Preamble
The value of mathematics lies substantially in human engagement with it: in understanding, explaining, thinking together and passing on insights. Mathematics aims not only at producing correct results, but at human insight and understanding, as well as interpreting and communicating results within a shared mathematical culture.
AI is already part of mathematical research, and its importance will continue to grow because of its capabilities and availability. Blanket bans will not permanently halt this development and risk shifting its use into opaque settings or other research communities. We must therefore actively and collectively shape this transition and develop the necessary competencies and conditions. In this way, AI can open up new possibilities for mathematical discovery, understanding and collaborative research.
Principles
On the basis of these starting points, we propose the following principles for the use of AI in mathematical research:
01The freedom of research and teaching must be preserved.
Decisions about which mathematical problems are worth studying and what significance results acquire must remain matters of human judgement and scientific exchange. This is particularly true of basic research, whose value often becomes apparent only in retrospect. Whether a problem is suitable for evaluating or marketing AI systems must not become the determining criterion for its scientific significance. Responsibility for this assessment remains with the mathematical community.
02Requirements for correctness and verifiability apply regardless of the tool used.
Any substantively or methodologically relevant use of AI must be disclosed. AI-assisted results must be presented intelligibly and be independently verifiable. Relevant prior work must be carefully checked and appropriately acknowledged. The effort involved in presentation and verification must not be shifted unilaterally onto the scientific community.
03Authorship and scientific recognition must be rethought.
AI can decouple the production and publication of a correct result from the understanding and contribution of the people named as authors. A published result alone therefore does not provide a sufficient basis for establishing authorship or assessing scientific competence. Human contributions and responsibilities must be made as transparent as possible and appropriately taken into account. This also applies to collective research achievements whose contributions cannot be clearly attributed to individuals. Criteria for authorship and scientific recognition must be continually reviewed in light of changing research practices.
04Not everything may be delegated.
Working with AI makes it possible to delegate important parts of mathematical research to automated processes. We must determine which mathematical abilities and responsibilities cannot be delegated. These include, in particular, critical judgement, also in the sense of Kant’s concept of intellectual maturity, and human responsibility for the correctness of published results. AI can support the formation of judgements without assuming this responsibility.
05Unpublished research must be protected by default.
Because the significance of mathematical ideas often cannot be anticipated, researchers cannot reliably decide which conversations or materials require protection. Institutional AI access must ensure that inputs, documents, outputs and information derived from them are used exclusively to provide the requested service. Any further use, in particular for training, model improvement, evaluation or independent research, requires explicit and informed consent. Data storage and access must be limited to what is necessary and governed by verifiable rules. Research requiring particular protection may need technically and institutionally controlled environments. This does not preclude voluntary sharing and collaborative research; they require a self-determined decision about access and use.
06Privileged access to others’ research information must not be exploited.
Access to others’ non-public ideas or research data must not be used to gain a priority advantage over the original researchers. This applies equally to researchers, reviewers, providers and institutions. As in the review of articles or proposals, the confidentiality of such information must be preserved. This requires not only individual responsibility but also binding and verifiable rules. By analogy with safeguards against front-running in finance, effective technical, organisational and contractual information barriers must prevent such information from entering providers’ or institutions’ own research and commercial activities without authorisation. This applies regardless of the technical processing pathway. Access and data flows must be traceable and independently auditable.
07Particularly affected groups must be protected and involved.
Doctoral researchers, postdocs and researchers without permanent positions bear many of the immediate risks of this development. Those in secure positions and leadership roles have a particular responsibility to include these groups’ perspectives, create fair conditions and enable their genuine participation in the decisions ahead. The substantial power imbalance between internationally operating technology companies and individual researchers, often in dependent employment, must be explicitly taken into account.
08Access to AI must not exacerbate existing inequalities.
Access to suitable tools and infrastructure, as well as expertise and training, must be fair, internationally inclusive and oriented towards the public interest. International participation in mathematics must not depend on access to paid AI systems. Critical AI infrastructure for research must not be determined solely by the interests of individual companies and requires effective public oversight. Researchers must not be disadvantaged solely because they do not wish to use particular AI systems, especially commercial ones.
09The rules must be collective and open to learning.
The use of AI requires an ongoing and transparent process in which the mathematical community reviews and develops its rules in light of new experiences. Given the uncertainty about future developments, these principles are a provisional contribution to that process. Through this initiative, we invite the community to discuss and further develop them together.
Acknowledgements
We thank Vadim Alekseev, Anne Schindler, Mario Ohlberger and Robin Sroka for helpful discussions and comments on a draft of this position paper. The views expressed are those of the authors.