AI Advances in Solving High-Level Mathematics

Recent developments in artificial intelligence (AI) have sparked significant interest in the field of mathematics, particularly regarding the ability of AI models to tackle complex problems. Notably, Harmonic, an AI start-up, announced that its technology, Aristotle, collaborated with OpenAI’s GPT-5.2 Pro to solve a problem from the renowned Erdos collection, a set of over one thousand conjectures established by Hungarian mathematician Paul Erdos. This collaboration has raised questions about the nature of AI's contributions: whether these systems are genuinely innovating or merely replicating existing human knowledge.

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Neel Somani, a software engineer, recently tested OpenAI's GPT-5.2 and discovered that it could effectively solve high-level math problems, including those related to Erdos. After inputting a problem into ChatGPT, he found that the model not only produced a solution but also formalized it using Harmonic's Aristotle. This marked a notable advancement in AI's capability to engage with mathematical reasoning, as the model demonstrated an ability to reference mathematical axioms and provide a more comprehensive solution than previous human efforts.

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Since the holiday season, 15 problems from the Erdos website have transitioned from "open" to "solved," with 11 of these solutions credited to AI models. Terence Tao, a distinguished mathematician, noted that while AI systems are not yet fully autonomous in solving math problems, they play a crucial role in advancing the field. He identified eight instances where AI made significant progress on Erdos problems, alongside six cases where AI built upon existing research.

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Critics of AI's role in mathematics, including Terence Tao, express a nuanced view. Tao suggests that AI systems are particularly suited for addressing the "long tail" of less complex Erdos problems, which often have straightforward solutions. He emphasizes that while AI can assist in solving these problems, it does not replace the need for human insight and creativity in more complex scenarios.

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Conversely, proponents argue that the integration of AI tools like Harmonic's Aristotle and OpenAI's GPT-5.2 is transforming the landscape of mathematical research. Achim, a mathematics professor, highlighted the credibility of AI usage among academics, stating that the endorsement of AI tools by respected professionals serves as compelling evidence of their effectiveness.

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The ongoing discourse surrounding AI's impact on mathematics reflects broader implications for scientific research. As AI continues to evolve, its potential to enhance human understanding and problem-solving capabilities remains a focal point of discussion among mathematicians and technologists alike.

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• “It feels to me like a really clever student who has memorized everything for the test but doesn’t have a deep understanding of the concept,” — Terence Tao, Professor, University of California, Los Angeles

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• “I was curious to establish a baseline for when LLMs are effectively able to solve open math problems compared to where they struggle,” — Neel Somani, Software Engineer

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• “As such, many of these easier Erdos problems are now more likely to be solved by purely AI-based methods than by human or hybrid means,” — Terence Tao, Mathematician

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• “I care more about the fact that math and computer science professors are using [AI tools],” — Achim, Mathematics Professor

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While there is consensus on the increasing role of AI in solving mathematical problems, discrepancies exist regarding the extent of AI's contributions. Tao's GitHub page presents a more conservative count of eight significant autonomous progressions compared to the broader claims of 11 AI-involved solutions reported elsewhere. This highlights the need for further investigation into the specific contributions of AI in mathematical research.

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