Recommendations on the use of AI for PhD students and supervisors

A collective of symplectic geometry researchers¹

SERIES · As application deadlines approach, Proofs and Prompts is publishing a series of posts from 19 to 23 October for people considering a PhD, doing a PhD or looking for a postdoc: guidelines, discussions and speculation about what to do and what careers in mathematics will look like. This post is one of them. Each is written independently and reflects only its authors’ views. All posts in the series

Mathematics is a human and social activity, and it is fundamental that this aspect be preserved. This must be a common goal for doctoral students, supervisors/advisors and universities, and it is essential that all be fully aware of it.

AI can be used as a tool in the service of mathematicians. But it is mathematicians who must determine which questions are important, and they must remain the sole judges of the interest of a result. Delegating this task to a machine, however “intelligent,” is never acceptable.

The arrival of AI in mathematical research has brought deep changes and justified concern, on the part of doctoral students as well as their supervisors. The recommendations that follow are only advice intended to help you, your supervisor, and your institution to deal with the place of AI in mathematical research and make the most of your doctoral years.

There seems to be no shared opinion on the dangers of AI, and it is not the purpose of these recommendations to discuss them, while acknowledging that such opinions will affect how they can be put into practice.

We do not deny the ethical, societal and ecological questions raised by AI, nor its implications for civil liberties, security and the economy. We are well aware that mathematics is currently being used as an “advertising vehicle” by large AI companies. But AI also exists outside such companies, for instance through open-source models installed locally.

In what follows, “AI” refers to the use of AI for mathematical research, not for other purposes such as editorial or bibliographical assistance.

A) For doctoral students

1. AI is going to have an impact on mathematical research, both by solving certain questions outright and by assisting you in your own work — sometimes on its most technical aspects, sometimes by helping you learn new material or discover connections between different areas of mathematics. Depending on many factors, both personal and scientific, you will find it useful to varying degrees. But whatever your opinion, ignoring AI is not an option.
2. If you use AI, heavily or occasionally, you must train yourself to use it efficiently and to know its limits. Mathematics produced by AI can be wrong while sounding perfectly convincing. Every step of a proof obtained with its help must be carefully checked by you, and you alone are responsible for its correctness. Since AI is not always reliable when it comes to attributions, you will need to be especially careful about this issue in your papers and thesis.
3. The use of AI to obtain mathematical content (an idea, a lemma, a computation) must be documented and declared. Keep the prompts and the corresponding answers, for instance in a “lab notebook”, and disclose this use in your thesis and in your papers, as many journals now require. In all cases, you must fully master any result obtained with the help of AI. Text produced by AI can be considered neither a preprint nor a thesis manuscript, and AI is never a co-author.
4. In the case of a collaboration, it is important to share early on your views on AI. In particular, do not submit to a commercial model unpublished results that are not your own (collaborators’ drafts, private communications) without the consent of those concerned.
5. Since a number of technical problems are now solved by AI, your thesis topic may be more open-ended than those given in recent years. In return for the help AI provides on technical questions, expectations will likely be higher in terms of independence, creativity, innovation and the breadth of your knowledge.
6. It would be a mistake to believe that AI removes the need to acquire technical knowledge, even if technical virtuosity may no longer carry the same weight. This knowledge is absolutely necessary in order to engage usefully with AI and to judge its answers.
7. Be careful not to find yourself one-on-one with the AI. On the contrary, it is essential to have regular, in-depth discussions with your thesis supervisor, the members of your laboratory and, furthermore, to develop as early as possible during your studies direct research exchanges with peers and other mathematicians through conferences, research visits, and other similar opportunities.
8. The format of teaching and of examinations will probably change, at both undergraduate and graduate level, including the PhD defense. You must prepare for this, as teaching, and more generally the communication of mathematics, may take up a larger share of a researcher’s activity and play a more central role in how their contributions are evaluated.
9. Plan for your future: the skills acquired during the thesis, including a considered command of AI tools, should also be of value outside academia.

B) For supervisors

1. Your students will use AI according to their personal inclination (and means of access). You should endeavour to support them in their choices rather than trying to forbid it outright or forcing them to adopt it. On the other hand, it is essential to bear in mind that the problems you are posing might be quickly solvable by AI. You should evaluate the proposed problems accordingly, just as you would check them against the recent literature.
2. The supervisor must make reasonable efforts to provide the doctoral student with the AI tools they may need. This is also a matter of fairness between doctoral students. The supervisor should agree with the student, from the start of the thesis, on how the use of AI will be documented (see A3).
3. It must be checked that doctoral students still acquire the techniques useful in the field, in particular – but not only- in order to interact with AI. Since AI knows no boundaries between mathematical fields, this culture will probably need to be broader than before. It is important to give doctoral students ample opportunities to interact with other mathematicians – starting with the thesis supervisor – so as to avoid a one-on-one with the AI (see A7).
4. The defense will have to check thoroughly that the student has full command of all the new results presented in the thesis, and to assess their mathematical contribution, creativity and maturity. Its format will probably need to evolve, and sufficient time should be set aside, before or during the defense, for such an assessment. In all cases, the student must know in advance what is expected of them.

C) For universities and research institutes

1. Since researchers are the best judges of their own needs, they must be left to decide whether or not to use AI and, if so, which version – commercial models or locally installed ones – and what training they need.
2. The cost of these resources (subscriptions, hardware for local models) must be covered at the institutional level, and not left to supervisors or doctoral students.
3. Institutions must set clear and simple rules on the disclosure of AI use in thesis manuscripts, consistent with the prevailing practice of reputable journals, and adapt the regulations governing defenses accordingly (see B4).

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Received 17 October 2026.

1. Devised and endorsed by A. Abbondandolo (Ruhr University Bochum, Germany), D. Álvarez-Gavela (Brandeis, USA), S. Anjos (Técnico Lisboa, Portugal), D. Auroux (Harvard, USA), İ. Baykur (UMass Amherst, USA), D. Cant (Université de Montréal, Canada), O. Cornea (Université de Montréal, Canada), M. Damian (Université de Strasbourg, France), J. Evans (Lancaster, UK), R. L. Fernandes (UIUC, USA), U. Frauenfelder (Universität Augsburg, Germany), V. Ginzburg (UC Santa Cruz, USA), F. Gironella (CNRS–Nantes Université, France), Y. Groman (Hebrew University, Israel), B. Gurel (UCF, USA), K. Inal (UMass Amherst, USA), A. Keating (Cambridge, UK), M. Kegel (Universidad de Sevilla, Spain), J. Latschev (Universität Hamburg, Germany), A. Libgober (UIC, USA), Y.-S. Lin (Boston University, USA), L. Macarini (IMPA, Brazil), M. Mazzucchelli (CNRS–Sorbonne Université, France; on sabbatical at IAS, USA, 2026–2027), K. Mohnke (HU Berlin, Germany), D. Nadler (UC Berkeley, USA), A. Oancea (Université de Strasbourg, France), A. Pedroza (Universidad de Colima, Mexico), A. R. Pires (University of Edinburgh, UK), P. Seidel (MIT, USA), S. Seyfaddini (ETH Zürich, Switzerland), I. Smith (Cambridge, UK), L.-S. Tseng (UC Irvine, USA), R. Vianna (USP, Brazil), C. Viterbo (Université Paris-Saclay, France), W. Wu (Zhejiang University, China), Z. Zhou (AMSS–CAS, China) ↩︎