Amateur Mathematician Cracks Erdős Conjecture with Help from ChatGPT

Introduction: When AI Becomes a Catalyst for Mathematical Discovery

In the world of mathematics, the name Paul Erdős represents a series of unscaled peaks. The most prolific mathematician of the 20th century posed hundreds of unsolved problems during his lifetime, many of which continue to baffle the world's top mathematicians to this day. Recently, however, a stunning piece of news sent shockwaves through both the mathematics and AI communities simultaneously — an amateur math enthusiast, with the help of OpenAI's ChatGPT, successfully solved one of those Erdős problems.

This event is not only a milestone in the history of mathematics but also profoundly reveals the entirely new role that large language models are playing in scientific research.

The Core Story: An Outsider's Unlikely Triumph

The problem solver is reportedly not a professional mathematician employed by any university or research institution, but rather an amateur enthusiast with a deep passion for mathematics. During his research process, he used ChatGPT as a "thinking partner" — posing questions to the AI, verifying lines of reasoning, and exploring different proof directions.

It is worth emphasizing that ChatGPT did not directly "produce" a complete proof. The actual breakthrough came from the deep interactive process between human and AI. The researcher used ChatGPT to quickly test whether his intuitions were correct, eliminate erroneous reasoning paths, and obtain inspirational suggestions at critical junctures. Ultimately, he assembled these fragmented insights into a rigorous mathematical proof.

In community comments, one person offered a succinct summary: "ChatGPT didn't solve this problem, but it helped a person solve it. The distinction between these two things is crucial."

In-Depth Analysis: A Paradigm Shift in AI-Assisted Research

The reason this event has attracted such widespread attention is that it touches on several deep-seated issues.

First, AI is lowering the barrier to entry for scientific research. Traditionally, cracking an Erdős-level mathematical problem typically requires years of professional training, comprehensive mastery of relevant literature, and close collaboration with peers. Now, ChatGPT serves to some extent as an "always-online math tutor" and "literature search engine," enabling an amateur researcher without institutional academic resources to engage in high-level mathematical exploration.

Second, human-AI collaboration has more potential than pure AI alone. Current large language models still have obvious limitations when it comes to independently completing rigorous mathematical proofs — they can produce reasoning that appears plausible but is actually incorrect, the so-called "hallucination" problem. However, when a human with basic mathematical literacy partners with AI, with the human responsible for judgment and verification and the AI responsible for association and computation, this complementary relationship can produce results far exceeding what either party could achieve alone.

Third, there is debate over the attribution of academic contributions. In comment sections, many people engaged in heated discussion around one question: if AI provided key inspiration during the proof process, who should be the "author" of the resulting paper? Should ChatGPT be listed as a co-author? The current mainstream consensus in academia is that AI tools should be explicitly acknowledged and described in papers but should not be listed as authors, since they cannot bear academic responsibility for research outcomes.

Some commenters raised an even sharper challenge: if amateur enthusiasts can use AI to solve long-standing open mathematical problems, what is the core competitive advantage of professional mathematicians? Supporters argue this demonstrates precisely the democratizing power of AI — scientific discovery should not be monopolized by academic gatekeeping.

Technical Perspective: The Boundaries of Mathematical Ability in Large Language Models

From a technical standpoint, ChatGPT's capabilities in mathematical reasoning have been a consistent research focus. OpenAI's GPT-4 and subsequent models have shown significant improvements on math competition problems, but when facing truly open-ended research questions, they function more as an "inspirer" than a "solver."

What large language models excel at is pattern recognition and knowledge association — they can extract potentially relevant mathematical tools and methods from massive training data, offering human researchers suggestions along the lines of "have you considered approaching this from this angle?" This capability is especially useful in combinatorics and graph theory, the fields Erdős cared most about, because problems in these areas often require clever constructions and unconventional thinking.

Outlook: The Era of Human-AI Symbiosis in Scientific Research

This event is likely just the tip of the iceberg. As large language models continue to evolve, and as models specifically trained for mathematical reasoning (such as AlphaProof) emerge, cases of AI-assisted scientific discovery will become increasingly common.

In the future, we may see more scenarios like this: a biology enthusiast using AI to propose new protein folding hypotheses, or a physics teacher leveraging AI to discover new conservation laws. The trend toward decentralization in scientific research will be unstoppable.

At the same time, however, academia needs to establish new evaluation systems and norms to accommodate this human-AI collaborative research paradigm. How to verify the reliability of AI-assisted results, how to delineate the respective contributions of humans and AI, and how to prevent AI "hallucinations" from contaminating academic literature — these are all questions that urgently need answers.

As one commenter put it: "We are standing on the threshold of a new era. The question is no longer whether AI can help us do research, but whether we are ready to embrace this transformation."