LLM Breakthrough | GPT-5.2 Cracks Open Erdos Problems
Edited By
Oliver Schmidt
A recent achievement by a team of mathematicians utilizing GPT-5.2 has made waves in the mathematical community, marking the first time an LLM has resolved an Erdos problem previously unsolved by humans. This milestone raises questions about the evolving role of AI in tackling complex math challenges.
Understanding the Challenge
An Erdos problem, named after the renowned mathematician Paul Erdos, involves open mathematical issues that have stumped researchers for years. When tasked with these problems, LLMs like Gemini faced significant obstacles, primarily due to their internet access, which hindered their ability to explore solutions effectively.
Navigating Barriers with GPT-5.2
The team initially encountered issues with other models, particularly with hallucinations—erroneous outputs that often derailed attempts to find valid solutions. However, GPT-5.2 promised improvements in math reasoning and proof-writing capabilities.
"Here is a conditional proof. What I couldn’t do is prove Lemma X due to some challenging aspects," GPT-5.2 reportedly stated, showing transparency in its problem-solving process.
This direct communication was a stark contrast to earlier attempts with models like Gemini, which provided incorrect or nonsensical answers.
The Breakthrough Moments
The journey began with GPT-5.2 tackling Erdos problems #333 and #728. While #333 was discovered to have been previously resolved, the uncovered proof shed light on existing literature. The actual breakthrough came with problem #728 when the model followed a detailed workflow that included brainstorming and crafting short prompts for proof.
Research Phase: The model analyzed Erdos problem #728 before generating creative ideas for proof.
Proof Development: Two instances of GPT-5.2 scrutinized the output, fixing minor errors and confirming plausibility.
Peer Review: Math student Acer helped formalize the proof in Latex, collaborating with other systems until the solution was deemed valid.
Community Response and Implications
The mathematical community responded positively, with comments highlighting the potential of AI to assist in research. "Incredible work. I’ve never heard of these types of problems Good luck on your continued success!" noted one commenter, while another suggested that this approach could lead to solving more open Erdos problems in the future.
Interestingly, Terence Tao labeled the submitted solution a partial fix, hinting at its ambiguous nature while aligning the solution with Erdos’ original intentions.
Takeaways
🎉 GPT-5.2 successfully resolved Erdos problem #728, previously unsolved by humans.
📈 The model's honesty improved confidence in output, contrasting earlier AI attempts.
🤝 Community collaboration played a crucial role in validating the proof’s accuracy.
In summary, while the landscape of mathematical research evolves, this breakthrough underscores the potential of AI to aid complex problem-solving. Experts are eager to see how these tools can further enhance mathematical inquiry and resolve challenges that have baffled generations.
What Lies Ahead for AI in Mathematics
Experts predict that the successful crack of Erdos problems by GPT-5.2 is just the beginning. There’s a strong chance we’ll see further collaboration between mathematicians and AI, with estimates suggesting that at least 30% of open problems may be tackled by AI tools in the coming years. The improvement in AI problem-solving is likely to encourage more researchers to integrate these technologies, fostering a culture of shared knowledge. As more complex queries are resolved, it’s reasonable to speculate that an increasing number of educational institutions will adopt AI-assisted learning. Collaborations in smaller, niche mathematical issues could also emerge, sparking innovations in teaching methods and proof validation processes.
A Fresh Perspective on Historical Collaborations
When reflecting on this breakthrough, one might consider the contributions of the Astronomical Society in the early 1900s, where skilled amateurs collaborated with professional astronomers. This partnership initially faced skepticism; however, collective efforts led to significant advances in celestial observations. Similarly, the union of AI capabilities with human intellect in tackling Erdos problems could evolve in unpredictable ways. Just as the enthusiasts once helped redefine our understanding of the cosmos, modern mathematicians and AI might discover new realms of knowledge, reshaping how we approach complex problem-solving. This historical parallel serves to highlight the inherent value in collaborative efforts that push boundaries, even amidst uncertainty.