For 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
November 2024 is when he posted the preprint on the arXiv: 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... "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.
>> “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.”
Professional 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.
This 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.
I 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.
For many publications you could be critisizing, I'd agree with you, but Quanta usually reaches a higher standard that I feel they deserve credit for. Here's the Quanta article on the same thing [1]. It goes into much more detail, it shows a picture of the perfect sofa, and links to the actual research paper. They're aimed at a level above "finished high school", and I appreciate that; it gives me a chance to learn from the solution to a problem, and encourages me to think about it independently.
I agree with you that Quanta doesn't always "allow specialists to understand exactly what's being claimed", which is a problem; but linking to the research papers greatly mitigates that sin.
And here's how they clearly explain the proof strategy.
> First, he showed that for any sofa in his space, the output of Q would be at least as big as the sofa’s area. It essentially measured the area of a shape that contained the sofa. That meant that if Baek could find the maximum value of Q, it would give him a good upper bound on the area of the optimal sofa.
> This alone wasn’t enough to resolve the moving sofa problem. But Baek also defined Q so that for Gerver’s sofa, the function didn’t just give an upper bound. Its output was exactly equal to the sofa’s area. Baek therefore just had to prove that Q hit its maximum value when its input was Gerver’s sofa. That would mean that Gerver’s sofa had the biggest area of all the potential sofas, making it the solution to the moving sofa problem.
Agree, but I wanted more. What is the intuition behind the optimality proof? I realize you cannot summarize a 119-page paper in two paragraphs, but still.
Looking 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...
> 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.
Now 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.
yep, 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.
This 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.
I 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.
dw, 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.
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[ 3.7 ms ] story [ 43.2 ms ] threadDiscussion on the paper (131 points, 2024, 36 comments) https://news.ycombinator.com/item?id=42300382
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-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-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 "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... "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.
“I’m closer to a daydreamer by nature, and for me mathematical research is a repetition of dreaming and waking up.”
beautiful!
https://colab.research.google.com/github/google-deepmind/alp...
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.
I agree with you that Quanta doesn't always "allow specialists to understand exactly what's being claimed", which is a problem; but linking to the research papers greatly mitigates that sin.
[1] https://www.quantamagazine.org/the-largest-sofa-you-can-move...
And here's how they clearly explain the proof strategy.
> First, he showed that for any sofa in his space, the output of Q would be at least as big as the sofa’s area. It essentially measured the area of a shape that contained the sofa. That meant that if Baek could find the maximum value of Q, it would give him a good upper bound on the area of the optimal sofa.
> This alone wasn’t enough to resolve the moving sofa problem. But Baek also defined Q so that for Gerver’s sofa, the function didn’t just give an upper bound. Its output was exactly equal to the sofa’s area. Baek therefore just had to prove that Q hit its maximum value when its input was Gerver’s sofa. That would mean that Gerver’s sofa had the biggest area of all the potential sofas, making it the solution to the moving sofa problem.
Edit: This article from September has a bit more: https://www.popsci.com/science/gervers-sofa-problem-solved/
So I don’t think this article can even qualify as a good example for explaining math problems to laymen.
This was also the problem in Dirk Gently’s Holistic Detective Agency, so fictionally this problem had already been solved.
https://centers.ibs.re.kr/html/living_en/housing/moving2.htm...
https://koreajoongangdaily.joins.com/news/2024-05-18/culture...
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.