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erdos unit distance conjecture

2 captures, most recent first.

Alvaro Lozano-Robledo @mathandcobb

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

Tenobrus @tenobrus

quoting Alvaro Lozano-Robledo @mathandc...

``` 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