Alternative Paths for AI in Mathematics: Six Scenarios

There were alternatives to a sudden release of hundreds of claimed solutions to mathematical problems, but no arrangement could guarantee both unrestricted mathematical automation and preservation of the profession as it previously existed. Some losses could have been avoided; others may follow from the capability itself.

I read Terence Tao’s statement about the “path not taken” as expressing two concerns: how the technology was introduced, and what mathematical activity it should serve. His subsequent account of Math 2.0 explicitly connects the health of the research community with the role of mathematical understanding. These are related goals, but they need not always agree. [1], [2]

Here are six possible scenarios. They are institutional choices and thought experiments, rather than predictions or claims about Tao’s exact proposals.

1. Independent evaluation before public deployment

Labs give independent mathematical teams substantial access to a fixed version of their models. The teams choose tests, investigate failures, assess originality and correctness, and publish their findings without company veto. Evaluation includes unsuccessful attempts and computational costs.

Advantages: Researchers obtain a more credible picture of capabilities than selected successes provide. Institutions receive warning before disruption. Evaluation can distinguish producing a plausible manuscript, proving the intended theorem, and producing mathematics that others can use.

Disadvantages: Evaluators receive privileged access and might gain research advantages. Selecting them creates opportunities for favoritism. Meaningful evaluation takes time, while competing labs may continue releasing systems.

Assessment: This is a strong improvement in scientific practice. It would reduce uncertainty and surprise, but would not prevent displacement once powerful systems became widely available.

2. Give researchers the tools before publishing large collections of results

Instead of first demonstrating superiority through autonomous problem solving, labs provide broad, subsidized access to working mathematicians. Researchers decide which parts of their projects to delegate: testing examples, finding counterexamples, proving lemmas, or attempting the entire problem.

Advantages: People can incorporate the technology into ongoing work. Expertise helps select meaningful questions and interpret answers. Benefits are distributed among researchers rather than concentrated in a few company announcements.

Disadvantages: Equal access to a model does not mean equal access to computation, time, or expertise. The competition to solve problems could simply move from companies to individual mathematicians. Researchers might feel compelled to automate their projects before someone else does.

Assessment: This could substantially improve fairness and agency. However, putting AI in a mathematician’s hands does not by itself make its role complementary. A tool can empower each individual while collectively undermining the scarcity on which their careers depend.

3. Release results gradually, with responsibility for their mathematical development

Labs release manageable groups of papers, each accompanied by a clear account of the main ideas, dependencies, verification status, and limitations. They fund independent scrutiny and provide continuing support for questions and corrections.

This addresses a specific part of Tao’s complaint: the absence of people available to explain and participate in developing the announced results. [1]

Advantages: The community has a better chance to understand the mathematics. Errors and attribution problems can be corrected. Workshops and follow-up projects can turn isolated proofs into usable methods.

Disadvantages: Someone controls the release queue and gets to decide which fields receive attention. Holding results privately creates information inequalities. If production continually exceeds the capacity to absorb results, gradual release produces an ever-growing backlog.

Assessment: A reasonable transition policy, especially for results already obtained. It becomes harder to defend as a permanent system of withholding knowledge. The strongest requirement is responsibility for quality and follow-up, rather than an arbitrary publication quota.

4. Build a publicly governed mathematical AI infrastructure

Universities, foundations, public agencies, and participating companies support shared models, computing resources, formal libraries, and repositories. Research priorities and access rules are governed through institutions with broad representation.

Advantages: Mathematical research becomes less dependent on a few vendors. Shared infrastructure supports reproducibility and collaboration. Funding can target neglected subjects and collective projects whose value is difficult to capture commercially.

Disadvantages: Frontier systems may be expensive to develop and maintain. Governance can become slow or dominated by prestigious institutions. Public ownership does not eliminate competition for priority, and open access could accelerate autonomous problem solving.

Assessment: This changes who controls and benefits from the technology. It does not settle how much mathematical work humans will continue to perform. Democratizing automation and protecting human employment are separate objectives.

5. Agree to limit autonomous attacks on open problems

Labs and research institutions adopt a temporary agreement to avoid large-scale autonomous problem solving, while allowing applications such as verification, exposition, computation, and researcher-directed assistance.

Advantages: A pause could buy time for evaluation, institutional adaptation, and protection of people whose projects face sudden disruption. It would express a collective judgment that the manner of transition matters.

Disadvantages: The boundary is unstable: proving a “supporting lemma” may resolve a major conjecture. Compliance is hard to monitor, and nonparticipants gain an advantage. Withholding useful discoveries has costs. Established researchers might also use restrictions to protect their own positions against outsiders.

Assessment: A short, specific agreement could have value. A permanent prohibition seems both difficult to enforce and difficult to justify. Open problems are shared intellectual opportunities, but nobody has an exclusive right to keep them unsolved.

6. Accept rapid discovery and reorganize the profession around it

Autonomous research proceeds, while universities and funders change what they reward. Contributions might include identifying important questions, developing coherent theories, explaining unexpected connections, verifying results, and applying mathematics. Transition funding supports researchers whose projects have been overtaken.

Advantages: Knowledge becomes available quickly. Institutions acknowledge actual capabilities rather than attempting to preserve an obsolete division of labor. Mathematical achievement can be judged more broadly than by priority in solving named problems.

Disadvantages: Institutional change may lag far behind technological change. Established researchers may adapt more easily than junior ones. Nor is there any guarantee that exposition, conjecture formation, or theory building will remain tasks at which human labor is economically necessary.

Assessment: This is the most direct response to lasting automation, but it can become an empty promise unless accompanied by jobs, funding, and credible standards for evaluating contributions.

Ultimately, the path forward is likely to be shaped by those in power and by economic and scientific trends that no individual or institution can fully control. The above scenarios are useful thought experiments, but events may unfold with little regard for our intentions or preferences.

References

1. Terence Tao, contribution to “100+ reactions to 100+ solutions,” Proofs and Prompts, October 2026.
   Collected reactions, including Tao’s statement.
2. Terence Tao, Math 2.0, public lecture at Caltech, October 9, 2026.
   Tao’s introduction to the lecture; lecture slides (PDF).

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