Here we collect important questions and different perspectives for the mathematical community.
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Develop concepts and human understanding. Solutions should enter mathematical culture through careful exposition, simplification, conversation and teaching.
Credit for being the first to prove a theorem was an imperfect proxy for understanding. Recognition and public presentation should focus more on concepts, insight and clarification.
Cultivate personal and shared moments of understanding, mathematical taste and cultural experience. Judge AI by whether it enriches that experience; a machine’s superiority does not, for him, determine the value of human mathematics.
Locate mathematics’ core value in applications, including through long chains of abstract theories. Wegner assumes reliable formal verification. As long as humans must set research directions and assess results, AI should open up previously unrealistic tasks and connect mathematical tools to scientific needs.
Preserve human understanding also as a safeguard for scientific independence. His positive vision of AI-assisted explanation assumes ethically and ecologically acceptable conditions. Ng regards present conditions as unacceptable and therefore rejects generative language models.
Separate predictions about capabilities from value judgements. Even assuming highly capable AI, insight, theory-building, education and the future of the community remain goals in their own right.
He does not regard complete abstention from AI as viable for application-oriented academic mathematics. At the same time, he defends human curiosity and intelligible science as values in their own right; the applications of fundamental research cannot be measured over the short term.
Protect the social and ethical conditions of human mathematics, even at the cost of slower progress. Chu calls for a boycott of collaboration with AI companies and for not using LLMs to generate new proofs, although she considers complete worldwide abstention difficult to enforce.
Assess research by its benefit to others, including downstream sciences. In his view, those who reject available tools and primarily cite education as their contribution should be funded as teachers rather than as researchers.
Technical progress does not create an obligation to accelerate as much as possible. Assess benefits alongside harms during the transition, listen to affected people and give researchers a say in the pace. Analogies cannot replace that assessment; she does not offer a complete transition programme.
Understanding, theory-building and consolidation remain tasks. Different interests and respective strengths could enable a division of labour between humans and AI. Litt does not guarantee a lasting human performance advantage.
AI models’ capabilities, genuinely usable products and organisational change are different things. Strengthen expertise, judgement and responsibility; rapid technical progress alone does not determine how professions change.
Reorient the goals and evaluation of mathematical work now. His expectation of a later reorganisation includes neither a timetable nor a secure transition strategy.
Select important questions, check results, organise them and make connections; in teaching, convey enthusiasm, trust and perseverance. His anticipated change of roles does not guarantee lasting human superiority in these tasks.
Understanding encompasses different mental approaches: images, language, intuition, logical structure and procedures. What matters is whether others can think more clearly; knowing a truth value or a formal derivation does not exhaust this.
Tao proposes a publication threshold: the authors should be capable of presenting their results correctly, knowledgeably, intelligibly and with appropriate attribution. This is a capability criterion, not a general requirement to submit a talk.
Formal proof assistants allow subtasks of a formalisation project to be checked separately. Tao considers a similar division of labour possible for new results: individuals could make specialised contributions without fully understanding the entire project. Formalisation would need to become more efficient for this.
Let novelty, correctness, impact and peer review suffice for publication; assess personal knowledge in hiring. He thus separates the value of a text from its authors’ understanding.
Research has long depended on other people’s established theorems and distributed expertise. Personally tracing everything back to its foundations is untenable. AI intensifies this dependence; he gives no general new boundary for acceptable trust.
Rivera requires his doctoral students to disclose AI use and strongly recommends limiting it. Statements used should be fully understood regardless of their origin; in supervision meetings, he asks questions down to fundamental principles. This is his personal supervision policy.
Human authors can receive full credit, even when AI supplied proofs, provided they can personally check, understand, explain and take responsibility for the content, and identify the AI contributions.
Try a model of recognition in which co-ownership of mathematical ideas can be extended later: anyone who subsequently demonstrates author-level understanding can join; journals should organise this demonstration.
A prompt alone does not establish authorship. For him, doing one’s own theory-building or proof work is constitutive of mathematical research.
A correct AI result can merit publication without demonstrating human discovery or understanding. Credit that cannot be attributed should not automatically go to the model operator. Even with data protection settled, Thom considers the existing system of personal priority barely sustainable: publications no longer reliably demonstrate their authors’ contributions and abilities.
Account for the spectrum from a mere prompt to decisive mathematical collaboration. How that contribution can be reliably checked and attributed remains an open question.
Identify and acknowledge the underlying human work behind AI-generated results. If attribution remains inadequate despite efforts, explicitly disclose this.
Shift recognition from first publication towards incremental collective work, including programming, data work, formalisation and explanation; reward contributions more fairly.
Using the formalisation of the sphere-packing theorem as an example, Avigad calls for appropriate recognition of prior human work and for bringing AI-generated code up to the project’s standards together with its team.
Disclose which substantial mathematical ideas or proofs came from AI. Under Hairer’s proposal, routine language correction and literature searches need not be declared.
For its journals, the London Mathematical Society requires disclosure of all AI use, including language assistance. Human authors bear full responsibility; generative AI may not be listed as an author.
Responsible use can be driven out both by reckless competition and by blanket exclusion. Good practice, education and targeted regulation should encourage helpful use and limit harmful or concealed use.
Reject shaming and sanctions solely for using AI. Norms set by permanently employed researchers can impose particularly high career costs on their students and precariously employed colleagues.
In Wang’s thought experiment, if the first solution receives most of the credit and unchecked adoption of AI output is undetectable, authors who check carefully are disadvantaged. Reducing priority rewards does not solve this while later work receives nothing. He leaves open a suitable replacement metric, especially for early-career researchers.
Disclose the exact model version, prompts and orchestration software; even nondeterministic experiments remain open to scientific scrutiny and investigation.
Available reasoning traces can help; he considers general requirements to provide prompts and consumption data impractical because of availability and lack of reproducibility.
Gonen Cohen discusses public access, access on request or access for trusted reviewers as possible options. Prompt and tool histories might offer a compromise; reasoning traces do not necessarily reliably reflect how an answer was actually produced.
Separate generation from checking: a small kernel checks the formal proof object independently of the reliability of the system that generated it.
Personally check, understand and explain arguments. For formalisation, also verify that the encoded theorem matches the intended statement; agreement among several models is not a proof.
Those publishing mathematical results obtained through language models should provide a machine-checkable formalisation. This is Boldt’s proposed norm, not a generally applicable rule.
Formalisation does not automatically check whether the encoded statement is the intended one. Motivation, heuristics and transferability remain additional contributions to knowledge.
Do not confuse convincing conversation with reliability. Maintain critical exchanges with colleagues and require formal evidence or detailed independent understanding; linguistic persuasiveness can shift one’s judgement unnoticed.
Distinguish three levels: proving the formal theorem from the axioms used, correctly translating the intended statement, and agreement with the original informal proof. A formally correct different proof does not automatically confirm the original argument.
Authors should facilitate checking through precise references and appropriate formal proofs; professional organisations could require additional human exposition or external pre-screening.
Consider AI pre-screening, while accounting for erroneous decisions. He discusses deposits or restricting access to trusted authors as problematic barriers, not desirable ones.
In the AI evaluation project First Proof, independent expert reviewers assess the solutions. According to the report, unrestricted corporate donations fund, among other things, research grants for reviewers; the editorial panel and board are not remunerated from these funds.
He considers a possible model of AI-assisted generation with human checking and assimilation of the mathematics. Reviewing could become a regular work duty with allocated time. For AI applications overall, he calls for clear limits and rapidly adaptable corrective mechanisms.
Automate routine tasks while leaving evaluative decisions to people. Otherwise, researchers lose influence over the development of their field.
For its journals, the London Mathematical Society prohibits AI reviewing and uploading manuscripts to AI systems. Reviewers may have a report they wrote themselves linguistically improved, but must disclose this and may transmit only the report text.
Those publishing must turn ideas into shared knowledge through explanations, conversations and talks; an arXiv upload alone is not enough.
Develop formal texts as a mathematical medium in their own right: organise recurring arguments using appropriate concepts and general auxiliary lemmas, and connect computation with abstraction.
For data-based science, openly provide data, programs and computations that can be reproduced with little effort, and use shared benchmarking procedures. Creating missing datasets and benchmark tasks can itself be a significant research contribution.
Formalisation can reveal unnecessary assumptions and simpler approaches and expand a reusable library; certification alone is only one possible purpose.
Explain to outsiders why a problem and its solution are interesting. Public communication can foster social support, one’s own understanding and better mathematical exposition; correctness alone does not convey significance.
A formal proof confirms a mathematical result; its significance, explanation and contextualisation require further work. For Thom, this process of making the mathematics one’s own is itself research.
First Proof tests AI on research tasks whose human solutions already exist but remain unpublished. Solutions, logs, costs and orchestration code are disclosed; two to three expert reviewers assess them anonymously. This test does not capture concept development or finding interesting conjectures.
Beyond success rates, assess whether AI works reliably on repeated attempts, is robust to small changes, correctly estimates its own errors and produces errors with manageable consequences.
Develop a broader scale of automation that also covers simplification, formulating questions, and developing concepts and theories.
Systematically test publicly available models on open problems, independently check outputs and disclose use. The community should assess significance and performance itself; his further conjectures about companies’ motives are not evidence.
Difficulty is relative to known methods: what is easy, achievable with effort or still out of reach? Tao sees this orientation threatened by rapid AI progress and AI companies’ failure to disclose unsuccessful attempts and solution processes. Competition for promising problems could encourage researchers to become secretive.
Develop shared standards for many classes of problems: a solution should also provide insights from the process that produced it and understanding of related difficulties. Without this analysis, a result may have little or even negative value for further research orientation.
Discuss whether unsuccessful runs and their costs should also be disclosed, to what extent and to whom. He does not commit to a general publication requirement; reporting only successful traces can conceal the total effort.
Tao describes an interplay of machine pattern recognition, human conjecture formation, cross-checking and proof work. A case study in knot theory shows how this can produce new insights; it does not establish a general performance forecast.
Wang proposes a possible division of labour: humans supply a proof plan with open intermediate steps, and AI helps with those steps. He also reports successful and failed runs of two prompts. The prompt comparison, devised with knowledge of the proof, does not allow a general prediction of success.
Research automated proving more broadly than language models, including symbolic and hybrid approaches. His goals are verifiable correctness, the ability in principle to find any proof that exists in the chosen formal system, and efficient search. He does not demonstrate that all these goals are generally achievable in practice.
Help develop formal libraries, symbolic methods, experiments and new forms of interaction, and recognise this as research. If mathematics merely recommends that other sciences use ready-made AI, it risks losing relevance. It should contribute its own methods and applications.
In his account of a group-theoretic construction, Zhang describes how the team stopped costly computational approaches, changed coordinates and strategy, and used AI for programming and analysis. The results were independently checked with mathematical software. More computing power alone would not have replaced the change of strategy.
Design programmes up to the doctorate around the requirements of the labour market, including academic careers. Problem-solving in collaboration with AI and making AI-generated results useful should be central.
Avigad calls for professionally relevant problem-solving with AI while preserving mathematical intuition. Commelin and co-authors recommend strengthening problem formulation, communication and critical scrutiny of arguments in the curriculum, and involving students in its design.
Orient mathematical education also towards perseverance, creativity, changes of perspective and responsibility. Its value extends beyond practically useful solutions.
Develop teaching and assessment from the target competencies for research and employment: precise use of concepts, checking proofs, examples and counterexamples, recognising structures and mathematical responsibility.
Start from learning goals and then permit, require or limit AI accordingly. Teach effective, responsible and ethical use in degree programmes and doctoral education.
Connect four elements: the lecture conveys guiding ideas and connections; a course-specific AI tutor supports self-study; the foundational exercise class trains independent mathematical thinking in person, largely without AI; the laboratory practises controlled use of AI, programming and other tools.
The lecture notes remain the authoritative reference; AI explanations should be checked against them and against one’s own reasoning. An illustrative redistribution is two weekly semester hours each for lecture, foundational exercise class and laboratory instead of four for lectures plus two for exercises; the AI tutor supports learning outside contact hours.
First secure shared foundations, then adjust emphasis by study pathway: for theory, for example, proof and literature seminars and formal verification; for applications, modelling, data analysis and simulation. Independent competence remains necessary in every pathway.
Try tasks on checking proofs, selecting and justifying interesting questions, writing intelligibly and giving short talks. These can be combined: work on one’s own questions, with AI where appropriate, write an understandable report and defend the results in class.
Attempt problems independently first, ask for hints rather than complete solutions and work through exercises oneself. AI should enhance learning.
Difficulties and debugging are part of developing the judgement that will later supervise AI. One must remain able to explain methods and decisions oneself.
Carefully work through any AI arguments used on paper. When correcting code, students should explain the cause of the error, the effect of the correction and suitable tests. He proposes joint prompting with supervisors as a teaching method he has not yet tried himself.
Tedious calculation can be delegated if its results can be checked. Conceptual difficulties are often themselves the object of learning; even AI explanations can take away this learning opportunity. Provide supervised use, independent failed attempts and joint checking of AI outputs.
A tutor should build on the learner’s own attempt: ask questions to test understanding, give hints as needed, clarify prerequisites and offer small examples or simpler subproblems. Preserve productive failed attempts instead of immediately supplying the solution.
For MIT, the report recommends oral examinations, semester portfolios, written work followed by discussions and trials of competency-based assessment. Every thesis should include an AI-use statement. AI detectors should not be relied upon.
Assess independent competence without AI through in-person tests, short oral examinations, error analyses and small proof or counterexample tasks. Assess tool competence through documented laboratory projects and oral defences; assumptions, proof status and independent checking of results should also count.
Assess good questions, justified strategies and perseverance even when no complete proof is available yet.
A practical requirement for understanding: be able to explain the reasoning used spontaneously and in detail.
Assess the solution and checking process; for suitable tasks, also require prompts and independent verification. Iterative projects may begin with the student’s own flawed attempts; use creative AI work only in moderation.
Assess understanding through students’ own examples, unfamiliar tasks and in-person work. Avoid language models in bachelor’s and master’s theses, with possible exceptions for subsequent language correction and image generation: independent reading, failure and asking questions are central learning goals for him.
Sarkar reports from a history of mathematics course: compare in-class writing with take-home essays, ask students about their own reasoning in conversation and have them explain passages written with outside help in their own words. This serves learning; it is not a validated AI detector.
Allow for additional preparation, coordination and supervision in Thom’s model of lectures, AI tutoring, foundational exercises and laboratories: smaller working groups, trained tutors, technical infrastructure and tasks focused on mathematical checking. Redistributing contact hours probably does not make the model cost-neutral.
Reduce content overload, routine calculation and purely reproductive formats instead of merely adding new demands. Trial individual modules gradually and evaluate supervision and assessment. Additional effort is justified only if independent competence and responsible tool use are demonstrably strengthened.
Recognise those who explain why an argument works, separate core ideas from technical details, find connections and fruitful questions, teach methods and enable others. Contributions also happen in talks, conversations, teaching and collaboration, not only in articles.
Share scientific credit for ideas, even after publication, with people who independently master the argument. Journals could assess this understanding through detailed explanation before a knowledgeable, critical audience, potentially on the scale of a graduate course. Weinreich calls this co-ownership.
Give greater recognition to explanation, reviewing and contextualisation. The video journal Mathematical Discourse is a concrete example: it reviews talks for clarity, novelty and mathematical interest. It explicitly does not replace checking the written proofs.
Separate the mathematical value of a result from the personal contribution. Deduct from the human contribution whatever specified AI systems can reproduce with a specified computing budget, even for entirely human work. Failure to reproduce does not prove originality. The text offers no empirical evidence that this is suitable for personnel decisions.
Give greater weight in hiring to contributions that integrate AI-generated results into mathematical culture; the same decoupling of product and competence affects theses. How such contributions can be measured comparably remains open at present.
Expand research internships and supervised participation. If students are replaced by AI agents for reasons of efficiency, they may lose learning opportunities and access to research communities. The report therefore calls for deliberately preserving mentoring and personal collaboration.
Open problems can sustain collaboration, methods and early-career training. Rapidly resolving them can interrupt this development, even with a short and elegant proof. He acknowledges the benefit of faster solutions in application-oriented fields; he gives no general boundary rule.
Provide an educational track for the planned AI mathematics competition Mathathon, with notes, explanatory videos and more elegant proofs of known theorems. Explanation, motivation and methods should be rewarded alongside results.
Preserve demanding education and solidarity with colleagues resisting pressure to use AI. He warns of personnel budgets shifting to subscriptions and work being reduced to checking output; these are concerns, not established predictions.
Invest deliberately in people and value supervision, role models and inspiring explanations. Community is built by people who understand results, improve them and make them accessible to others. The appeal contains no specific funding formula.
Treat advanced AI as a basic public service like water or electricity: reliable, widely available, with public obligations, strong data protection, independent oversight and safeguards against discriminatory or self-serving use. This also concerns education, public administration, the economy and everyday life.
Support public computing infrastructure at university, national and international levels, and research laboratories that are administratively and financially independent of industry.
Build open academic infrastructure with transparent decision-making and community oversight; reduce dependence on individual companies.
Support community-maintained smaller models and a nationally or multinationally funded, publicly accessible AI resource. The authors also warn that when universities tie researchers to one provider, differences in models’ capabilities across disciplines can create new inequalities.
Organise national or Europe-wide AI infrastructure as a basic service: publicly owned or strongly regulated. Treat intelligence as a generally available resource whose use and provision must not be designed abusively.
Consider colleagues in countries with limited financial resources who cannot afford commercial AI offerings. Thom connects this concern with equal access to AI as a public or strictly regulated basic service. How international access should be financed is currently an open question.
Provide institutionally funded access across providers and expand it where teaching needs are greater; also consider computing resources for running one’s own models.
The organisers aim to use computing credits for their AI mathematics competition to improve access, particularly for young researchers. The open letter, in contrast, questions whether a research model requiring US$20,000 of computing credits per result could be broadly affordable.
Public infrastructure and institutional AI access are approaches to financial inequality. However, the contributions cited here contain no fully developed global funding or allocation model.
Direct more public and philanthropic support towards open, locally runnable and less expensive models, and towards transferring powerful methods to more economical models. This is an access proposal, not a guarantee of equal opportunities.
When assurances are made about unpublished research chats, distinguish use for training from direct access; disclose the basis of those assurances in settings, datasets and model versions. Anonymisation does not remove intellectual content.
Secure consent to training use and opt-out possibilities in publication contracts; strengthen authors’ rights.
Limit institutional access by default to the requested service; any further use of inputs, outputs and derived information should require informed consent. Limit storage and access and make them auditable.
Require technical, organisational and contractual information barriers. Non-public research information must be separated from providers’ or institutions’ own research and commercialisation activities; access and data flows should remain independently auditable.
The draft’s required separation of confidential research data from providers’ own research activities is an institutional safeguard. It proves neither a specific instance of misuse nor that such information barriers are already effective in practice.
AI providers must not use their informational advantage about the use of others’ ideas against the people who entrusted those ideas to them.
Recognise sincere reasons for using or abstaining from AI. Whether to use tools, and which ones, remains a responsible choice.
Abstain from AI in one’s own research. Do not review machine-written articles or submit to journals that permit machine-generated reviews. Do not supervise doctoral students or postdocs, or support hiring, when AI replaces their own work.
Protect abstention institutionally through reserved positions and greater recognition of AI-free work in promotions.
Using astrophysics as an example, reject both blanket AI bans and unrestricted delegation. Education should develop independent thinking and the ability to supervise and check scientific work competently.
Open up the debate broadly, especially to the younger generation. Develop shared rules for intelligible mathematical exposition and allow alternative evaluation frameworks; individual prominent voices should not speak for the whole field.
Use AI for collaboration and learning; value varied contributions and good teaching. Early-career researchers may abstain from AI. Monitor one’s own dependence, acknowledge prior work and inform researchers with related projects early. Wildon makes these recommendations on the assumption that current AI capabilities are close to a temporary plateau.
Thom considers firm opposition to AI by individuals or whole groups substantively futile, but regards continuing conflicts as possible. How to address them is currently an open question.
Pause or abandon the planned AI mathematics competition Mathathon. The letter fears commercial appropriation, rushed and inadequately understood results, and review work shifted onto others. Its criticism addresses the announcement before the organisers’ response.
Continue Mathathon as a modified experiment. For selected teams, the organisers plan a six-month second round with an arXiv preprint, video and automated formalisation. Sceptical voices should be included; the organisers do not promise consistently sufficient quality.
First Proof combines evaluation of mathematical AI performance with separate scientific oversight and foundation governance. According to its ethics statement, governing-body members may not take paid roles at AI companies during their terms; finances, including corporate funding, are disclosed annually.
Responsible collaboration remains his goal. However, he describes growing divergence between corporate goals and mathematical culture and calls on the community to reject unsustainable uses. He discloses his contacts and preferential access; in retrospect, he should have objected more strongly to the promotional abridgement of an OpenAI interview.
Allow Mathathon as a one-off AI mathematics competition with access to substantial computing power. For Livshyts, participation does not commit anyone to abandoning conventional research. Her addendum stresses that the event does not replace traditional research, but she does not consider that a reason to reject the individual experiment.
Demand stronger public oversight; leave harmful collaborations and consider smaller, more economical or open tools. Professional organisations should develop shared rules.
Make financial and environmental usage costs visible, examine one’s own footprint and encourage more economical methods; a standing body should evaluate experience.
Organise working groups on education and publication policy and work collectively towards institutional independence from corporate interests.
Include social displacement, unequal opportunities, and energy and water consumption in benefit assessments. Concentrated gains do not justify unlimited harm to others.
Researchers with permanent positions in particular should devote time and expertise to social and ecological tasks. On these grounds, he rejects additional use of generative AI and the provision of company benchmarks.
Discuss resource and climate impacts collectively, explain LLMs publicly and do not support their marketing. While the current development philosophy, which he regards as harmful, continues, Marchand abstains from LLM use, related collaboration and reviewing. He does not require everyone to adopt his personal rule.