GPT-5.4 Pro solves Erdős number theory problem: Amateur math enthusiasts use AI to complete 50-year-old unsolved proof
An amateur math enthusiast used ChatGPT (GPT-5.4 Pro) to successfully solve Erdős problem #1196, a difficult problem that has remained unsolved in number theory for over 50 years. AI constructed a complete mathematical proof after 80 minutes of in-depth thinking, marking a milestone breakthrough in large-scale language models in the field of mathematical research.
Core conclusion
In April 2026, Liam Price, an amateur mathematics enthusiast, successfully solved Erdős problem #1196 - a classic number theory problem about primitive sets (primitive sets) using OpenAI's latest model GPT-5.4 Pro (through the ChatGPT interface). After 80 minutes and 17 seconds of in-depth thinking and reasoning, the AI constructed a complete mathematical proof, which was included in the erdosproblems.com database and the status was marked as "PROVED (LEAN)".
Key Points
- Time of incident: April 15, 2026 (included in database)
- Solved by: Amateur math enthusiast Liam Price (non-professional math researcher)
- Tools used: GPT-5.4 Pro (ChatGPT paid version)
- Thinking time: 80 minutes and 17 seconds
- Problem status: "Open" → "Solved", flagged in erdosproblems.com #1196
- Historical significance: AI independently solves a truly open mathematical problem for the first time
Background and trigger events
Erdős Problem #1196, jointly posed by mathematicians Paul Erdős, András Sárközy, and Endre Szemerédi, explores asymptotic upper bounds on the sum of reciprocals of primitive sets (i.e., sets in which one element does not divide another element). In the decades since the problem was posed in the late 1960s, only partial progress has been made in 2023 by mathematician Lichtman, who improved the upper bound to about 1.399.
Liam Price gave a well-crafted problem description in ChatGPT that requires models to "not search the Internet, demonstrate creative reasoning, and provide unconditional complete proofs." GPT-5.4 Pro then entered into 80 minutes of deep thinking, during which it demonstrated a step-by-step reasoning process and finally produced a complete and novel mathematical proof.
The result was reviewed by the erdosproblems.com community, officially marked as resolved, and widely disseminated in a feature story in Scientific American, with the related HN post receiving over 400 likes and over 250 comments.
Key Impact (by Dimension)
| Dimensions | Change | What it means to us | Recommended actions |
|---|---|---|---|
| The upper limit of AI capabilities | LLM independently solved open mathematical problems for the first time | AI has entered the "research collaboration" stage from "auxiliary tools" | Focus on the commercial application of AI in complex reasoning tasks |
| Mathematics research paradigm | Non-professionals + AI can participate in top mathematics research | The threshold for "AI-assisted research" has been significantly lowered | Explore combined innovation in AI-assisted code/content production |
| Model capabilities | GPT-5.4 Pro demonstrates 80 minutes of deep reasoning | Long-chain reasoning capabilities are maturing | Adjusting AI usage strategies in automated processes |
| Content Creation | LLM for tasks that require strict logic | AI-generated content further increases in credibility and sophistication | Using AI for more complex analytical content production |
| Community reaction | HN 400+ upvotes, 250+ comments and lively discussion | Public perception of AI capabilities has undergone a qualitative change | Produce relevant Guide/Case content in a timely manner to seize the traffic window |
Adaptation suggestions
- For content creators: Use GPT-5.4 type models to create in-depth analytical content. It is no longer a simple "polishing and rewriting". You can try long articles that require logical reasoning.
- For automation workers: Long chain reasoning (80 minutes level) means that AI Agent is no longer limited to simple instructions and can undertake more complex multi-step workflow design
- For AI tool users: The quality of prompts remains key - Liam Price owes much of his success to well-crafted problem descriptions and constraints
- For developers: Pay attention to the potential of upgrading automated processes after the GPT-5 series of open APIs, especially strict logic scenarios such as mathematical verification.
Task List
- Follow the price and availability of GPT-5.4 Pro API launch
- Try to use a similar "deep thinking" approach to handle complex content production tasks
- Update the AI Agent usage strategy based on the AI mathematical capabilities mentioned in the article.
- Produce matching Guide/Case content
Example: Prompt word (core command used by Price)
The underlying reasoning capabilities of AI-driven tools such as ```text don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem.
problem statement
REMEMBER - this unconditional argument may require non-trivial, creative and novel elements.
GPT-5.4 Pro "Thought for 80m 17s" 。
##
- [Erdős Problem #1196](https://www.erdosproblems.com/1196)
- [HN : Amateur armed with ChatGPT solves an Erdős problem](https://news.ycombinator.com/item?id=47903126)
- [ChatGPT (80)](https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba)
- [Scientific American （）](https://www.scientificamerican.com/article/amateur-armed-with-chatgpt-solves-an-erdos-problem/)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems](https://arxiv.org/abs/)
## （）
AI ——`OpenAI` `ChatGPT`（ `GPT-5.4 Pro`）。，`DeepSeek`、`Gemini` 。 AI ， `Claude Code`、`OpenClaw`、`n8n` are rapidly being upgraded.
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