The Transformation of Mathematics Through Artificial Intelligence

The field of mathematics is experiencing a significant transformation due to advancements in artificial intelligence (AI). Mathematicians like Daniel Litt from the University of Toronto have noted a rapid evolution in AI's ability to tackle complex mathematical problems, leading to a reevaluation of the role of human mathematicians. In March 2025, Litt expressed skepticism about an earlier bet he made regarding AI's capabilities, stating, “I now expect to lose this bet.” This sentiment is echoed by Jeremy Avigad from Carnegie Mellon University, who remarked that AI is approaching the point where it can prove theorems more effectively than humans.

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In February 2025, Nikhil Srivastava and his team at the University of California, Berkeley, initiated the First Proof project to assess AI's mathematical skills through real-world problems. The project featured ten problems that researchers typically encounter in their work. Following the release of these problems, AI models from companies like OpenAI and Google DeepMind began submitting solutions, demonstrating a remarkable speed of progress in AI's mathematical capabilities.

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Google's AI tool, Aletheia, employs a sophisticated version of its Gemini chatbot, which iteratively refines solutions and checks for errors. However, the accuracy of AI-generated proofs remains a topic of debate. For instance, in one problem concerning geometry, only five out of seven experts agreed on the correctness of the AI's proposed solution. Ivan Smith from the University of Cambridge acknowledged the AI's sensible approach, likening its output to that of a promising PhD student.

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Despite the advancements, verifying AI-generated proofs poses challenges. The speed at which AI can produce proofs may outpace human ability to check them, raising questions about the validity of unverified theorems. AI's role in formalizing proofs—translating them into a computable format—could alleviate some of these concerns. A recent achievement involved a proof concerning sphere packing, which was formalized into approximately 200,000 lines of code, representing a significant portion of existing formalized mathematics.

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Experts like Johan Commelin from Utrecht University believe that the integration of AI could revolutionize mathematical practice, particularly in peer review and error detection. However, there are concerns about the potential loss of learning opportunities for students and professionals who might rely too heavily on AI tools. Anna Marie Bohmann from Vanderbilt University emphasized that the struggle to solve problems is crucial for consolidating knowledge.

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Tony Feng from Google DeepMind expressed caution about over-reliance on AI, advocating for the importance of developing personal intuition in mathematics. As the field evolves, it is anticipated that the essence of mathematics will remain recognizable, albeit in a new form, as noted by Commelin.

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• “I now expect to lose this bet,” — Daniel Litt, Mathematician, University of Toronto

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• “We have to face up to the fact that AI will soon be able to prove theorems better than we can.” — Jeremy Avigad, Mathematician, Carnegie Mellon University

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• “If this was a PhD student coming back with their thoughts, it would be encouraging and would build confidence that the result was actually true,” — Ivan Smith, Mathematician, University of Cambridge

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• “This is a big deal. This is Fields medal-winning work, and it’s being auto-formalised.” — Johan Commelin, Mathematician, Utrecht University

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• “Struggling to create and formulate new ideas and to solve new problems is one of the main ways in which both students and mathematics professionals consolidate their knowledge.” — Anna Marie Bohmann, Mathematician, Vanderbilt University

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• “I think similar things will happen here, where we radically change what we’re doing, but 10 or 20 years from now, we will still recognise what we’re doing as mathematics, in a new style.” — Johan Commelin, Mathematician, Utrecht University

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