by kiicia on 5/5/25, 7:48 PM
> Mathematicians Weinan Lin, Guozhen Wang, and Zhouli Xu have proven that 126-dimensional space can contain exotic, twisted shapes known as manifolds with a Kervaire invariant of 1—solving a 65-year-old problem in topology. These manifolds, previously known to exist only in dimensions 2, 6, 14, 30, and 62, cannot be smoothed into spheres and were the last possible case under what’s called the “doomsday hypothesis.” Their existence in dimension 126 was confirmed using both theoretical insights and complex computer calculations, marking a major milestone in the study of high-dimensional geometric structures.
by uxhacker on 5/5/25, 6:06 PM
I’m not a mathematician (just a programmer), but reading this made me wonder—doesn’t this kind of dimensional weirdness feel a bit like how LLMs organize their internal space? Like how similar ideas or meanings seem to get pulled close together in a way that’s hard to visualize, but clearly works?
That bit in the article about knots only existing in 3D really caught my attention. "And dimension 3 is the only one that can contain knots — in any higher dimension, you can untangle a knot even while holding its ends fast."
That’s so unintuitive… and I can't help thinking of how LLMs seem to "untangle" language meaning in some weird embedding space that’s way beyond anything we can picture.
Is there a real connection here? Or am I just seeing patterns where there aren’t any?
by bee_rider on 5/5/25, 7:32 PM
Is it conventional for mathematicians to talk about “the dimensions” like this? I think they are talking about a 126 dimensional space here, but I am a lowly computerer, so maybe this went over my head.
by jebarker on 5/8/25, 2:08 PM
I had this article on the back burner the past couple of days. Low and behold when I read it my PhD supervisor (Vic Snaith) is mentioned and it has all sorts of connections to the work I did, but this is the first time I've ever heard of the problem! Goes to show just how intricate modern math is.
by elpocko on 5/5/25, 6:13 PM
The "Mathematical Surgery" illustration is funny. Mathematicians can make a sphere from a torus and two halves of a sphere. Amazing!
by Xmd5a on 5/6/25, 8:40 AM
>And dimension 3 is the only one that can contain knots — in any higher dimension, you can untangle a knot even while holding its ends fast.
Ok. So, this is a BDSM universe. Interesting.
by ReptileMan on 5/5/25, 8:49 PM
>And dimension 3 is the only one that can contain knots — in any higher dimension, you can untangle a knot even while holding its ends fast.
Do we have anything in the universe that is knotted? Both on large and small scales. Or it is just coincidence?
by anthk on 5/5/25, 8:16 PM
Network optimizing problems are just better with 4D hypercubes.
by lifefeed on 5/5/25, 8:16 PM
Well, shit.
by m3kw9 on 5/5/25, 9:49 PM
This is some Dr Strange stuff
by impish9208 on 5/5/25, 10:56 PM
This got me thinking — is there a version of “in mice” for math papers?
by zchrykng on 5/5/25, 7:47 PM
Seeing as mathematicians proving things in math has minimal relation to the real world, I'm not sure how important this is.
Mathematicians and physicists have been speculating about the universe having more than 4 dimensions, and/or our 4 dimensional space existing as some kind of film on a higher dimensional space for ages, but I've yet to see compelling proof that any of that is the case.
Edit: To be clear, I'm not attempting to minimize the accomplishment of these specific people. More observing that advanced mathematics seems only tangentially related to reality.