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It's a paper by Terrence Tao, and Rachel Greenfeld. Terrence Tao features here often. They disproved a longstanding conjecture in geometry known as the periodi
by isaacfrond 4y ago
It's a paper by Terrence Tao, and Rachel Greenfeld. Terrence Tao features here often.
They disproved a longstanding conjecture in geometry known as the periodic tiling conjecture. This conjecture stated that it was impossible to devise a tile that could cover a higher-dimensional space aperiodically, but not periodically. The two mathematicians were able to construct a tile that could do just this, breaking the conjecture. This finding has implications for the understanding of patterns and symmetry in higher-dimensional spaces.
- ndsipa_pomu 4y agoI feel that Terrence Tao doesn't get much recognition outside of maths circles but he's one of those people who just seem to be in a totally different league. Maybe it's just that maths doesn't capture the public's imagination as it's incomprehensible to people not involved with the field.
- evolve2k 4y agoWe’ll this article is maybe a good case in point. Surely as they were talking of tiled geometry there could have been space for a few visual examples, even if they hit a practical limit and said ‘It’s theoretical from here but this gives the idea’.
- klyrs 4y agoI was too. I mean, they show the aperiodic Penrose tiles, which is nice because that's approachable. But the punchline of the story quashes the hope of a nice illustration of the result: the proof works in 2^(100^100)-dimensional space. We always joke that one must only visualize n-space and set n to 2^(100^100)... but that isn't much of a help. It really is a nasty geometry.
- voxl 4y agoTerrence Tao is just another human, who had a lot of investment at a young age from world renowned mathematicians. The guy also isn't a huge fan of "genius"-type hype around his work. Don't let the existence of someone be the excuse you use to tell yourself you couldn't also do something cool or great.
- thereare5lights 4y agoI'd bet any amount of money you want that you could just do the same thing with any arbitrary human and create a mathematician of his caliber. The idea that any kid who gets a lot of investment at a young age from world renowned mathematicians will be another Terrence Tao or even 10% of Tao is not plausible. He may not like the genius label, but in his case, it is absolutely true.
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- pgayed 4y agoCommenter doesn't say you would produce another Terrence Tao: > Don't let the existence of someone be the excuse you use to tell yourself you couldn't also do something cool or great.
- robinhouston 4y agoMeta: I’m fascinated by the way that a string of five comments, by different users, have all copied the misspelling of Terence Tao’s name from the original comment by isaacfrond.
- pyinstallwoes 4y agoIs that something GPT would do?
- Ygg2 4y agoNot really. Terrence and Terence are too visually similar and tbh I've seen more former than latter.
- ndsipa_pomu 4y agoI hadn't realised I'd misspelled his name until I saw your comment. For some reason, it looks better with two 'r's.
- _0ffh 4y ago> doesn't get much recognition outside of maths circles I don't know. I'm definitely not "maths circles" and I don't know a whole lot of mathematicians by name. Those I do know are either personal acquaintances or people I consider to be more or less famous (people like Gauss, Fermat, Laplace, Hilbert, von Neumann, or Perelman). I definitely know Tao's name. He's not an acquaintances of mine, so I reason he must be more or less famous. =)
- ndsipa_pomu 4y agoWell, I wouldn't include myself in 'maths circles' either, but I enjoy reading popularised maths articles and occasional maths videos (e.g. 3Blue1Brown, Mathologer). It just seems far more niche than other topics - I wonder how many people are familiar with Perelman as well.
- _0ffh 4y agoYes, Perelman was by far the hardest to come up with, but I really wanted at least one contemporary name in there.
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- tromp 4y agoWhat I found interesting about the construction is that they used dimensions like lines of code in a program, each trying to accomplish one small task. PS: Terence is with one r.
- User23 4y agoYeah, it’s really neat seeing mainstream mathematicians finally applying mathematical methods computing scientists discovered half a century ago. The isomorphism between programs and proofs implies we’ll see this or similar techniques developed for constructing programs that can be readily mathematically reasoned about applied more and more often in different areas. Good stuff.