The uncertainty is larger than mathematics

Discussions of AI and mathematics often ask when a machine will prove the next great theorem. This may be too narrow. The decisive question is whether AI will automate isolated intellectual tasks or complete scientific projects. The difference is enormous. A 2026 special issue of Dædalus frames the future of discovery in similarly broad terms, ranging from scientist–machine collaboration to autonomous laboratories and discoveries without human understanding [12].

Imagine that a person can say, “Develop a better antibiotic against pneumonia,” and that one year later a tested medicine is delivered to that person’s door. Between the request and the delivery, AI systems formulate the biological problem, search the literature, invent candidate molecules, prove or compute whatever mathematics is required, plan experiments, direct robots, interpret results, redesign the candidates, conduct production, and organize distribution. If this becomes possible, mathematics at every level could be embedded inside autonomous scientific and industrial systems. The same system might count inventory, solve differential equations, develop new statistical methods, and create cutting-edge mathematics for quantum chemistry or biophysics. Human mathematicians would no longer be needed as inputs to ordinary scientific progress.

This thought experiment is useful precisely because it is extreme. It forces us to see that the future of mathematics does not depend only on theorem-proving benchmarks. It depends on robotics, experimental reliability, energy, manufacturing, regulation, institutional trust, and the ability of AI agents to pursue goals coherently for months or years.

The antibiotic example should not be interpreted too literally. A new drug must pass through discovery, preclinical research, clinical research in human participants, regulatory review, and continuing safety monitoring [5, 6, 7]. Robots might automate much of the laboratory work, and AI might compress discovery and analysis, but a drug cannot be fully tested without observations in living populations over time. Neither faster calculation nor better robotics automatically abolishes this biological time. The example nevertheless identifies the relevant threshold: end-to-end autonomy, not merely an impressive answer at one point in the pipeline. There are already restricted demonstrations of this direction. The AI Scientist automates ideation, literature search, experiment design, execution, analysis, writing, and review within machine-learning research, where the experiments themselves are digital [13]. This is far from an autonomous biomedical enterprise, but it shows why the end-to-end question is not merely science fiction.

Five capabilities that should not be conflated

It is tempting to speak of “AI capability” as if it were a single quantity. For the present question, at least five dimensions must be distinguished.

1. Mathematical competence. Can the system calculate, prove, formalize, find counterexamples, and create useful concepts?

2. Scientific judgment. Can it select a consequential question, formulate the right model, recognize an artifact, and decide which anomaly deserves investigation?

3. Long-horizon agency. Can it maintain a coherent project over weeks or years, recover from unexpected failures, change strategy, keep reliable records, and know when to seek help?

4. Physical competence. Can robots manipulate unfamiliar materials and instruments, maintain and repair a laboratory, respond to accidents, and function outside a tightly standardized environment?

5. Institutional authority. Will society permit an autonomous system to recruit clinical participants, spend substantial resources, certify safety, manufacture drugs, or make decisions for which legal and moral responsibility must be assigned?

These capabilities may advance at very different rates. A system might prove a difficult theorem while remaining unreliable on a long, poorly specified project. It might design an experiment that existing robots cannot perform. It might be technically able to approve a treatment while society reasonably insists on an accountable human decision-maker.

The 2026 International AI Safety Report describes current capabilities as rapidly improving but “jagged”: systems can excel at some expert tasks and fail on apparently simpler ones, especially in longer workflows [1]. Measurements of AI agents’ task-completion horizons also show rapid historical improvement, while emphasizing that the tested tasks are mainly well-specified work in software, machine learning, and cybersecurity; they do not establish comparable autonomy across science or ordinary jobs [2, 3]. Meanwhile, self-driving laboratories already combine algorithms, automation, and robotic experimentation in restricted domains, but general laboratory autonomy remains a separate challenge [4]. The evidence therefore supports both urgency and humility.

Four plausible scenarios

No scenario deserves to be treated as a forecast. Their purpose is to expose which decisions depend on which assumptions. Existing discussions span much of the same range. Interviews with leading mathematicians reveal substantial disagreement about the timing and extent of automation [14]. Tao instead conditions on the arrival of research-level AI and asks what goals and values mathematics should preserve [15]; Litt constructs a deliberately adverse future in which AI is superhuman but mathematical progress nevertheless stalls [16].

The immediate uncertainty faced by researchers

Radical uncertainty is not only a problem for students deciding whether to enter mathematics. It is already a problem for established researchers. They must repeatedly make decisions whose value may change before a paper is finished: how much work to delegate to AI, which problems to pursue, what to share with colleagues, and what standards to apply as referees or editors. There is no settled equilibrium from which to answer these questions. The resulting stress is not simply fear of a new tool. It is a rational response to working in a profession whose capabilities, incentives, and unwritten rules are changing simultaneously. Recent interviews with Steven Strogatz and Alex Townsend give unusually direct expression to this mixture of scientific excitement, professional threat, and loss of orientation [24].

Why teaching may outlast research

The demand for mathematical research and the demand for mathematical teaching need not decline at the same rate. Even in a world where AI proves theorems better than people, mathematics is likely to remain in elementary schools, high schools, and colleges for at least one generation, and perhaps indefinitely.

There are several reasons. Most people will continue to need elementary quantitative competence in ordinary life: to compare prices, understand interest, mortgages, insurance, taxes, probabilities, and claims based on statistics. Mathematics also has a longstanding reputation for training general habits of reasoning, precision, and persistence even when its particular content is not used later. Whether transfer from every kind of mathematics instruction is as large as this reputation suggests is a separate empirical question; a review of the evidence found no adequate basis for a strong general claim that mathematical training by itself improves higher-order cognition [17]. The reputation itself influences what parents, schools, and governments want students to learn. Finally, performance in mathematics is commonly treated as a proxy for broader academic ability. Examinations and admissions systems may therefore preserve mathematics as a selection device even when machines perform most workplace calculation.

If mathematics remains in schooling, teachers will be needed. Human teachers do more than supply correct answers: they notice confusion, adjust an explanation, set standards, motivate reluctant students, manage a classroom, and build relationships of trust. AI tutors may take over some of these tasks, but it does not follow from rapid progress in mathematical problem solving that schools will quickly transfer the whole social and institutional role of a teacher to a machine. A related UNESCO analysis argues for a “pedagogy-first” approach in which teachers and learners remain in charge, while the OECD’s review of generative AI in education stresses that learning effects depend on pedagogical design and that the evidence is still developing [8, 9]. A living meta-analysis devoted specifically to mathematics education likewise reports modest positive average effects in the first available studies, but with substantial uncertainty and a rapidly changing evidence base [10].

The consequence is a chain of preparation several levels deep. Elementary teachers must be taught by college instructors and mathematics educators. Secondary teachers require more advanced mathematics and pedagogical training. College instructors are usually prepared in graduate programs by university faculty. The people who educate these teacher educators must themselves be recruited, trained, and intellectually renewed. In practice, the chain can be three or four levels high. The Association of Mathematics Teacher Educators accordingly treats the preparation, recruitment, and professional learning of mathematics teacher educators—as well as the strengthening of research and research-based practice—as long-term goals [11].

Traditionally, people near the top of this chain were expected not only to teach mathematics but also to conduct mathematical research. This arrangement was not merely ceremonial. Research keeps advanced teachers in contact with open questions, provides a demanding test of their own understanding, attracts talented students into the field, and transmits the experience of creating rather than merely repeating knowledge. It does not follow that every teacher educator must always be an active research mathematician. But if research is severed entirely from teacher preparation, the curriculum risks becoming static and secondhand.

This gives a human research community an additional form of option value. It may remain worth supporting not only for the theorems it produces, but because it forms the apex of an educational infrastructure serving millions of students. The effect of dismantling that apex would be delayed: schools might continue normally for years while the supply of well-prepared teachers and teacher educators gradually weakened. Rebuilding the chain would then take a generation. Scenario IV could eventually automate teaching as well as research, but training policy should not assume that technical capability, public trust, parental acceptance, regulation, and institutional change will all arrive at the same speed. Moradifam’s discussion of what remains human in mathematics reaches a compatible conclusion from a different direction: it emphasizes mathematics as a practice that develops attention, judgment, creativity, and genuine understanding, while warning about cognitive offloading and an illusion of mastery [18].

Why the speed of change creates an educational paradox

Training a research mathematician takes roughly a decade from the beginning of undergraduate study, and mathematical maturity continues to develop afterward. AI capability can change conspicuously within six months. We are therefore asked to design a ten-year education for a labor market and research practice that we cannot predict even two years ahead.

This tension is now explicit in the surrounding literature. The statement by 25 Fields Medalists warns that years of training develop understanding and the ability to formulate questions, whereas AI can increasingly produce the final output without reproducing that developmental process [19]. Portegies makes a related case for urgent institutional action [20], while research on AI and cognitive offloading in education describes the more general danger that improved immediate performance may coexist with erosion of unaided competence [21].

Every simple response is risky. Training students exactly as in the past may prepare them for work that machines will perform. Abandoning traditional proof training may produce graduates unable to detect when AI output is wrong or superficial. Teaching only the current generation of tools may leave them with knowledge that is obsolete before graduation. Reducing the number of students too quickly may destroy the human expertise needed if AI progress slows. Ignoring the possibility of contraction may encourage young people to invest years in a profession with sharply declining demand.

This is a problem of decision-making under radical uncertainty. The proper goal is not to guess the winning scenario. It is to preserve option value: choose policies that work tolerably well in several futures and that can be changed when new evidence arrives.

A robust educational strategy

Institutions should adapt by measurements, not by headlines

A curriculum cannot be rewritten every time a company releases a model. Nevertheless, a five-year review cycle is now too slow. Mathematical organizations and universities should conduct a limited review every six months and a deeper review annually. The review should examine stable tests, not publicity.

Useful indicators include:

• reliability on unfamiliar mathematical problems, not only the best successes selected after many attempts;

• ability to explain a proof in a form experts find conceptually useful;

• performance on month-long projects with incomplete specifications;

• ability to notice and repair its own errors without a human pointing to them;

• successful replication of scientific results in independent laboratories;

• robotic performance when instruments, materials, or conditions vary;

• the cost of successful work, not merely its technical possibility; and

• the distribution of access across institutions and countries.

Policy should be tied to thresholds in these indicators. For example, a department might alter qualifying examinations only after systems repeatedly complete a defined class of research tasks under independent evaluation. A funding agency might shift from individual AI subscriptions to shared public infrastructure once access costs become a material source of inequality. Such rules will not eliminate judgment, but they reduce the tendency to redesign education in response to each dramatic announcement. Both the Leiden Declaration and Portegies emphasize community standards, independent scrutiny, and the danger of allowing commercial systems or their benchmarks to set the terms of mathematical practice [22, 20].

Research funding and the preservation of options

Public policy should maintain several options simultaneously.

First, preserve a smaller but strong human capacity for independent mathematics. If AI progress plateaus, this capacity will be essential. If AI progress accelerates, it will still provide independent criticism during the transition. Once the chain of teachers and researchers has been broken, it cannot be reconstructed quickly.

Second, support access to advanced AI and computing at universities. Human mathematicians cannot discover the best division of labor if only corporations can experiment with the systems. Public or nonprofit infrastructure also allows evaluation whose objective is knowledge rather than advertising. The Leiden Declaration similarly identifies unequal access to powerful systems as a threat to participation and calls for broadly accessible infrastructure [22]; Tao also recommends new shared workflows and institutions able to organize, verify, and communicate mathematics under conditions of much greater output [15].

Third, shorten some funding and curricular commitments. Pilot programs, renewable two-year initiatives, and modular courses are more appropriate than irreversible reorganizations based on a single forecast. This does not mean that all planning should become short-term. The durable goals—logical competence, scientific judgment, transparency, and broad access—require long-term support.

Fourth, collect evidence about what happens to novices who use AI extensively. The crucial educational question is not whether students finish assignments faster. It is whether they later solve new problems, detect subtle errors, retain concepts, and create good questions. Longitudinal studies of these outcomes are more valuable than arguments based solely on analogy.

What remains for humans?

In the first three scenarios, substantial human work remains, although its form changes. Humans may choose ends, decide which risks are acceptable, interpret mathematical structures, connect results to experience, teach one another, and assume responsibility. Some of these functions may eventually be automated too. We should not define a supposedly unique human faculty merely to move the boundary each time AI crosses it.

The stronger point is normative. Even if AI can formulate every theorem and run every experiment, humans must still decide whether the resulting world is desirable. A statement such as “develop a better antibiotic” already contains human purposes: disease should be relieved; safety matters; scarce resources should be used in one way rather than another. An autonomous system can optimize an objective, but the authority to determine social objectives and distribute benefits should not pass to a company or machine merely because it is technically competent. Klowden and Tao likewise argue for a fundamentally human-centered integration of AI, directed toward human needs, quality of life, and expanded understanding rather than automation as an end in itself [23].

Human mathematics may also retain value without economic necessity. People run even though vehicles are faster, play chess though computers are stronger, and learn music though recordings are abundant. Mathematics can remain a form of understanding and achievement. Tao’s analysis similarly separates solving problems from the deeper goals and values of mathematical practice [15], while the Fields Medalists’ statement stresses conceptual understanding, the growth of ideas, and human transmission rather than a mere stockpile of true statements [19]. That future might support far fewer paid mathematicians, but it would not make the activity meaningless.

Conclusion

The mathematical community is planning under an unusual mismatch of time scales. AI capabilities may change every six months; developing a mathematician takes many years. No honest forecast resolves this conflict. End-to-end autonomous science is possible enough to deserve serious analysis, but it should not be smuggled into policy as a certainty. A plateau or a long period of human–AI partnership is also possible.

The sensible response is a portfolio rather than a bet. Preserve independent proof and judgment. Train students to use AI at the frontier. Measure capabilities on long, messy, real tasks. Revisit tactics frequently while keeping durable educational goals. Maintain public access and an independent human research community. Give current researchers clear temporary rules that can be revised without being applied retrospectively. Be candid with students about uncertainty.

If humans remain essential to science, these policies will prepare them to work well. If AI becomes dominant but incomplete, the policies will produce the supervisors, interpreters, and critics that it needs. If end-to-end autonomy arrives, no mathematics curriculum can preserve the old labor market; but humanity will enter that transition with more understanding, more independent capacity, and a better chance of deciding what the new abundance is for.

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