AI Breakthrough in Math: 15 Erdős Problems Solved Using GPT-5.2 and Formal Verification

Chen Ling
8 minutes ago
5 min read

The landscape of mathematical research is undergoing a profound transformation as artificial intelligence increasingly moves from assisting in calculations to generating original proofs. Recent advancements in AI, exemplified by models such as GPT-5.2, have enabled both amateur and professional mathematicians to solve long-standing mathematical problems with unprecedented speed and accuracy. These breakthroughs are not only reshaping the way mathematics is conducted but also redefining the role of human expertise in research.

The Rise of AI-Assisted Mathematics

Historically, mathematical research has relied heavily on human intellect, intuition, and years of specialized training. However, AI’s ability to process massive datasets, detect patterns, and simulate reasoning has begun to complement, and in some cases accelerate, traditional workflows. The convergence of large language models (LLMs) and formal verification tools has allowed AI to transition from a supplementary tool to an active participant in mathematical problem-solving.

Paul Erdős, a prolific Hungarian mathematician, left behind a collection of over 1,000 unsolved conjectures spanning number theory, combinatorics, and other mathematical disciplines. These problems, simple to state but notoriously difficult to solve, have become a proving ground for AI models. As Thomas Bloom of the University of Manchester observes, these Erdős problems serve as signposts for progress across various mathematical fields, providing both amateurs and professionals with measurable challenges to test the capabilities of AI systems.

GPT-5.2 and the Solving of Erdős Problems

In a series of recent developments, GPT-5.2 Pro has successfully solved several Erdős problems, including Problem #397, #728, and #729. This marks a milestone in AI’s evolution from pattern recognition to autonomous proof generation. Neel Somani, a software engineer and former quantitative researcher, reported that after prompting GPT-5.2 with Problem #397, the model produced a complete proof. Verification was achieved using Harmonic’s Aristotle tool, which converts conventional proofs into Lean, a formal proof verification language. Fields Medalist Terence Tao validated these results, emphasizing that while these problems represent the “lowest-hanging fruit,” the methodology illustrates AI’s growing mathematical competence.

According to recent reports, 15 Erdős problems were updated from “open” to “solved” on the official Erdős repository between November and January, with 11 of the solutions credited directly to AI involvement. These accomplishments highlight GPT-5.2’s ability to combine literature review, formal reasoning, and computational verification to produce original proofs. As Tao noted, the scalable nature of AI makes it particularly well-suited for systematically addressing the “long tail” of less-studied mathematical problems, which traditionally receive little human attention due to resource constraints.

Democratizing Problem-Solving: Amateurs Leverage AI

AI tools are not limited to professional mathematicians. Amateur mathematicians like Kevin Barreto and Liam Price have leveraged GPT-5.2 and Aristotle to tackle long-standing problems, including Problem #205, which had no pre-existing solution. Barreto explains, “I looked at the statement and thought, ‘This one might be able to get solved by ChatGPT, so let’s try it.’ Sure enough, it came back with an argument that was quite sophisticated.”

This democratization of mathematics represents a paradigm shift. Previously, solving complex conjectures required years of specialized training, collaboration, and access to comprehensive literature. AI allows individuals with limited formal expertise to contribute meaningfully, accelerating the research process and uncovering overlooked pathways. Thomas Bloom underscores this shift, noting that AI allows mathematicians to draw on fields outside their specialization, effectively increasing the breadth of research conducted globally.

Formalization and Verification: Ensuring Accuracy

A critical factor in AI-driven mathematics is verification. Tools like Aristotle convert human-readable proofs into Lean, which a computer can instantly validate. This formalization process addresses the risk of error in AI-generated proofs and ensures that findings are reproducible and reliable. Tudor Achim, founder of Harmonic, emphasizes that the acceptance of AI-assisted tools by top mathematicians is a key indicator of legitimacy: “These people have reputations to protect, so when they’re saying they use Aristotle or ChatGPT, that’s real evidence.”

Formal verification also enables scalability. AI can tackle a larger number of problems simultaneously than human researchers could feasibly manage, allowing systematic exploration of the vast corpus of unsolved conjectures. This approach contrasts sharply with traditional mathematics, where resource limitations often restrict focus to a narrow set of challenging problems.

Quantifying AI’s Mathematical Competence

GPT-5.2 exhibits a distinct performance profile:

Competition-Level Mathematics: 77% accuracy
Open-Ended Research Problems: 25% accuracy

While these numbers indicate that AI is not yet capable of replicating human intuition in genuinely novel mathematical insights, they demonstrate competence in structured problem-solving and pattern recognition. AI’s ability to process complex mathematical literature, identify relevant results, and formalize proofs is already reshaping the field’s productivity metrics.

Moreover, AI’s aptitude for low-hanging fruit problems provides immediate practical benefits. By solving simpler or underexplored conjectures, AI frees human mathematicians to focus on deeper, more nuanced challenges, creating a synergistic partnership between human and machine intelligence.

Implications for Knowledge Work Beyond Mathematics

The techniques developed in AI-driven mathematics have far-reaching implications beyond academia. Domains requiring structured reasoning, such as contract analysis, regulatory compliance, and engineering optimization, stand to benefit from AI’s emerging capability to autonomously reason through complex problems. As highlighted by the GPT-5.2 results, AI’s strength lies in combining rapid literature review, logical deduction, and formal verification—a combination directly applicable to fields where rigorous reasoning is critical.

Industry experts suggest that organizations can begin experimenting with AI on their domain-specific “Erdős problems”—persistent, unsolved challenges that have eluded solution due to resource or knowledge constraints. The lessons from mathematics offer a blueprint for leveraging AI to accelerate innovation systematically.

Challenges and Ethical Considerations

Despite the promise, several challenges remain:

Originality vs. Discovery: Debate continues about whether AI is genuinely generating new solutions or rediscovering overlooked results. In many cases, AI identifies pre-existing solutions that were buried in obscure literature, raising questions about authorship and credit.
Model Limitations: GPT-5.2 performs significantly better on structured problems than on open-ended research questions, highlighting the limitations of current LLMs in creative problem-solving.
Verification and Trust: While tools like Aristotle formalize proofs, the broader adoption of AI in mathematics necessitates rigorous standards to maintain trust in the results.
Access and Equity: As AI tools become more central to research, ensuring broad access to models like GPT-5.2 is critical to prevent the concentration of mathematical innovation in privileged institutions.

These considerations highlight the need for a measured approach, balancing enthusiasm for AI’s capabilities with careful oversight and methodological rigor.

The Future of AI in Mathematical Research

Looking ahead, the trajectory of AI in mathematics suggests increasing integration with human research:

GPT-5.3 and other next-generation models are expected to tackle the remaining unsolved Erdős problems, potentially addressing hundreds of challenges within the next 6–12 months.
Automated formalization tools will continue to evolve, reducing verification time and allowing real-time validation of proofs.
Hybrid approaches, combining AI’s breadth with human intuition and creativity, are likely to become the norm, fostering a new paradigm of collaborative problem-solving.

As Terence Tao notes, AI enables a type of large-scale, empirical mathematics that was previously impossible, systematically exploring vast swaths of problems and generating insights that may otherwise remain undiscovered. This shift could accelerate discovery across mathematics and related disciplines, from cryptography to algorithmic design.

Redefining Mathematical Discovery

AI’s recent breakthroughs, particularly GPT-5.2’s autonomous solutions to Erdős problems, signal a fundamental shift in the methodology of mathematical research. By combining natural language reasoning, formal verification, and large-scale literature analysis, AI enhances both the efficiency and scope of human inquiry. While challenges remain regarding originality, verification, and model limitations, the potential for AI to transform knowledge work is undeniable.

For organizations and researchers, the lesson is clear: integrating AI into structured problem-solving workflows can accelerate discovery, democratize access, and enhance productivity across diverse domains. The progress in AI-assisted mathematics also underscores the importance of cross-disciplinary collaboration, where human insight and machine intelligence complement each other to achieve unprecedented outcomes.

Read more insights from Dr. Shahid Masood and the expert team at 1950.ai on the evolving role of AI in science, technology, and mathematical innovation, and explore how predictive AI models are shaping the future of research across industries.