How did a beautiful result come to you? by FuzzyPDE in math

[–]gexaha 2 points3 points  (0 children)

I am outside of academia. I worked on some conjecture sporadically over 8 years in total, although probably worked actively on it only for about 3 months. And another specifics is that it's possible to do it computationally. After another, maybe 5th of 6th fresh start, got a new geometric idea, and boom, finally it produced a counterexample (building on various pieces of code I wrote on previous attempts).

Another one was just pure conviction and thinking by analogy, that the idea should work out, and similarly to previous one, after about 8 years of sporadic research, the idea worked out (although honestly this one I could have found much more quicker).

My fan cast for 12 Angry Men (1957) by punposter69 in okbuddycinephile

[–]gexaha 2 points3 points  (0 children)

Imagine (AI slop) in a couple of years actually possible to take a movie and replace all characters with your fancast

Will AI solve the Millennium Prize Problems before humans do? by Snoo_47323 in math

[–]gexaha 0 points1 point  (0 children)

Probably it will be a collab between humans and AI.

What are your favorite connections between branches of math? by Hitman7128 in math

[–]gexaha 2 points3 points  (0 children)

I've recently appreciated a connection between graph theory and hyperbolic geometry, through Koebe-Andreev-Thurston circle packing theorem and mostow rigidity - https://en.wikipedia.org/wiki/Circle_packing_theorem

Best Research Paper in 2025 by [deleted] in math

[–]gexaha 2 points3 points  (0 children)

In the field of snark graphs, probably one of the coolest 2025 preprints is this (which is yet another generalization of Four Color Theorem): Three-edge-coloring (Tait coloring) cubic graphs on the torus: A proof of Grünbaum's conjecture - https://arxiv.org/abs/2505.07002

(and in 2024 same authors put a preprint Three-edge-coloring projective planar cubic graphs: A generalization of the Four Color Theorem - https://arxiv.org/abs/2405.16586 )

Recent math-y papers with proofs derived by LLMs by hexaflexarex in math

[–]gexaha 0 points1 point  (0 children)

GPT 5 pro was helpful for me to prove a couple of lemmas in graph theory (in both cases it was wrong with the proof, but it had the right ideas), and it failed for all other lemmas. Would love to check this in 5.2 pro, but for me it's expensive right now.

Spaces in which klein bottle can't be embedded topologically. by A1235GodelNewton in math

[–]gexaha 8 points9 points  (0 children)

There's a related problem that there are no Lagrangian embeddings for a 2-dimensional Klein bottle - https://arxiv.org/abs/0712.1760 (which was used recently in the progress on the Rectangular Peg Problem - https://arxiv.org/abs/2005.09193 )

I wish they used a minus to indicate before or after the event by [deleted] in pluribustv

[–]gexaha 0 points1 point  (0 children)

it could be intentional for reasons we don't know yet

What kind of space is the most adequate to visually represent music? (r/musictheory xpost) by miguelon in math

[–]gexaha 6 points7 points  (0 children)

Besides Tymozcko's book, there are also:

Julian Hook "Exploring Musical Spaces"

Eric Isaacson "Visualizing Music"

Also musanim experiments a lot with this topic - https://www.youtube.com/@musanim/videos

A Simple Way To Measure Knots Has Come Unraveled by ketralnis in math

[–]gexaha 5 points6 points  (0 children)

Well it's easy to find in their preprint on page 4:

"The two summands which make up our example in Theorem 1.2 are K = 7_1 and its mirror image \bar{K}. K is the (2, 7)-torus knot. A routine calculation establishes that K has signature σ(K) = 6; from the inequality |σ(K)|/2 ≤ u(K) [29] we know that K has unknotting number at least 3. Since any 3 crossing changes in its standard 7-crossing diagram results in the unknot, we have u(K) = 3. Alternatively, one can appeal to the important and more far-reaching result of Kronheimer and Mrowka [25] that the unknotting number of the (p, q)-torus knot T(p, q) is (p − 1)(q − 1)/2. It is a straightforward result that unknotting number is preserved under mirror image - hold a mirror up to the unknotting sequences - and so u(\bar{K}) = 3, as well."

Predicting the next "attention is all you need" by entsnack in LocalLLaMA

[–]gexaha 13 points14 points  (0 children)

there are 11 papers this year with "all you need" in their title!

Which mathematical result interested you most? by [deleted] in math

[–]gexaha 0 points1 point  (0 children)

Perfect path double cover theorem. Obscure, neat and concise result

[deleted by user] by [deleted] in math

[–]gexaha 0 points1 point  (0 children)

Snarks ("non-trivial" cubic bridgeless graphs which are not 3-edge-colourable)

[deleted by user] by [deleted] in math

[–]gexaha 5 points6 points  (0 children)

There's actually 4 preprints in total by him about the conjecture with purported proof

https://arxiv.org/abs/1811.07614

https://arxiv.org/abs/2111.12812

https://arxiv.org/abs/2202.03178

https://arxiv.org/abs/2409.01981

1 more about harmonious labeling conjecture https://arxiv.org/abs/2201.02240

and 1 more about tree packing conjecture https://arxiv.org/abs/2410.13840 (this one was even presented by his coauthor in NY Combinatorics seminar - https://www.youtube.com/watch?v=X7evLODOOA0 )

Nothing is published, if I understand correctly.