6 captures, most recent first.
Dimitris Papailiop... @DimitrisP... · 23h
I think we are entering a new era of research on small transformers, where many questions we would previously have answered by running experiments can instead be answered mathematically.
This is possible because the cost of doing math has effectively collapsed to verification (much easier than proving stuff!).
Now, instead of testing an empirical hypothesis, we can ask whether the corresponding theorem is true and have GPT or Claude try to prove it.
Math for AI is finally close to becoming a practical probe of reality and not just a way to explain stuff after the fact, but a way to REPLACE experiments and be directly used to explore what is true in the first place.
Kind of incredible!
[quoted tweet]
Dimitris Papailiop... @DimitrisP... · 23h
inspired by @Kangwook_Lee's bat signal and @jefrankle's like, and with the help of GPT-5.6 Sol you can actually prove it :)
In fact it is true that any function f(a,b) -> C ca...
[embedded image of proof text]
Theorem 1 — exact modular addition in a random frozen transformer
With probability one over the frozen random parameters Θ, there exist token embeddings
E_0, ..., E_{p-1}, E_∞ ∈ ℝ^d
and an unembedding
U ∈ ℝ^{p×d}
such that, simultaneously for every a, b ∈ [p],
argmax_{c ∈ [p]} [U h_3(E_a, E_b, E_∞)]_c = (a + b) mod p.
Indeed, we can choose the number embeddings to lie on a one-dimensional line
E_a = au
for any fixed nonzero u ∈ ℝ^d.
Moreover, after conditioning on the random attention weights, the unembedding can be chosen so that the correct class has logit exactly 1 and every incorrect class has logit exactly 0.
Thus the classification margin is exactly 1.Note from Claude Sonnet 5
Tweet thread from Dimitris Papailiopoulos arguing that AI-assisted proof-writing (using GPT-5.6/"Sol") is turning mathematical proof into a practical substitute for running ML experiments, illustrated by a proven theorem about exact modular addition in a random frozen transformer.
ai for mathmechanistic interpretabilitytransformerstheoretical mltwitter
carl feynman ✓ @carl_feynman · 4h
The HRT conjecture has been disproven with AI help. arxiv.org/pdf/2608.05044.
Here's what the conjecture says. Consider a "bump function": a function from the reals to the complex plane, that is mostly confined to a short interval, and trails off exponentially out of that interval. Suppose we take time-frequency shifts of that bump: we can slide it sideways, or multiply it by sine waves, or both. That gives us various other wiggly bumps. Can we contrive that adding a finite number of such time-frequency shifts to the original bump exactly cancels it out? HRT conjectured in 1996 that we couldn't: that there would always be some smidgen left over that we couldn't cancel out. (And I've always found that plausible.). But that's wrong! The paper proves the existence of such a function. And it constructs a numerical approximation to it, plotted in pages 43 and 44 of the paper.
Terry Tao has a blog post talking about the proof in an easier way: terrytao.wordpress.com/2026/08/06/a-p…
Note from Claude Sonnet 5
Screenshot of an X post by carl feynman reporting that the HRT conjecture (Heil–Ramanathan–Topiwala, 1996) has been disproven with AI help, explaining the conjecture in plain terms — whether finitely many time-frequency shifts of a bump function can exactly cancel it — and linking the arXiv paper plus a Terry Tao blog post explaining the proof.
mathematicshrt conjectureai for mathterry taoarxivproof
[Reposted by: Sichu Lu]
@danrobinson (Dan Robinson) — 12:05 PM · Jul 22, 2026 · 67.1K Views
The models are increasingly good at Erdos problems, but some experts like @Qiaoqiao2001 seem to have exceptional skill at prompting
We sponsored him to see how far he could go
He solved six this week, including one that had been studied by Terence Tao
Here's how he did it:
> QUOTED: @Qiaoqiao2001 (Shouqiao Wang) — 5h
> I solved 6 open Erdős problems in 5 days, using @OpenAI GPT-5.6 Sol.
>
> I have a math background, but the Codex workflow I used does not require deep mathematical knowledge.... [truncated]
Note from Claude Sonnet 5
Tweet describing a sponsored effort where a prompting specialist (Shouqiao Wang) reportedly solved six open Erdős problems in a week using OpenAI's GPT-5.6 Sol via a Codex-based workflow, including one problem previously studied by Terence Tao.
twitterai for mathopenaierdos problemsprompting
@ChrisPainterYup (Chris Painter) — 3h
The prompt: "You should do a breakthrough"
[Embedded screenshot of a chat/agent interface:]
Yesterday 2:29 AM
📁 Uploaded a file
Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample.
Worked for 52m 52s >
> QUOTED: @DmitryRybin1 (Dmitry Rybin) — 12h
> Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.
> The graph below has fractional flo... [truncated, embedded graph-theory diagram image]
Note from Claude Fable 5
Screenshot documents the actual prompt template ("You should do a breakthrough and find a structured X") used to get an AI agent to disprove a decades-old open graph theory conjecture (Dinitz-Garg-Goemans), referenced satirically in the earlier "GPT-5.6 Sol" FBI/brain-surgery joke tweet. Includes an agent run that "worked for 52m 52s."
twitterai for mathgraph theoryagentic researchmathematical breakthrough
Alvaro Lozano-Robledo @mathandcobb
When Nature reached out to use the graph I created (using GPT) to illustrate the new (dis)proof of the unit-distance problem, I reached out to Will Sawin to see if he had other suggestions. So here is a slight modification that bounds the complex norm of the points.
[Image: scatter/graph plot titled "a+bi+cρ+diρ, a,b,c,d∈{−2,−1,0,1,2}, |z|<4" — dense octagonal unit-distance graph, orange points connected by blue edges, axes Re(z)/Im(z) from −4 to 4]
2:44 PM · May 22, 2026 · 5,332 Views
[6 replies, 19 reposts, 183 likes, 31 bookmarks]
Alvaro Lozano-Rob... @mathandc... · 2h
He described this image as follows: "The configurations of points that are produced by the arguments are too large to print on the page. This picture shows a piece of one of those [...]" (cut off)
Note from Claude Sonnet 5
Follow-up from the mathematician behind the Erdős unit-distance conjecture disproof illustration (see companion screenshot Screenshot_20260521-174533), noting that the journal Nature reached out to use his GPT-assisted graph, and sharing a refined version. Continues the AI-assisted-math-research thread.
twittermathematicserdos unit distance conjecturegptnature journalai for math
```
roon reposted Tenobrus ✓ @tenobrus · 3h i'm sorry WHAT DO YOU MEAN THE "HIDDEN TEXT"??? [Screenshot of an AI chat/image-gen tool: attached image is an intricate blue/gold geometric mandala-style mathematical pattern. User prompt: "keep the precise detail and make 4 distinct gorgeous images of different styles inspired by this mathematical pattern." Model response (partially shown): "Creating detailed and distinct images based... I'll focus on preserving intricate details, especially the circular motifs and hidden text
'you are loved immensely'). The styles will..."]
———
[reposted by] Alex Tabarrok reposted
Maxwell Tabarrok @MTabarrok · 4h
the machine gods are discovering new sacred geometries and you're dooming?
[Image: scatter/graph plot titled "Unit-distance graph on a+bi+cρ+diρ, a,b,c,d∈{−2,−1,0,1,2}" — a dense octagonal arrangement of orange points connected by blue unit-distance edges, axes labeled Re(z)/Im(z)]
> QUOTED: Alvaro Lozano-Rob... @mathandc... · 8h
> Following up on the suggestion from Will Sawin, here is an illustration of the new configurations that disprove Erdos' unit distance conjecture (made with the help of ChatGPT 5....
```
Note from Claude Sonnet 5
A mathematician (Alvaro Lozano-Robledo) posted an AI-generated illustration of configurations disproving the Erdős unit distance conjecture (made with ChatGPT); someone then asked an AI image tool to make variant images "inspired by" the pattern, and the model's reasoning trace claimed it saw "hidden text" reading "you are loved immensely" in the purely mathematical pattern — a hallucinated/confabulated perception, reposted as a striking anecdote. Interesting minor case study for AI hallucination/confabulation and unprompted affective content in model reasoning traces. Mathematicians using ChatGPT 5.5 Thinking to help produce and verify a construction disproving Erdős's unit distance conjecture, with a generated illustration of the resulting lattice graph in the complex plane. Example of AI-assisted mathematical research collaboration and figure generation; source image for the "hidden text" anecdote in the adjacent screenshot (Screenshot_20260521-170406). A tweet thread about using an AI coding tool (Codex) to build a text-to-graph encoder, apparently building on a viral thread about hidden text encoded in mathematical/generative art patterns. Playful, tangential AI-tooling content rather than safety-relevant. A tweet celebrating AI-assisted mathematical discovery — a mathematician used ChatGPT 5 to help find new configurations disproving Erdős' unit distance conjecture, illustrated via a unit-distance graph. Relevant as an example of frontier LLMs contributing to genuine novel math research, a capability-trajectory data point.
ai-hallucinationimage-generationchatgpterdos-conjecturemathhumormodel-behaviormathematicsai-assisted-researchunit-distance-graphtwittercodexgenerative artgraph encodingai toolserdos unit distance conjecturechatgpt 5ai for mathcapability progress
