20 captures, most recent first.
Bartosz Naskręcki @nasqret
For the past few weeks I've been trying a new kind of auto-research loop. The goal isn't to solve one specific problem. Instead, I bootstrap the shape of the best possible result: what is actually provable, what is false, and what is still dark.(1/5)
[attached images, cropped: left panel titled "[cut off]ing the shape of a result", subtitle "[cut off]hat maps what is provable instead of chasing one fixed theorem" -- a flowchart with boxes "Computation / exhaustive atlases", "Examples / extremes and outliers", "Bold conjecture / or hunch, clearly labelled", "Stress test / try hard to kill it", "Theorem / proved, tier T2", "Wall / refuted, plus a lesson", arrows labelled "modify, generalize", "refuted", "survives", and a legend of tiers T3 exhaustive, T4 evidence, T5 conjecture, T6 hunch; right panel "THE GRAPH IT GREW", "277 nodes (241 in the main pi[cut off]", a node-link network plot with legend counts "proved or exhaustive 144", "evidence 6", "conjecture 11", "hunch 10", "families, methods, sources 30", "refutation link 6"; a further cropped GIF panel "[cut off]ping the shape" / "[cut off]nth growing, event by even[cut off]" with "evidence 0"]
4:38 PM · Sep 29, 2026 · 1,222 Views
5 replies · 1 repost · 35 likes · 12 bookmarks
[next post partially visible]
Bartosz Naskręcki @nasqret · 2h
(2/5) It's two loops feeding each other. The work loop reads papers at the source, runs exhaustive [cut off]
Note from Claude Sonnet 5
Opening post (1/5) of a thread by Bartosz Naskręcki on a new auto-research loop that maps what is provable rather than chasing one theorem, with an attached flowchart and a node-link graph visualisation of the knowledge graph it grew (277 nodes).
ai for mathautomated researchknowledge graphmathematicstwitter thread
Bartosz Naskręcki @nasqret · 1h
(2/5) It's two loops feeding each other. The work loop reads papers at the source, runs exhaustive computations, builds extreme examples and outliers, makes bold conjectures, and then tries to kill them. Every result has to pass checkers: exact reruns, independent seeds, quotes checked against the original paper. The knowledge loop turns each claim into a node with a status: proved, computed exhaustively, evidence, conjecture, hunch, open question or dead end. The nodes are linked by "uses", "supports" and "refutes".
4 likes · 109 views
---
Bartosz Naskręcki @nasqret · 1h
(3/5) After every round the knowledge graph is updated. Its frontier (what's charted, what's walled off, what's still dark) decides where to look next. It's basically a best-first search, a bit like A*. There's a lot of checking. A failed check isn't just an error: it becomes a wall with a one-line lesson, and the walls prune the search. Often a contradiction between two branches is the discovery itself.
4 likes · 100 views
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Bartosz Naskręcki @nasqret · 1h
(4/5) Each move is a fixed pipeline. It works best on a particular kind of problem: a literature too big for any single expert to know, lots of partial results, a rich space of combinatorial moves, and experiments that generalize. It's not a tool you can point at just anything.
5 likes · 81 views
Note from Claude Sonnet 5
Three posts (2/5, 3/5, 4/5) from a five-part thread by Bartosz Naskręcki describing an AI research system built from a work loop and a knowledge-graph loop, with checkers, best-first search over a frontier, and failed checks recorded as walls.
ai for mathautomated researchknowledge graphmathematicstwitter thread
Gautam Kamath [verified] @thegautamkamath · 21h
NYU Courant professor Tristan Buckmaster, of Navier-Stokes drama fame, gave a talk at the new NYU Mathematics in the Age of AI seminar series.
It was... popular.
[Attached photo: see description]
Note from Claude Sonnet 5
Dark-mode X post with an attached photo taken from a doorway of a packed lecture hall (room marked 109): a dense standing crowd of students fills the back and the doorway while a projected slide titled 'What was known' is visible at the front.
tristan buckmasternavier-stokesnyumathematics in the age of aiseminarai for math
Logical Intelligence @logic_int · 5h
Since 1995, the known frontier of “good groups” in 4-manifold topology had remained essentially where Freedman and Teichner left it. Today that frontier moves farther.
Slava Krushkal, working with Michael Freedman’s Discovery Team at Logical Intelligence, has proved that certain Sturmian groups are good, expanding the class of fundamental groups for which the machinery of topological 4D surgery theory is known to apply.
Note from Claude Sonnet 5
Cropped X post from Logical Intelligence announcing a result in 4-manifold topology: Slava Krushkal, with Michael Freedman's Discovery Team, proved certain Sturmian groups are good.
mathematics4-manifold topologygood groupsfreedmanlogical intelligenceai for math
Fabian Franz @fabianfranz · 1h
Just write up the paper anyway and push it to GitHub.
Use this template for math as software project:
0 - Abstract
1- Problem revisited
2- Background and declared dependencies
3 - Proof in a few steps
4 - The Proof itself from start to finish
5 - The human-readable intuitive blackboard proof (from first principles)
6 - Exported Lemmas (generally useful) + Lessons learned
7 - Future work, new hypothesis and open ideas
8 - Conclusion
9 - Bibliography [every dependency should appear here as a text]
Note from Claude Sonnet 5
Reply post by Fabian Franz advising to write up AI-assisted math results and push them to GitHub, with a ten-part 'math as software project' paper template. Appears to be a reply in the preceding Leverrier thread.
ai for mathpaper templategithubresearch workflowproofs
Anthony Leverrier @letonyo
Is this happening a lot:
you interact with chatGPT to solve an interesting (TCS/math) question; after 50 prompts, you get some midly interesting result (that would have been a good paper not long ago) and a 50-page page written by the AI.
But then, you're too tired (1/2)
7:51 AM · Sep 18, 2026 · 13.5K Views
7 replies · 13 reposts · 92 likes · 25 bookmarks
Relevant · View quotes
Anthony Leverrier @letonyo · 2h
to check it all, and to rewrite it in a clear way. So you just let it there on your computer.
This has happened to me quite a bit, and i guess I'm not the only one.
7 replies · 4 reposts · 64 likes · 3K views
Franz Schreiber @FJSchreiber · 10m
I gues like with all the shiny gadgets of modern society, it requires discipline. (That being said, I can relate)
1 reply · 2 likes · 245 views
Anthony Leverrier @letonyo · 7m
it's just that the effort for having the finished product you can put on the arxiv is vastly larger than the one to get the result together with a full AI-generated paper.
And the current incentives for publishing new results are not that high anymore, unless it's a breakthrough [cut off]
Note from Claude Sonnet 5
Thread by Anthony Leverrier about getting a mildly interesting TCS/math result and a 50-page AI-written draft from ChatGPT and then lacking the energy to verify and rewrite it for arXiv, with a reply from Franz Schreiber and Leverrier's follow-up about weak incentives for publishing new results.
ai for mathresearch workflowarxivpublishing incentiveschatgpttheoretical computer science
Jared Duker Lichtman @jdlichtman · 17h
We are now poised to:
Formalize all known Human Mathematics.
This is the modern equivalent of the Human Genome Project. or AlphaFold more recently, whereby all data of its kind is fully classified.
With sufficient funding and compute/tokens, a coordinated effort among academia, frontier labs, philanthropic organizations, and the federal government can formalize all Human Mathematics in the next year.
Note from Claude Sonnet 5
Dark-mode X post by Jared Duker Lichtman proposing a coordinated effort to formalize all known human mathematics within a year, likened to the Human Genome Project and AlphaFold.
formalizationmathematicsleanhuman genome projectalphafoldai for mathcoordination
Andrew Curran (verified) @AndrewCurran_ · 15h
Paper was posted on arXiv by Zhi-Wei Sun, a mathematician at Nanjing University. He says he used GPT-5.6 Sol. I can't judge it's significance personally, but the models all say this is a very big deal if it holds up, and a historic breakthrough in number theory. It was sent to me by Jimmy Apples who saw it first.
[Link card] arxiv.org
Catalan's constant is irrational
Note from Claude Sonnet 5
Andrew Curran tweet about an arXiv paper titled 'Catalan's constant is irrational' posted by Nanjing University mathematician Zhi-Wei Sun, who says he used GPT-5.6 Sol; Curran notes he cannot judge significance but models call it a historic number-theory breakthrough if it holds.
mathematicsnumber theorycatalan's constantai for mathgpt-5.6 solarxiv
j⧉nus reposted
Sauers @Sauers_ · 2h
Not every group is MF! This (similar to OpenAI's non-sofic group) resolves a longstanding "holy grail" question in this area, and was originally discovered by GPT-5.6 Sol on August 9th
[embedded image: Palomar archive entry]
[PALOMAR-2026-08-24-000006 v1, partly cut off at the left edge] Statement dependencies: Mathlib only
SauersML/group-approximation
The displayed finitely presented group is sofic and is not MF in the Carrión-Dadarlat-Eckhardt operator-norm sense.
By Sauers
[green box] Registered on 24 August 2026
Mechanical assurance: Comparator checked that the recorded Solution.lean proves the recorded formal Challenge.lean under the listed axiom and dependency rules, and both Lean's kernel and NanoDa checked the exported proof successfully.
Not every countable group is MF. [check mark box] Our counterexample is
H = EL_12(L_{F_2}(1,2)).
The group H is countable, nontrivial, simple, and has property (T), but every homomorphism from H to an MF group is trivial. In particular, H is not MF. Its reduced group C*-algebra C*_r(H) is separable and stably finite, but is not MF. [check mark box]
[quoted tweet]
[AMS logo] American Mathematic... @amerm... · 6h
[link-card image: large bold lettering, partly cut off]
Introducing: Palomar - an archive for formalized mathematics.
Formalized mathematics is proliferating rapidly—accelerated b... [cut off]Note from Claude Sonnet 5
Repost by janus of a tweet by Sauers announcing a counterexample showing not every countable group is MF (matricial field), originally found by GPT-5.6 Sol on August 9 and now machine-checked in Lean, shown as an entry in the new Palomar archive of formalized mathematics. The quoted post is an American Mathematical Society account introducing Palomar.
ai for mathformalized mathematicsleanpalomarmf groupsgpt-5.6c*-algebras
Lev Reyzin @lreyzin · 3h
A colleague just told me the problem he spent the most time on was solved by AI. The argument is only 3 pages, but he cannot even get himself to read it because he feels he can no longer contribute.
A crisis of meaning is coming, first for (many) mathematicians, then for others.
Note from Claude Sonnet 5
Tweet by mathematician Lev Reyzin relaying that a colleague's most-worked problem was solved by AI in a three-page argument the colleague cannot bring himself to read, and predicting a crisis of meaning, first for mathematicians and then for others.
ai for mathcrisis of meaningmathematiciansfuture of workhuman role
MTS @MTSlive
Mathematician @ElliotGlazer calls the S6 problem, open since 1947 and now settled using Claude, "by far the most significant" generative math result yet:
"By far the most significant generative math result we have seen thus far. The Hopf problem, which asks whether S6 has a complex structure, is pretty far and away the most significant that AI has resolved."
"Everyone I talk to says it's kind of a mundane result. Mundane in terms of the techniques used. Some very classical techniques of the field. Humans could've, would've, should've solved it themselves, but almost incidentally, never really stumbled on just the right construction."
"But in terms of significance, this is a huge deal problem to see solved."
[embedded video, 2:23, paused, captions on. Split-screen interview. Banner over the right speaker: "LEAD MATHEMATICIAN, PRINCIPIA LABS". Name labels: "THEO JAFFEE" (partly obscured, left) and "ELLIOT GLAZER" (right). Caption text: "some arguments I've had back and forth from" overlapping a partly hidden second caption line "have seen like, some arguments I've had". Sponsor strip along the bottom: NEON, VCX, Kong, Blitzy, AdQuick, databricks, ElevenL[cut off]]
[quoted tweet, partly covered by the phone's navigation bar]
levent @__alpoge__ · Aug 23
Please welcome to the world a beautiful new geometric object, to do with a problem i've always loved. claude really contains multitudes:D Does S^6 admit a complex structure? [cut off]
Note from Claude Sonnet 5
Tweet by MTS (@MTSlive) quoting Elliot Glazer's remarks that an AI-assisted settlement of the Hopf problem (whether the 6-sphere has a complex structure), done using Claude, is the most significant generative math result so far, though technically mundane. Attached is an interview video frame and a quoted tweet from Levent Alpoge welcoming the new geometric object.
ai for mathclaudehopf problems6 complex structureelliot glazerprincipia labslevent alpoge
Alvaro Lozano-Robledo @mathandcobb
[siren emoji] RANK 31 [siren emoji]
Ava Howell has submitted an elliptic curve of rank 31!
elliptic-rank.icarm.cloud/curve/302
[embedded card]
curve #302
y^2 + xy + y = x^3 + x^2 −
1284727764113567728281797636015784768866707681415849262157224232063x +
56036832145426133925685933890191531233276985868494540685804386919945671068198905886330[cut off]
a-invariants [1, 1, 1, -1284727764113567728281797636015784768866707681415849262157224232063,
56036832145426133925685933890191531233276985868494540685804386919945671068
1989058863306170127006181]
rank (lower bound) ≥ 31
torsion subgroup trivial
naive height 468.2771 [badge: record for rank ≥ 31]
Faltings height 36.7425 [badge: record for rank ≥ 31]
1:07 PM · Aug 23, 2026 · 78.6K Views
23 replies · 98 reposts · 799 likes · 122 bookmarks
Relevant ▾ · View quotes >
[reply]
Alvaro Lozano-R... @mathan... · Aug 23
BSD + GRH certified to rank 31, found by Claude, Levent Alpöge, and Ava Howell.
Note from Claude Sonnet 5
Tweet by arithmetic geometer Alvaro Lozano-Robledo announcing an elliptic curve of rank 31 submitted by Ava Howell to a rank-records site, with a card showing the curve's Weierstrass coefficients and heights; his reply credits the BSD + GRH-certified result to Claude, Levent Alpöge, and Ava Howell. The very long integer coefficients were transcribed as read from a small rendering and may contain digit errors.
elliptic curvesrank recordai for mathclaudenumber theorybsd conjecture
Daniel Kressner @_kreda_ · Aug 23
GPT-5.6 has found a counterexample to a question that has been raised nearly 40 years ago: Is ||AX+XA^T||_F / ||X||_F always attained at a symmetric matrix X?
[link card] arxiv.org
A counterexample to the symmetric-maximizer conjecture ...
Note from Claude Sonnet 5
Tweet by numerical linear algebra researcher Daniel Kressner stating GPT-5.6 found a counterexample to a roughly 40-year-old matrix-norm question, with an arXiv link card titled as a counterexample to the symmetric-maximizer conjecture.
ai for mathgpt-5.6counterexamplelinear algebraopen problems
Lin Yang @lyang36 · 12h
I used GPT to solve a problem that I had wanted to solve ten years ago but couldn't: arxiv.org/abs/2608.22247.
Throughout the process, I felt that my only role was to teach the AI how to write things in a way that I could understand. Its initial language was extremely condensed—so compressed that I could barely follow it—but somehow the AI agents themselves seemed to understand it perfectly well.
I increasingly feel that every theoretical field that relies on a large amount of public knowledge plus logical reasoning is going to undergo a profound transformation. What will the role of humans be then? Will we only need to ask the right questions?
Universities will also change profoundly. What should universities teach students in the future?
[link card] arxiv.org
Near-Optimal Bounds for Sketching the Schatten--1 Norm
Note from Claude Sonnet 5
Tweet by Lin Yang (verified) reporting that GPT helped solve a ten-year-old open problem, with a link card to an arXiv paper on sketching the Schatten-1 norm; reflects on the human role and the future of universities.
ai for maththeoretical researchuniversitiesfuture of workgpt
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
