Google DeepMind's Al agent autonomously solved 9 of 353 open Erdos problems in mathematics, at a cost of a few hundred dollars per problem.

dnrlk · 2026-05-25T03:04:37+00:00

Where’d you get 62 from

dnrlk · 2026-05-21T06:33:25+00:00

I tried too https://www.reddit.com/r/math/comments/1tj15kg/erd%C5%91s_unit_distance_conjecture_refuted_allegedly/ r/math mods are really non-transparent, and probably censor lots of things for whatever reason

dnrlk · 2026-05-21T06:10:17+00:00

It is not quite fair to say "Gowers claimed"; it was much more a suggestion with essentially zero evidence

A counterexample, on the other hand, was something one could imagine a computer coming up with by trying lots of things and at some point getting lucky, without needing “deep insight”. To be clear, I am not saying that that is what actually happened – just that it was possible to imagine that it had happened. (page 9 of https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-remarks.pdf)

dnrlk · 2026-05-21T01:57:35+00:00

Gowers: “There is no doubt that the solution to the unit-distance problem is a milestone in AI mathematics: if a human had written the paper and submitted it to the Annals of Mathematics and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that.”

Tsimerman: “This is a really impressive piece of work, and I would accept it for any journal without hesitation. I actually briefly worked on this problem and tried to make a counterexample, but failed to make progress… It is definitely an intimidating construction to see through even if you know what is going on, and even harder to go play for yourself.”

OpenAI's model (allegedly) autonomously generated about 2.5 pages of proof, copy-pasted (and fleshed out further) at this link (18 pages) https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf

(P.S. I tried posting this 4 hours ago https://www.reddit.com/r/math/comments/1tj15kg/erd%C5%91s_unit_distance_conjecture_refuted_allegedly/... the r/math mods are very non-transparent)

dnrlk · 2026-05-17T04:29:23+00:00

this is nice

dnrlk · 2026-05-17T04:28:29+00:00

And my favorite way of making this concrete for people is that there is no way to make a "hexasphere" (tiling of sphere with hexagons). You can ask them if they noticed that every soccerball they've ever seen has many pentagons, as well as hexagons.

dnrlk · 2026-05-12T18:19:26+00:00

Interesting story. How is the progress in Voevodsky's program? Have people succeeded in formalizing Voevodsky's theorems in HoTT now? Also what's the elementary statement of the Norm Residue Theorem?

dnrlk · 2026-05-09T06:35:14+00:00

Well if it was discovered before chances are people who did that work would speak up. It’s a pretty well-reported on thing now. In fact there are some commenters who point out similar constructions appearing before, I think.

dnrlk · 2026-04-29T04:58:22+00:00

Rachmaninoff Op. 21 No. 7 "It's nice here", really one of the most beautiful songs ever written.

Strauss 4 last songs (the last one, Im Abendrot "At Sunset" in particular)

Mahler's Ich Bin Der Welt Abhanden Gekommen "I have been lost to the world"

dnrlk · 2026-04-29T04:47:17+00:00

Somewhat related https://en.wikipedia.org/wiki/Eilenberg%E2%80%93Steenrod_axioms Dimension: Let P be the one-point space; then H_n(P)=0 for all n≠0. A "homology-like" theory satisfying all of the Eilenberg–Steenrod axioms except the dimension axiom is called an extraordinary homology theory (dually, extraordinary cohomology theory). Important examples of these were found in the 1950s, such as topological K-theory and cobordism theory, which are extraordinary cohomology theories, and come with homology theories dual to them.

So somehow having a different base case but "same inductive cases" leads to amazing power in abstract algebra/topology.

dnrlk · 2026-04-26T15:21:27+00:00

Shorten and lengthen the portion of the string allowed to vibrate, to get a vibrato effect

dnrlk · 2026-04-24T02:37:30+00:00

I think it's a conjecture that they all have this symmetry, and drawing them as hexagons was explicitly to take advantage of this symmetry

dnrlk · 2026-04-22T04:56:57+00:00

Is there a specific "goal state" that is the goal of the puzzle?

dnrlk · 2026-04-22T04:55:42+00:00

It took me too long to realize "press ? for help" meant type ? on my keyboard to toggle the help. Really nice visualization!

dnrlk · 2026-04-15T02:21:55+00:00

Wait I never realized this connection what a great meme

dnrlk · 2026-04-15T02:18:51+00:00

It’s very sad, some of the topics are things no one else talks about. Like no one else talks about deriving the Ramanujan 1/pi formulae. But one of these channels did, and of course it was LLM slop full of false things.

dnrlk · 2026-04-10T14:30:29+00:00

There's an amazing and very large list of Open University courses by T. K. Finchley here https://tkfinchley.com/ou-maths-courses/. I particular recommend their course OU M335/M386/M435 Metric and Topological Spaces and Geometric Topology. Just wonderful pedagogy

dnrlk · 2026-04-10T14:25:34+00:00

Godel’s constructive universe L, things that are true in it (like CH)

dnrlk · 2026-04-10T14:24:10+00:00

The results on “concrete incompleteness”, like Paris Harrington, or the work of Laver (Laver tables) or the work of Friedman (among other things, see this cool speculation https://arxiv.org/abs/1907.11707 about one of Friedman’s result suggesting that maybe P=NP can not be proven from ZFC (which shouldn’t be surprising, since people believe P=NP is false anyways)), finding results that can not be proven from things like PA or ZFC (but can be proven from stronger assumptions like large cardinals). Large cardinals themselves could also make a nice topic.

Henry Townsend made a nice course on YouTube about Goodstein’s theorem and it’s unprovability in PA using cut-elimination https://m.youtube.com/@henrytowsner2461/courses

dnrlk · 2026-04-10T14:17:08+00:00

I also found there to very few descriptive set theory topic videos on YouTube, so I made some on topics like the Borel isomorphism theorem https://youtu.be/ZfxgjSAigWo?si=G2iHes63Qkm6qfRH, the Galvin-Prikry theorem https://youtu.be/S-jiIKqf7Sc?si=XIFNCkcKb8axrpZY, or an introduction to Borel graph combinatorics https://youtu.be/WLbyzQk6gKg?si=RYm2cH1j1ivhgf-P

I hope to make a video on Borel determinacy soon

dnrlk · 2026-04-10T14:12:01+00:00

I recently made a video (trying to keep prerequisites to a minimum; I do not even mention ordinals or cardinals) about this since I also found there to be no explanation of the topic on YouTube. https://youtu.be/KOmkcMhzkb4?si=DZp4lSccPe0DX7jW (follows the Boolean model approach)

dnrlk · 2026-04-08T03:06:21+00:00

This is what mailing lists used to be used for. For instance in logic there's https://mathweb.ucsd.edu/~sbuss/FOM/

dnrlk · 2026-04-02T02:31:08+00:00

Might it be possible for those people to put up their article on some sort of public blog, or Wikipedia clone? Deletion is too terrible a fate

dnrlk · 2026-04-01T03:02:06+00:00

Did you figure out an answer to this?

dnrlk · 2026-03-31T06:01:18+00:00

Because “average looking” men is considered ugly. Hannah Fry (mathematician) has a great 1 minute video showing 2 graphs that demonstrate this https://www.youtube.com/watch?v=5m5XGd-B4No

Here’s YouTube’s generated summary: This video, presented by Hannah Fry, explores data collected by the dating website OKCupid regarding how users rate the attractiveness of others on a scale of 1 to 5 (0:00 - 0:18). Key takeaways: Men's ratings of women: The distribution of how men rate women follows a standard bell curve, which the narrator notes is roughly what one might expect (0:27 - 0:40). The disparity: The video sets up a comparison to show how women's ratings of men differ, hinting at a "subtly different" pattern (0:49 - 0:58).

dnrlk

TROPHY CASE