Mathematics has long been considered beyond the reach of AI. That changed in July 2024, when two AI models from Google DeepMind achieved silver-medal-level performance at the International Mathematical Olympiad (IMO) [1]. The event resonated throughout the mathematical community, sparking discussion and controversy about the role of AI in mathematical research.

Because mathematics requires deep understanding and conceptualization, it has been one domain where the human mind was assumed to reign alone. Yet AI tools are increasingly being adopted by researchers. The remedy is not prohibition, but transparency: clear disclosure norms, pedagogy, and publication policies. Some mathematicians have been open, most notably Terence Tao, who used an AI to formalize the proof of the Polynomial Freiman-Ruzsa conjecture in 2023 [2]. Many others remain silent, fearing backlash. Reticence can be stronger in mathematics, given its symbolic status as a science at the edge of human abstraction.

A contentious debate surrounds the use of AI, plagiarism risks, and questions of fairness. As models have become more capable, the scientific community has yet to delineate the boundary between legitimate tool use and plagiarism. The greatest risk lies not in adoption but in AI becoming taboo. When used extensively yet in secret, the integrity of the field is imperiled.

Calls to ban AI tools miss the broader implications. Just as the scientific community embraced online search, it is now embracing AI. Applied mathematics, from engineering to mathematical finance, has moved quickly. These fields rode the machine-learning wave in the 2010s, and adopting modern large language models (LLMs) is a natural progression. An expanding range of AI tools implies a growing user base. More leading universities are integrating AI tools into teaching and research [5]. The Lean proof assistant, used by Tao, reported in May 2025 that it was taught in over fifty graduate courses worldwide [3].

A side effect of adoption is misuse: AI has been used to fabricate publications. Such abuses, hallucinated literature reviews, compromised imagery, and spurious proofs, undermine standards. In mathematical research, the risk is heightened by abstraction: while AI can help review proofs, it can also be deceptive during peer review. Yet the upbeat headlines of an AI revolution seem misleading. Research problems faced by mathematicians differ from IMO-style questions, so the advantage of tapping into large databases of existing proofs is limited. Even Tao's paper relied mainly on the authors; Lean helped with formalization after initial publication [2]. As of writing, AI remains a poor innovator. By design, these models predict conventional sequences of ideas and struggle with genuinely novel concepts. Even for literature reviews, human curation remains indispensable.

For the vast majority of researchers, however, AI tools can support innovation, curation, and dissemination. AI already helps at various stages of the research process: as an assistant for time-consuming tasks, in synthesizing literature, as a check against inadvertent plagiarism, as a helpful editor for LaTeX (the standard typesetting system in the field), and in flagging notation inconsistencies. In mathematics, where writing is often concise, tools that improve clarity are welcome. While specialized proof assistants like Lean are increasingly robust, general-purpose generative models remain prone to errors. Their lack of genuine conceptualization and tendency to hallucinate are incompatible with mathematical rigor. In my own experience as a practitioner in financial mathematics, AI tools are already transforming quantitative analysis. Assistants can accelerate routine calculations and data preprocessing, freeing time for conceptual work. Yet their limits are clear when facing novel problems, especially in markets outside the mainstream corpus, such as digital assets and cryptocurrencies. AI excels at verification and formalization, but struggles beyond that.

If an AI suggests an idea during a review, can the scientist take credit? Licensing terms may allow it, but the ethics are murkier. An AI performing a search essentially compresses a library, as does a web search, with ideas emerging as a result; those ideas still derive from underlying sources. AI should not be listed as a co-author; disclosure, at least to teach the next generation how to use tools ethically, is the minimum.

When AI generates code, the output can be checked. When AI generates data, reproducibility becomes a more serious concern, because LLM outputs are stochastic. Nature has adopted such a policy, requiring documentation of AI use in the Methods section while exempting AI-assisted copyediting from disclosure [4]. Other prominent journals in mathematics and engineering should follow suit. Regardless, researchers should share how they use AI, so best practices can develop, and the next generation can learn to use these tools well. Many students rely on appendices to see how results are derived, which references matter, how tools are used, and what good practice looks like.

Another issue, beyond ethics, is opacity. Given their complexity, many AI models are effectively black boxes. This need not be a problem if outputs are critically reviewed. Some tools, such as Google's NotebookLM, aim for more transparency and control over sources, but most models do not. Much material, even in scientific papers, is uneven. There is a real risk that AIs trained on lower-quality data will propagate lower standards, rather than elevate them. Using AI is about judgment. Just as a tuner reports pitch, and musicians exert judgment; scientists orchestrate tools, from mathematical methods to new technologies, and set the tune.

What should happen next? Mathematical journals should adopt clear guidelines distinguishing uses: formatting, literature review, and proof verification should be accepted; while reliance on AI for core insights should be disclosed and scrutinized. AI-usage statements should become the norm at submission. Departments should teach students not just how to use these tools, but when and why.

Above all, our community should reward transparency, so researchers can discuss their use of AI without fear of stigma or reprisal.

[1] "AI solves IMO problems at silver-medal level." Google DeepMind, July 2024. https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level

[2] Tao, Terence. "Formalizing the proof of PFR in Lean4 using Blueprint: a short tour." What's New, November 2023. https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr-in-lean4-using-blueprint-a-short-tour

[3] "Courses using Lean." Lean Community, 2025. https://leanprover-community.github.io/teaching/courses.html

[4] "Artificial Intelligence (AI)." Nature Portfolio, 2025. https://www.nature.com/nature-portfolio/editorial-policies/ai

[5] Boles, Sy. "AI leaps from math dunce to whiz." Harvard Gazette, July 2025. https://news.harvard.edu/gazette/story/2025/07/ai-leaps-from-math-dunce-to-whiz