Theo Conjecture solves 35-year-old math problem, finds a term no one predicted
Something went wrong while submitting the form.In the 1980s, a program called Graffiti started asking questions nobody had thought to ask, and one of them caught the attention of Paul Erdős. Almost forty years later, Randy Davila handed that same question to Theo-Conjecture, an automated discovery system supported by a large language model that proposes, tests and revises mathematical ideas in a loop. What came back was a proof of the answer Erdős and his collaborators had guessed at, an unexpected extra term nobody had predicted, and a glimpse of what it looks like when an AI agent and a human mathematician work a problem together.Here's the picture to hold in your head.
- ▪Something went wrong while submitting the form.In the 1980s, a program called Graffiti started asking questions nobody had thought to ask, and one of them caught the attention of Paul Erdős.
- ▪Almost forty years later, Randy Davila handed that same question to Theo-Conjecture, an automated discovery system supported by a large language model that proposes, tests and revises mathematical ideas in a loop.
- ▪What came back was a proof of the answer Erdős and his collaborators had guessed at, an unexpected extra term nobody had predicted, and a glimpse of what it looks like when an AI agent and a human mathematician work a problem together.Here'
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| Original publisher | Firstprinciples |
| Canonical URL | https://firstprinciples.com/blog-article/ai-system-theo-conjecture-solves-35-year-old-math-conjecture |
| Publication time | Wed, 29 Jul 2026 20:21:48 +0000 |
| Retrieval time | 2026-07-29T20:51:05.141Z |
| Last seen | 2026-07-29T20:51:05.141Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | FxyAIg6CGHJk · 1 stories |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
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Opening excerpt (first ~120 words) tap to expand
Blog ConjecturingAI system 'Theo Conjecture' solves 35-year-old math conjecture, finds a term no one predictedFirstPrinciplesJul 29, 2026•4min readShare Subscribe to newsletterThank you! Your submission has been received!Oops! Something went wrong while submitting the form.In the 1980s, a program called Graffiti started asking questions nobody had thought to ask, and one of them caught the attention of Paul Erdős. Almost forty years later, Randy Davila handed that same question to Theo-Conjecture, an automated discovery system supported by a large language model that proposes, tests and revises mathematical ideas in a loop.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Firstprinciples.
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