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A 17-year-old teen refutes a mathematical conjecture proposed 40 years ago
- scythe 1y agoPaper here: https://arxiv.org/abs/2502.06137 https://arxiv.org/abs/2502.06137 I had the opportunity to take a harmonic analysis course in grad school. I passed it up. It was only tangentially related to my research at the time.
- munchler 1y agoI had never heard of the X-Ray Transform until I happened to read about it in the New York Times today, and then here it is again. https://www.nytimes.com/interactive/2025/06/30/science/math-strogatz-calculus-bowling.html https://www.nytimes.com/interactive/2025/06/30/science/math-...
- dekhn 1y agoThis sort of transform (what I think many people call inverse problems) is quite common in reconstruction problems- that is, where you pass light or other EM through an object, the light scatters, and hits a detector. Typically you want to find the minimum error reconstruction. See more here: https://en.wikipedia.org/wiki/Radon_transform https://en.wikipedia.org/wiki/Radon_transform
- schoen 1y agoThat's a funny coincidence that the "Radon" there is a person's name and not the radioactive element or its emanations.
- echoangle 1y agoNot really related but similar situation and I found it funny when I realized it: The Poynting-Vector (https://en.wikipedia.org/wiki/Poynting_vector https://en.wikipedia.org/wiki/Poynting_vector) indicates the direction of the energy flow of a magnetic field, but it’s named after a physicist called „Poynting“, not because it is „pointing“ somewhere. I thought the „y“ in poynting was a typo when I first read it.
- BenjiWiebe 1y agoNominative determinism strikes again.
- rendall 1y agohttps://archive.is/Nr1hH https://archive.is/Nr1hH
- old_man_cato 1y ago[flagged]
- dang 1y agoCould you please stop posting unsubstantive comments to Hacker News? we're trying for something different here.
- old_man_cato 1y ago[flagged]
- kemitchell 1y agoRefuted?
- qsort 1y agoThe Mizohata-Takeuchi conjecture is a statement in the form "For all <x> (a bunch of math)". Showing that there exists an x such that the statement is false disproves the conjecture. She found a counterexample.
- mgiampapa 1y agoShe found more than one way of disproving it in the process.
- gilleain 1y agoYes, found a counterexample to the conjecture.
- zahlman 1y agoYes, either proving a true conjecture or refuting a false one is "solving" it.
- Keyframe 1y agoOriginal title is more informative than the edited one here.
- leephillips 1y agoI submitted under an approximation of the original title, and it was edited within seconds.
- miles 1y agoThere is too much "helpful" title modification of late. The original title itself fits within HN limits: "A 17-year-old teen refutes a mathematical conjecture proposed 40 years ago" The site's guidelines are clear[1] but increasingly ignored by some moderators: "...please use the original title, unless it is misleading or linkbait; don't editorialize." [1] https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- deleted 1y ago[deleted]
- miles 1y agoAfter several hours, the HN title has been modified again to match the original much more closely, from "Hannah Cairo has solved the Mizohata-Takeuchi conjecture"[1] to "Hannah Cairo: 17-year-old teen refutes a math conjecture proposed 40 years ago". [1] https://web.archive.org/web/20250706185220/https://news.ycombinator.com/item?id=44481441 https://web.archive.org/web/20250706185220/https://news.ycom...
- layer8 1y agoAs the submitter, you can re-edit the title after submission (for some limited time period).
- ledauphin 1y agohere's a dumb question: she's starting her Ph.D. this fall - hasn't she already achieved it? What is the theory behind expecting someone who has solved a decades-old problem to do some "second" thing to prove that they have extended the bounds of human knowledge?
- deleted 1y ago[deleted]
- nextos 1y agoA PhD in the US requires a lot of coursework, aside from research. Perhaps, she is interested in that. Otherwise, some universities, especially in EU, offer PhDs by publication. She could simply wrap up her counter-example publication (https://arxiv.org/pdf/2502.06137 https://arxiv.org/pdf/2502.06137) as a thesis and possibly graduate. Sometimes, you can even do this without a supervisor.
- xg15 1y agoSounds as if she even has a potential supervisor: > “It took me a while to convince Ruixiang Zhang [the professor of the course where the problem had been posed] that my proposal was actually correct,” Cairo says > At the University of Maryland, she will continue working under the supervision of Zhang. “He helped me so much, and I’m really grateful. Beyond his class, which I loved, he spent countless hours tutoring me,” she recalls.
- pclmulqdq 1y agoPhD by publication usually takes a bit more work. I think they tend to want 3 related papers in a field.
- paulpauper 1y agoTrying to do anything original and novel in math is extremely hard at any age. to do it at 17 is insanely talented. congrats
- marvinborner 1y agoThere's a video by Hannah Cairo that explains the conjecture and her results [1] Also, Terence Tao hinted at some further advances some time ago [2], does anyone know more about that? [1]: https://www.youtube.com/watch?v=3ZeH_8sTyKA https://www.youtube.com/watch?v=3ZeH_8sTyKA [2]: https://mathstodon.xyz/@tao/114003793236630744 https://mathstodon.xyz/@tao/114003793236630744
- mellosouls 1y agoYes, presumably this: https://terrytao.wordpress.com/2025/02/25/the-three-dimensional-kakeya-conjecture-after-wang-and-zahl/ https://terrytao.wordpress.com/2025/02/25/the-three-dimensio...
- ykonstant 1y agoI will try to incorporate Hannah's notes style into my own stuff; I am using a similar lecturing device with the tablet, but her presentation is soooo far beyond mine. So beautiful!
- tomjen3 1y ago>One day, he proposed proving a special, much simpler case of the conjecture as a homework assignment. As an optional part, he included the original conjecture There is a lesson there: always give people an opportunity to excel, if you can.
- sshine 1y agoI remember at first year of university being presented with a bunch of “simple” problems early on, such as the Collatz conjecture. I remember wanting to spend time trying to explore what a solution might look like, because such simply formulated problems must have equally simple solutions. Maturing and getting a better understanding of my intellectual capacity, I have opted to solve practical problems with a much bigger chance of success and absolutely no groundbreaking qualities. But I liked being taken serious from the start, and I think it’s important to try and solve hard problems before you grow stuck in the real world.
- gopher_space 1y agoI give all of my hard problems to juniors.
- cjensen 1y agoThe best thing about juniors is they don't know a problem is impossible, so they just do it.
- raincom 1y agoGreat achievement. Now Princeton Math department will ask her to join their school for Ph.D.
- xyst 1y ago[flagged]
- fourthark 1y agoHarmonic analysis?
- bradly 1y agoWhile extremely talented, I am not surprised to find this coming from a teen. Major mathematical discoveries often have come from those in their mid 20’s with the greater discoveries being skewed towards the younger 20s and teens. I think this because pure mathematics is just so creative.
- fhdkweig 1y agoThe Fields Medal has a cutoff age of 40 years old.
- jebarker 1y agoMy understanding is that that’s more about encouraging younger mathematicians rather than an expectation that older ones won’t produce anything worthy.
- ameliaquining 1y agoSort of. It's complicated and there was politics involved. https://web.archive.org/web/20210324121533/https://www.nature.com/articles/d41586-018-00513-8 https://web.archive.org/web/20210324121533/https://www.natur...
- jebarker 1y agoThanks for sharing, it's much more complicated than I believed.
- TechnicalVault 1y agoIt doesn't help what we've designed a rather silly academic system where principal investigators are forced to spend a good deal of their time thinking where they'll be applying for their next grant. We also optimise the system for short term thinking rather than long games. There are some exceptions in research institutes but I think young people are the ones who have the clearest minds because of it.
- lordnacho 1y agoHow often does someone produce work that is normally taught to people who are older than the person who discovered it? Euler was 41 when he discovered his famous identity, the kind of thing people learn in school. Even Newton was 21 when he invented calculus, the sort of stuff that you might find late teens learning. Galois by a couple of years? He died at 20, and I suppose they teach that stuff sometime mid uni?
- louistsi 1y agoGalois Theory was a third year second semester course at my university when I studied there, which corresponds to 20-21yo in the UK system.
- make3 1y agoI would assume by having parents involved one way or another early on, with things like private, 1:1 education or the parents themselves being researchers You also need the young person needs to also be extremely motivated and have what it takes. So both the contextual and individual means.
- lazyasciiart 1y agoCarl Gauss, Mozart, Blaise Pascal - his famous theorem was at 17, I believe “Child prodigies” lists some more candidates https://en.wikipedia.org/wiki/List_of_child_prodigies https://en.wikipedia.org/wiki/List_of_child_prodigies
- andrewinardeer 1y ago"Ciaro says it required several tools, including fractals, and she had to arrange everything very carefully." Article could at least spell her name correctly.
- chengiz 1y ago> The conjecture was widely believed to be true — if so, it would have automatically validated several other important results in the field — but the community greeted the new development with both enthusiasm and surprise: the author was a 17-year-old who hadn’t yet finished high school. This article is quite poorly written. Case in point above. If the conjecture was believed to be true, refuting it would be news in itself, deserve more than half a sentence, and have nothing to do with the age of the refuter. It should have been simple to add a line about the "other important results" and not violate show not tell. AlsO I fail to see the relevance of mentioning the Spanish academy? The researcher is from Bahamas/USA, it's just the writer is from Spain?
- MarcelOlsz 1y ago>This article is quite poorly written. Her last name is misspelt in the very first paragraph as well.
- libraryofbabel 1y agoOh come on. This is in the Spanish newspaper El Pais. Context and audience matters. It’s simultaneously news about a math problem, an article about a young mathematician, and an article about things that happened at a math conference in Spain, which is where they presumably interviewed her.
- uselesswords 1y agoSure context and audience matters, but even outside of that the article is rather poorly written. This part in particular should really emphasize that she disproved the conjecture, as it stands it almost sounds like she proved it: > Cairo solved the so-called Mizohata-Takeuchi conjecture, a problem first proposed in the 1980s that had kept the harmonic analysis community had been working on for decades. The conjecture was widely believed to be true — if so, it would have automatically validated several other important results in the field — but the community greeted the new development with both enthusiasm and surprise: the author was a 17-year-old who hadn’t yet finished high school.
- deleted 1y ago[deleted]
- waym0re 1y agoAnyone have a link to her supposed first paper on number theory? I have my doubt on her counter-example. It uses asymptotic methods rather loosely.
- ablaba 1y agoposted 4 days ago https://news.ycombinator.com/item?id=44441730 https://news.ycombinator.com/item?id=44441730