabgib 10mo ago(2024) Source is Scientific-American https://www.scientificamerican.com/article/mathematicians-solve-infamous-moving-sofa-problem/ https://www.scientificamerican.com/article/mathematicians-so... (https://news.ycombinator.com/item?id=42946052 https://news.ycombinator.com/item?id=42946052) Discussion on the paper (131 points, 2024, 36 comments) https://news.ycombinator.com/item?id=42300382 https://news.ycombinator.com/item?id=42300382
- svat 10mo agoFor what it's worth, the article posted here is not from 2024, but from this week: "Published : Jan. 4, 2026", and contains original reporting (quotes from the researcher). The mention of "Scientific American" in this article refers to something more recent: > US magazine Scientific American named the research by Baek Jin-eon among its top 10 mathematical breakthroughs of 2025 This is a reference presumably to https://www.scientificamerican.com/article/the-top-10-math-discoveries-of-2025/ https://www.scientificamerican.com/article/the-top-10-math-d... "The 10 Biggest Math Breakthroughs of 2025" (dated December 19, 2025). It's more recent than your link https://www.scientificamerican.com/article/mathematicians-solve-infamous-moving-sofa-problem/ https://www.scientificamerican.com/article/mathematicians-so... "Mathematicians Solve Infamous ‘Moving Sofa Problem’" (dated February 4, 2025). November 2024 is when he posted the preprint on the arXiv: https://arxiv.org/abs/2411.19826 https://arxiv.org/abs/2411.19826 "Optimality of Gerver's Sofa" (submitted on 29 Nov 2024). There has been other reporting since then, such as in Quanta Magazine: https://www.quantamagazine.org/the-largest-sofa-you-can-move-around-a-corner-20250214/ https://www.quantamagazine.org/the-largest-sofa-you-can-move... "The Largest Sofa You Can Move Around a Corner" (dated February 14, 2025). (Contains quotes from his adviser Michael Zieve, and from Gerver himself.) The paper is still under review at the Annals of Mathematics, so there will be likely be another round of reporting when it has finished peer review and is published.
- gnatman 10mo ago>> “You keep holding on to hope, then breaking it, and moving forward by picking up ideas from the ashes,” [Baek] said in an interview with a web magazine published by Korean Institute for Advanced Study. “I’m closer to a daydreamer by nature, and for me mathematical research is a repetition of dreaming and waking up.” beautiful!
- yearoftherabbit 10mo agoProfessional mathematician here. Jin's description is spot on. Each repetition of the cycle he describes above feels like you're able to see things in progressively higher resolution. Then one day you wake up and realize you're now an expert.
- jey 10mo agoDan Romik has a nice intro on the moving sofa problem: https://www.math.ucdavis.edu/~romik/movingsofa/ https://www.math.ucdavis.edu/~romik/movingsofa/
- lostlogin 10mo agoYikes. When you’re taking the window frame out to get furniture in, I’m arguing for smaller furniture.
- modeless 10mo agoIs the equivalent problem in 3D harder or easier? Seems like it would be harder but you never know with these things.
- shermantanktop 10mo agoMy intuition says that with vertical walls, the problem collapses to 2d, but that 2d is a cross section of a 3d shape, and an infinite number of 3d shapes can hold that as the max cross section envelope.
- avadodin 10mo agoAs in a hyper-sofa moving around arbitrary unit hyper-square corners? The volume has to be greater than 1 unit in order to be a solution so it could be harder in higher dimensions.
- gcanyon 10mo agoI think it depends on what you mean by "equivalent" 1. If the walls are vertical and you are maximizing the horizontal area of the sofa and you are not allowed to reorient the sofa, then the problem collapses to the 2D case and the solution is the same. 2. If you are allowed to reorient the sofa while moving it, and the sofa doesn't have a minimum height, and the ceiling is arbitrarily high, then the sofa can be arbitrarily large by angling it to an arbitrary degree and then setting it flat for measuring. 3. So the in between case is where the ceiling is of some limited height and/or the sofa is of some arbitrary height, and then you have to decide whether the sofa has to be an extrusion of a 2D shape, or if it can be an arbitrary shape, at which point you're maximizing volume rather than area. And for that the obvious lower bound is the 2D maximum shape * the ceiling height. But maybe there's better?
- hugh-avherald 10mo agoWhat if you to traverse a tunnel that turns 90° in both the x and y directions?
- gcanyon 10mo ago
- OsrsNeedsf2P 10mo agoActual paper: https://arxiv.org/pdf/2411.19826 https://arxiv.org/pdf/2411.19826
- cm2012 10mo agoSo Gerver’s 1992 curved “sofa” (area ≈ 2.2195) is not just a good guess but actually optimal. The problem asks for the largest 2D shape that can be slid around a right-angle corner in a unit-width hallway. Here is the perfect fitting sofa: https://en.wikipedia.org/wiki/File:Gerver.svg https://en.wikipedia.org/wiki/File:Gerver.svg
- plagiarist 10mo agoI think it would be cool to have a sofa in that shape as a joke. It could go in a room tiled with a single shape non-repeatable pattern.
- intrasight 10mo agoA very functional sofa joke as it's the optimal shape for moving.
- eru 10mo agoNot really, because it's only optimal in 2d.
- pixelpoet 10mo agoMost of us don't live in Escheresque labyrinths
- eru 10mo agoIf you've ever moved any furniture at all, you'll notice that it's often much easier to get around corners (or through doorways), if you can turn them sideways. That's especially easy to imagine with tables, but sofas also count. There are also sofas that can be easily taken apart. Eg one of our sofas at home, an L-shaped sofa, comes apart into two pieces.
- throwawayk7h 10mo agoThis is the famous sofa problem! It's hard to believe it's finally solved; I've spent many evenings staring at the wikipedia article wondering at how even what seem to be the simplest of problems defy the reach of mathematics.
- sdenton4 10mo agoThere are times when mathematics is a bit like a full set of wrenches trying to take apart a problem held together by screws.
- llmslave2 10mo ago[flagged]
- thrwaway55 10mo agoBefore or after the solution was published?
- esjeon 10mo agoFinding good-enough solutions is easy. Figuring out if that's the best you can get is another story.
- 3OCSzk 10mo agoThere are like hundreds of unsolved mathematical problems in math on wikipedia page and I can't wait for llmslave2 to solve them all under 1 hour using only AI!!
- srean 10mo agoWhy don't you take its help and offer us a proof of Goldbach's conjecture. LOL. I presume HN textbox is too small. I suspect you were being sarcastic.
- keybored 10mo agohttps://news.ycombinator.com/item?id=46506652 https://news.ycombinator.com/item?id=46506652
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- ukuina 10mo ago*PIVOT!*
- deleted 10mo ago[deleted]
- cousin_it 10mo agoI love the kind of science reporting on display in this article! It stays at a consistent, objective level of detail throughout (no "imagine a vector space as a block of jello" or whatever it is that Quanta and other publications are always doing). It allows specialists to understand exactly what's being claimed, and at the same time stays accessible to laypeople. It feels like it's written for the kind of reader that I aspire to be: not necessarily a specialist on every topic under the sun, but someone who has finished high school and is paying attention. Though I guess writing like this doesn't pay off in the modern world. Most readers don't consistently pay attention when reading, and to be honest, I don't either.
- trehalose 10mo agoI agree that Quanta can be irritatingly stretchy with the metaphors sometimes, but to be fair, "What's the biggest couch you can fit through this hallway corner" is inherently easier to explain to laypeople than like, the Riemann Hypothesis.
- huflungdung 10mo ago[dead]
- Y_Y 10mo agoζ(z)=0⇒-z/2∈ℕ ∨ Re(z)=1/2 i.e. if you apply the zeta function to a complex number, and you get zero, then that number must have been either a negative even integer or had a half as its real part. What could be simpler than that? Those are all fairly simple concepts, and the definition of the function itself is nothing too exotic. I think any highschooler should be able to understand the statement and compute some values of zeta numerically. I'd like to see a statement about couches written so succinctly with only well-defined terms! (I'm being intentionally a bit silly, but part of the magic of the Riemann Hypothesis is that it's relatively easy to understand its statement, it's the search for a proof that's astonishingly deep.)
- StilesCrisis 10mo ago
- noduerme 10mo agoLooking at that graphic... it almost seems obvious. The outer corner radius would be relative to the inner curve radius in some fixed relationship, wouldn't it? The shallower the inner curve, the larger the outer curve has to be. A completely convex outside could have a flat inside. An inside that was concave from end to end could have a flat outside. Kudos to the guy for writing a proof! I wish this article explained better why it took 60 years to solve this...
- kadoban 10mo agoIt's usually hard to explain why proving something is hard, because it's often just: existing/known/obvious approaches didn't succeed. Not terribly satisfying. Often you just have to try doing it and see, and even that won't be satisfying.
- xarope 10mo agoProofs need to be comprehensive. Here's a silly one: since 1, 3, 5 and 7 are primes, it almost seems obvious that all odd numbers are prime. Naturally, they are not, and there are countless proofs about various prime number generators to show that they can generate prime numbers, which are really prime.
- saagarjha 10mo ago1 is not prime.
- xarope 10mo agodarn, I just dated myself back to 1914...
- ezequiel-garzon 10mo agoI agree, modern definitions exclude 1 since "we lose" unique factorization. It's interesting to note [1] that this viewpoint solidified only in the last century. [1] https://mathenchant.wordpress.com/2025/04/21/is-1-prime-and-does-it-matter/ https://mathenchant.wordpress.com/2025/04/21/is-1-prime-and-...
- dirkgwntly 10mo ago> The so-called moving sofa problem asks how large a rigid shape can be while still being able to pass around a right-angled corner in an L-shaped corridor of a constant width of 1 meter. This was also the problem in Dirk Gently’s Holistic Detective Agency, so fictionally this problem had already been solved.
- SecretDreams 10mo agoNow I might need to rewatch that very odd, charming, detective show :).
- lproven 10mo agoThere were at least 2 separate and independent TV series, but I highly recommend going to the original: the 2 later novels from Douglas Adams, after he wrote the Hitchhiker's Guide to the Galaxy. https://en.wikipedia.org/wiki/Dirk_Gently%27s_Holistic_Detective_Agency https://en.wikipedia.org/wiki/Dirk_Gently%27s_Holistic_Detec... https://en.wikipedia.org/wiki/The_Long_Dark_Tea-Time_of_the_Soul https://en.wikipedia.org/wiki/The_Long_Dark_Tea-Time_of_the_... In the novels, a stuck sofa is revealed to have got there because a retired Time Lord, Professor Urban Chronotis, briefly materialised his TARDIS in such a place it provided a doorway. So the books are extremely loosely tied into the Dr Who universe. Don't let this put you off.
- ahazred8ta 10mo agoThe DG novel was partly based on the Doctor Who story where there were six copies of the Mona Lisa, and the bad guy wanted to go back to primitive Earth before multicellular life. "The atmosphere is poisonous. I'm not sure what's in it but it would certainly get your carpets nice and clean."
- calvinmorrison 10mo agoThis is why i keep whittling at the squaring a circle ;)
- teekert 10mo agoNow I want a sofa of that shape to go with my ein-stein tiled floor and decorative Knuth’s dragon. I’ll add some nice art in a shape that can’t pass through itself as well.
- turbonaut 10mo agoIronic. In Korea sofas would often bypass the corridor by way of a ladder lift (which can be scarily high). https://centers.ibs.re.kr/html/living_en/housing/moving2.html https://centers.ibs.re.kr/html/living_en/housing/moving2.htm...
- seoulbigchris 10mo agoyep, I see those often here -- scary. Another sofa-related irony is that a lot of Koreans don't actually sit on their sofas. Rather, they sit on the (heated) floor and use the sofa as a back rest. https://koreajoongangdaily.joins.com/news/2024-05-18/culture/lifeStyle/WHY-Why-Koreans-love-the-floor-The-cultural-secret-behind-ignoring-sofas/2049113 https://koreajoongangdaily.joins.com/news/2024-05-18/culture...
- cubefox 10mo agoThis won't be popular [1], but research breakthroughs in theoretical mathematics seem to be often useless in a way that useless science is not. Scientific breakthroughs are also often useless (nothing practical is gained from the first detection of a gravitational wave, or from finding out how flight first evolved in insects) but scientific insights still have more information content: they tell us facts specifically about our world, while mathematical proofs merely tell us about all possible worlds. About some consequence of made-up assumptions we happen to find interesting. It's a bit like finding the fastest way possible to beat Super Mario Bros 3 while collecting the minimum number of coins. A solution to a neat puzzle, but it doesn't carry the epistemic weight of finding out how the universe works, even if both pieces of knowledge are equally useless. 1: And of course this point doesn't apply to applied math.
- srean 10mo agoNumber theory was deemed useless and celebrated for it being so.
- leonvoss 10mo agoI agree with you. I would rather this brain power go to modeling genetics, politics, and evolution. Fake problems like the sofa problem are overcelebrated while important issues like theory of eugenics are villified and undercelebrated.
- gn4d 10mo agodw, you're not alone in this. Researchers like this are extremely impressive, but it seems like an absolutely massive misallocation of his brainpower. Sure, people can say the same about art/literature/chess/etc., but I would argue that more people benefit from viewing or experiencing the latter than will benefit from working through all 119 pages of this paper. This guy could be doing medical or other scientific research, but instead is working on some contrived problem. Even here, let's assume there is some remote application for a nanobot for targeted drug delivery transiting a capillary... "rough" computational solutions will be more than adequate, especially when taking into account wall elasticity and other variables. I do wonder why some of the top institutions in the world like KIAS are even funding this.
- webdoodle 10mo agoLooks like a couch, should have just given the prize too a furniture mover. /s
- 1over137 9mo agoI love how the article ends with an email address as signature. No bloody social media, just normal universal email.