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.
From a Platonist perspective, research explores an independently existing mathematical reality. AI can provide better tools for this, much as satellites do for cartography. Bader advocates embracing the new possibilities and adapting professional practice; beauty, understanding and socially fruitful connections to the physical world remain goals for him.
Problem-solving and conceptual understanding can each serve as a means to the other. Different mathematical motivations are legitimate; in his view, simply declaring understanding to be the sole overriding goal fails to do justice to this diversity.
Understand mathematics as a language for making sense of the world and as a form of personal expression. On this view, a machine-generated solution does not deprive one's own mathematical work of meaning; researchers should also be able to pursue their own questions.
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.
Technological progress does not create an obligation to accelerate as much as possible. Assess benefits and transitional harms together, listen to those affected and let researchers help determine the pace. Analogies cannot replace this judgement.
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.
Distinguish mathematics as a body of ideas, as a vocation practised individually and collectively, and as an institutionally organised profession. Rivera expects changes above all in professional structures. He regards the pleasure of aesthetically guided understanding and the community of mathematical friendships as more enduring; he leaves open how AI should be used within them.
Prepare institutions for the possibility that AI also becomes highly capable at explanation and theory-building. Human understanding nevertheless arises only through human learning. Seminars, supervision and thinking together should therefore remain goals in their own right; this approach should not depend on a lasting human advantage in performance.
Do not assume that AI can generate proofs but cannot provide good explanations. Examples, connections to the literature and clear exposition could also improve. A future role for humans therefore cannot rest solely on an asserted permanent advantage in explanation.
Make human well-being an explicit goal of research. According to Loh, for people to steer research directions and AI systems responsibly, they need their own expertise at the research frontier and must maintain it through active research.
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 their AI use and strongly recommends limiting it. Statements they use should be fully understood, whatever their source; in supervision discussions, he asks questions down to fundamental principles.
For Nguyen, mathematical understanding is changing, distributed and selective; even human theories often exceed any individual's knowledge. It is therefore possible to build on formally verified AI results before every detail has been understood by humans. Deciding which parts should be explained and understood collectively remains a task of mathematical judgement.
Before publication, authors should be able to reproduce the main ideas themselves, write intelligibly for humans and take intellectual responsibility. He permits linguistic revision by AI but rejects a language model generating the first draft of a manuscript.
Do not present either the end of mathematics or their own redundancy to young researchers as inevitable. Evans sees a task for experienced colleagues in sustaining interest and scope for action, and in grounding the value of mathematical work in the advancement of human understanding.
New mathematical insights can be a source of shared pride even when individual researchers also feel a sense of loss. New professional and communal structures should enable as many people as possible to continue participating in mathematics.
His account shows that enthusiasm for new possibilities and wider access can coexist with grief over familiar ways of engaging with mathematics. He attributes his feelings to the abrupt transformation of a long human tradition and offers no simple resolution.
In the abstract, Friedman interprets uncertainty as a crisis of orientation concerning mathematicians' place in research increasingly shaped by AI. He connects this with opaque mathematical processes and changing roles. The approach is a psychoanalytically informed interpretation.
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.
Recognise the spectrum from a mere prompt to decisive mathematical involvement. How this contribution can be reliably assessed and attributed remains an open institutional question.
Link originality and recognition also to independent interpretation: connecting, contextualising and organising already generated and verified results into a theory can constitute an original scholarly contribution.
Journals should require a substantial human mathematical contribution and reject fully AI-generated work. For Craven, checking and understanding alone do not establish authorship. Human-designed strategies executed by machines may, however, be admissible; editors should judge borderline cases.
Connect human authorship with intellectual responsibility: authors should be able to explain the mechanism of a proof and how they arrived at it, answer questions and distinguish new ideas from borrowed components. Merely disclosing AI use and checking correctness is not enough.
Tao proposes that priority should require a publicly accessible scholarly explanation, in addition to the preprint and, potentially in future, formalisation. The latest date among these components could be decisive. An explanatory blog post or a recorded talk could also count; an early announcement of a solution alone would not suffice.
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.
Make generation, checking, correction, formalisation and clear re-exposition visible as distinct contributions. They need not receive the same kind of recognition. A shared platform could also document later contributions to a result and thereby acknowledge collective work more appropriately.
Understand advances in AI also as the fruit of mathematical knowledge built collectively.
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.
Experiment with a public, free repository in which AI-generated proof attempts are collectively checked, corrected and linked to the literature. It should remain clear what has merely been generated, what has been checked, what has failed and what remains uncertain. Unverified claims can also be discussed there; Trombetti explicitly describes ProofForum as an experiment.
Change incentives and attribution so that sharing early remains a reasonable choice for young researchers too. He cites agreements on rapid data release and recognition in genomics as an inspiration. He explicitly acknowledges that he does not yet know a suitable mathematical counterpart; supervisors and young researchers should develop one together.
Establish a register for drafts, partial calculations and notes with verifiable timestamps. Initially restrict access, then expand it gradually until public release. Later assessment should also consider contributions from unfinished ideas; a timestamp certifies their existence, not their significance. The procedure should rest on shared norms, without central permission to publish.
Even effective protection of private inputs does not eliminate the advantage of well-funded actors: unfinished ideas shared publicly could be developed more quickly with substantial computing resources. The author sees this as an incentive for secrecy and a threat to open exchange.
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.
Anyone publishing mathematical results obtained through language models should provide a machine-checkable formalisation.
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.
Improve the shared infrastructure for formal verification through more efficient algorithms and representations. For specified computational tasks, the Lean Kernel Challenge also requires a proof that the algorithm developed satisfies the specification for every input; speed alone is not enough.
Plan and supervise AI-assisted formalisation closely so that libraries remain organised, understandable and reusable. Alongside machine checking of proofs, verify that the formal statements express the intended results. Work on a trustworthy shared foundation reduces repeated checking of the same definitions.
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 testing project First Proof, independent expert reviewers assess the solutions. According to the report, unrestricted corporate donations fund, among other things, research grants for the reviewers.
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.
Use formal certificates to reduce the burden of reviewing; humans continue to check correspondence with the stated theorem, understanding, context and exposition. Journals could favour broader projects; she proposes separate repositories or journals for individual results largely generated by machines.
Consider temporary submission restrictions per author. Acceptance could lift a restriction; substantial deficiencies in the content could extend it. Craven aims to protect scarce reviewing capacity from excessive and inadequately checked output.
Poorly explained proofs, even if correct, can create additional work for others to make sense of them. Those publishing such results should reduce this burden themselves: contact experts, explain how the work developed and use available AI or computing access to clarify it. Traditional reviewing cannot absorb arbitrarily large amounts of unprocessed output.
More results can enable both more unprocessed and more understood mathematics. Researchers could choose what to explore in depth; databases or AI-assisted overviews could help them navigate. He sees the greater danger in losing the social structures that sustain this work of understanding.
AI laboratories should help fund clear exposition and the incorporation of reusable formal proof components into shared libraries. Formal verification, explanation and library maintenance are distinct tasks and can take place at different times.
Those claiming credit for generating a proof should make their best effort to explain it and prepare it for publication. When this is not possible, Tao proposes a regulated procedure allowing a proof that has not yet been sufficiently worked through to be explicitly handed over to other authors for further development. Details and rules of recognition remain open.
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.
Authors should have AI check papers for errors and inaccurate references before submission. Craven also recommends AI pre-screening to reviewers; the subsequent assessment of significance and correctness remains their responsibility. He does not wish to review for journals that prohibit him from using AI in this way.
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.
After an AI solution has been verified and made understandable, investigate the new concepts, structures and applications it enables. For the announced Navier–Stokes construction, Sharma asks, for example, about consequences for partial differential equations, turbulence models and hidden algebraic structures. Accessible talks and collective work to understand the result should support this transition.
Seek simple explanations, clarifying language and a suitable level of abstraction so that others can absorb complex ideas. Making existing knowledge accessible should be valued as highly as advancing the research frontier.
Motivating explanations should show how one might arrive at ideas, concepts and questions. They may include understandable wrong turns and are also intended for experts. Important results that are not yet adequately explained could be collected as open exposition problems and addressed according to jointly developed criteria.
Make formal proofs accessible through an interactive map of their dependencies. Abramov marked central theorems in Lean code and used the resulting diagrams to look for detours and simplifications. The map supports reading; it does not replace expert scrutiny.
Organise results and partial advances collectively, explain them clearly and incorporate them into usable databases and Lean libraries. The authors connect this infrastructure work with courses, workshops and personal exchange; their case study also describes a strengthened sense of community.
Make the human development of mathematical work publicly visible: tell stories of collaboration, unexpected encounters and shared learning in blogs, media contributions and social media. Papers could also include sections on how they came about or informal explanations of their significance; he presents these formats for discussion.
Through sustained exchange with the media, educational institutions, policymakers and funders, explain what mathematical work achieves beyond benchmark successes. Even when corporate goals differ, societal recognition can sustain the discipline's work and culture.
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, check outputs independently and disclose their use. The community should assess significance and performance for itself.
Assess models by reliable assistance, verifiable results and ongoing costs of use. Publications should also report failures and limitations so that independent teams can reproduce and adapt the work.
Evaluate results in light of the actual working process. Epoch describes the reported advance on committee elections as collaboration between humans and AI: it emerged from extended interaction; according to a co-author, a simple prompt did not appear sufficient. Solving a benchmark problem therefore does not establish a corresponding autonomous capability.
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.
Before new computational runs, be able to check which solutions and failed attempts already exist for a problem. The shared catalogue should avoid duplicate searches and preserve knowledge of verified, failed and still uncertain approaches.
Tao describes an interplay between machine pattern recognition, human conjecture formation, cross-checking and proof work. A case study from knot theory shows how this can lead to new insights.
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.
Study automated theorem proving more broadly than language models, including symbolic and hybrid methods. His goals are verifiable correctness, the ability in principle to find any proof that exists in the chosen formal system, and efficient search.
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.
Develop large collaborative research programmes with leadership, early-career positions and quality standards. Their outputs should also include teaching texts, databases and explanations. Do not conduct research faster than results can be understood and communicated.
Explore new mathematical questions and phenomena through exchange with other sciences. This is an additional possibility; independent, curiosity-driven mathematics should retain its fundamental place.
Examine repeated failures for common obstacles and, where appropriate, reformulate research goals. In the case study, human direction shifted a stalled search for better constructions towards investigating a general bound. The authors distinguish technical execution from research judgement and long-term project direction.
Alternate phases of AI-assisted result generation with phases of working through, connecting and reformulating the results oneself. Valentini cites experimental sciences, which separate data collection and analysis in time, as a model; larger collaborative projects could emerge instead of many individual results.
Develop new ideas only a little ahead of formal verification, verify crucial intermediate steps promptly and start afresh when unchecked dependencies accumulate. In his experiment, AI criticism and extensive drafts alone proved insufficient.
Develop a researcher-controlled working profile from recurring corrections: record instructions, the experiences underlying them and the mathematical state of the project separately. Test instructions on later tasks, discard them if harmful and reassess them when changing models. Hofer proposes this as a testable experiment.
Alongside a complete archive, maintain a carefully curated account of the project's state that preserves outstanding proof obligations, failed approaches and the evidential status of each item. In the case study, repeated summarisation lost crucial qualifications even though they remained in the archive; an apparent advance had to be withdrawn.
Clarify the task and its background, break difficult projects into subtasks and develop AI outputs through specific follow-up questions and corrections. Collaboration can open up new ideas but does not necessarily save time. Computer algebra and formal proof checking should complement oversight.
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.
Practise mathematical communication deliberately: student seminars without fear of disparagement, informal conversations, sharing one's own lecture notes publicly and analysing good exposition. A welcoming conversational culture can prevent young researchers from turning exclusively to AI for help out of fear of embarrassment.
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.
Combine traditional foundational work with observing new tools. Read standard texts and work on problems alone and in groups; at the same time, discuss with colleagues which problems AI can actually handle in one's field. Aougab recommends neither switching entirely to AI nor rejecting it wholesale.
Deep understanding develops through one's own active investigation: questioning statements, reconstructing arguments and exploring ideas oneself. Good explanations and personal or AI-assisted guidance can support this process but cannot replace active engagement.
Read existing proofs actively too: first try to find solutions oneself and use small hints only when needed. An AI tutor could adapt such hints to prior knowledge. He leaves open whether this could replace the distinctive depth of many years of one's own research.
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 on a history of mathematics course: compare texts written in class with take-home essays and ask students in conversation about their own reasoning; have them explain passages written with outside help in their own words. This serves learning.
Design the doctorate around acquiring deep expertise in an interesting field and the ability to communicate it. A thorough defence should be decisive; whether results originate in human or AI work is not the determining factor. Regular supervision discussions can test whether doctoral students can independently tackle unfamiliar examples and apply methods to new cases.
Even smaller tasks during a doctorate could conclude with a presentation to fellow students and teachers. The aim would be to understand and explain a solution, perhaps already known or found with AI, so that others understand it too.
Plan additional preparation, coordination and supervision for Thom's model of lectures, an AI tutor, foundational exercises and a laboratory: smaller working groups, trained tutors, technical infrastructure and tasks for mathematical checking. Redistributing contact hours 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 separation between product and competence affects theses. How such contributions can be measured comparably explicitly remains open.
Give more weight to talks, sustained mathematical conversations and the development of convincing research programmes. Litt also recommends interviews for admission to doctoral programmes, since a submitted text alone does not reliably reveal its submitter's mathematical expertise.
Demands for understanding must be reflected in hiring criteria, funding decisions and journal practices. Influential mathematicians should advance concrete changes to incentives and rules; Doğan criticises the community for having long rewarded publication output while young researchers have little influence.
Journals and systems of recognition should distinguish and acknowledge discovery, proof, formalisation and explanation. New concepts, well-chosen questions, talks and informal knowledge exchange also create scholarly value and should be recognised beyond their role as accompanying activities.
For him, the goal of human well-being implies taking teaching and other work that directly benefits people seriously in hiring and decisions on permanent positions.
Raise the academic status of new, effective explanations: establish appropriate journals and assessment criteria, and recognise textbooks and exposition in hiring and decisions on permanent positions, including at early career stages.
Give greater recognition to originality, collaboration and connections between fields, rather than basing prestige predominantly on solving famous problems. For Marcolli, which contributions count is a decision the community can change.
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 the training of young researchers. Their rapid resolution can interrupt this development, even with a short and elegant proof. He acknowledges the benefits of faster solutions in application-oriented areas.
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.
Maintain demanding training and solidarity with colleagues who resist pressure to use AI. He warns against shifting staff budgets to subscriptions and reducing work to checking outputs.
Invest deliberately in people and recognise supervision, role models and inspiring explanations. Community is built by people who understand results, improve them and make them accessible to others.
As a possible doctoral model, first obtain AI results, understand and connect them across fields, and develop a thorough grasp of the state of research. Complementary projects by several doctoral students could be brought together. Valentini identifies this as a preliminary proposal for broader, more collaborative training.
Preserve not only exceptional achievements at the top but a sufficiently large community with diverse abilities. Even researchers with especially original ideas need teachers, mentoring, colleagues and time. As a possible scenario, Schwartz warns that automated problem-solving could weaken these conditions even without solving all mathematical questions.
Do not deliberately use AI to overtake other people's known projects, and do not reward such successes. Exercise restraint when publishing solutions generated incidentally, because simple problems also serve training purposes; he does not claim ownership rights over problems.
Supervisors should develop new, meaningful ways of working together with doctoral students. He fears that losing the prospect of making discoveries of one's own will deter young researchers, and regards safeguarding mathematical expertise and society's support for it as urgent.
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.
International institutions could coordinate public and private contributions on a neutral basis with jointly agreed goals. Valentini cites the organisation of large experiments at CERN as an inspiration.
Distinguish language models as a technology from the business models of large providers. Investigate open models and smaller systems based on carefully selected mathematical data as independent infrastructure; expand public funding and effective oversight.
Create publicly controlled research infrastructure with capable models, computing capacity and easily accessible chat and agent interfaces. Basic access should be free; large projects apply for additional capacity. Governance, funding, technical competitiveness and protection against capture explicitly remain to be clarified.
Develop community-governed models with openly licensed weights and code, published training methods and reproducible evaluations. The initial aim is to support everyday research tasks. Public decision-making rules and scientific independence from industry partners are among the announced principles; implementation is still being planned.
Create a European AI research centre with long-term basic research, interdisciplinary teams and shared computing infrastructure. A non-profit legal structure, transparent management, conflict-of-interest rules, freedom to publish and multiple funding sources should safeguard scientific independence. Open models are supported insofar as releasing them does not endanger the public.
Fund lasting structures for training, independent evaluation, clear exposition and shared mathematical libraries. According to Collas, free model access alone does not create a viable partnership; a community must retain the ability to understand and integrate results itself.
Strengthen publicly funded and smaller community projects as alternatives to commercial AI services. For Harris, mathematical understanding depends on a culture of freely shareable ideas and self-directed work; technological progress alone does not safeguard this culture.
Consider colleagues in financially disadvantaged countries who cannot afford commercial AI services. Thom connects this concern with a demand for equal access to AI as a public or strictly regulated basic service. He leaves open how international access should be financed.
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.
Direct public and philanthropic funding more strongly towards open, locally runnable and cheaper models, and towards transferring powerful methods to less resource-intensive models.
Inequality also exists when private laboratories make stronger, unpublished models available only to selected researchers. Public infrastructure should therefore offer a capable independent alternative; merely funding commercial subscriptions does not meet this goal.
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.
Use usage data to train or improve models only with explicit consent and on previously agreed terms. Document the provenance and permitted uses of training data, and leave rights to independent prior work with researchers.
Authors should be able to choose on arXiv whether automated systems may retrieve full text and source files or only titles, abstracts and citation data. The petition distinguishes open access for humans from consent to automated data use.
Prohibit the reuse of private research communications for model improvement, enforce this through technically verifiable safeguards and complement it with academic usage rules. The author cites locally run models with openly accessible weights and a documented training history, or credible commitments not to retain usage data, as possible protections.
Keep ongoing research and private collaboration records confidential by default. Researchers should see the exact information, abstracted where appropriate, and separately approve it before it is shared. Universities should not demand private collaboration records or use working profiles as a measure for staff assessment.
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.
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 regards resolute rejection of AI by individuals or entire groups as substantively futile, but expects lasting conflicts. He asks how to deal with them without proposing a procedure.
Guide one's own AI use by three questions: does it advance the search for truth, does it support learning, or would thinking for oneself be more enjoyable? Drohmann accepts different decisions and continues to understand mathematics as a human search for justified, communicable truth.
Recognise slow and fast mathematical work as different ways of working without dividing researchers into opposing camps. Debate shared rules, but do not judge people solely for their AI use.
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 increasing divergence between corporate goals and mathematical culture and calls on the community to reject unsustainable uses. He discloses his contacts and preferential access.
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.
The Association for Human Mathematics asks members to make two public commitments: not to work for AI companies and not to publish AI-generated texts. Refraining from AI in core mathematical activities is an additional, voluntary commitment. The announcement thus distinguishes general organisational rules from further individual choices.
Even while using AI tools, one can reject advertising for providers, supplying problems as demonstrations of capability and adopting their competitive logic. Evans considers benchmarks for companies misguided because they primarily support their efforts to attract investment; the community should represent its own goals.
Co-design tools with academic partners and smaller companies so that mathematical practices and values shape development. Clarify expectations about recognising contributions early; she also identifies trade-union organisation as a form of collective action worth considering.
For announced results, ask for the complete argument, how the task was selected and formulated, independent verification and a named expert contact. It also matters whether others can question, attribute and build on the result.
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.
Assess improvements in mathematical performance against ecological and human goals. Chatterji sketches an explicitly utopian vision of locally and sustainably operated AI that supports shared mathematical conversations. At the same time, she criticises competition and incentives based on quantity, and stresses the value of collaboration with human colleagues.
Learn about the effects of AI infrastructure on neighbouring communities and speak with those affected. Distinguish the abstract possibility of helpful AI from the actual conduct of commercial providers; Aougab favours collaboratively developed, freely accessible open models.
Learn from other professions transformed by platforms: jointly analyse accessible usage data and traces, investigate opaque processes and work together for transparency and professional self-determination. The trade union offers to share such experiences; a profession can lose its autonomy before being fully automated.
Develop general principles collectively through concrete cases. The event series treats recommendations of the Leiden Declaration as open questions of implementation and explicitly invites differing assessments.
Deliberately open discussion spaces to early-career researchers, women and people outside Western Europe and North America; also include experts in developing and evaluating language models. Publicly anonymous contributions are possible when identity is verified by the editors. Disagreement alone is not grounds for exclusion. The editors connect broad participation with developing joint initiatives.
Try an independent advisory channel and gather feedback from the community even amid distrust of corporate motives. Hairer describes the advisory group AGMAI as unpaid and independent of AI companies. At the same time, he acknowledges its lack of representativeness, purely advisory powers and the risk of being used for publicity; companies can ignore the advice.
Doctoral students should discuss pay, work requirements and university resource allocation, join forces across disciplines and use existing trade unions or build comparable organisations. Aougab understands securing time, supervision and resources for mathematical thinking as a shared institutional task.
An independent, unpaid advisory group offers recommendations to AI companies, intends to publish them and seeks input from the community. Its initial focus is the coordinated publication of numerous results reported by OpenAI. Specific publication rules have not yet been established. The group has no decision-making authority within the companies; their responsibility remains unchanged.
The Royal Society should use its public and political influence to warn of possible existential risks from rapidly advancing AI. The signatories base their concerns on observed progress in mathematics and its possible transfer to other technical fields.
Consider potential loss of control, dangerous technical applications and accelerating AI development together. He advocates directing mathematical expertise towards relevant safety and alignment problems and weighing the pace of development against catastrophic risks.