A New Infrastructure of Trust

OpenAI has published ten new results addressing mathematical problems that had remained open, with no substantial progress, for at least ten years — and in some cases considerably longer.

The work covers high-dimensional geometry, coding theory, group theory, computational complexity, quantum computing, lattice-based cryptography and extremal combinatorics.

The significance of this development extends far beyond mathematics. It suggests that artificial intelligence is beginning to evolve from a supporting tool into an independent cognitive participant in the scientific process.

However, as the role of AI systems becomes more autonomous, another question becomes increasingly important:

How can we verify that a scientific result produced with significant AI involvement can genuinely be trusted?

From a tool to a participant in discovery

Until recently, AI in science was primarily viewed as an assisting technology. It could:

• analyse scientific literature;

• identify connections between publications;

• perform calculations;

• review computer code;

• suggest hypotheses;

• help researchers prepare and structure their findings.

In the approach presented by OpenAI, the model performed a more independent function.

According to the company, the mathematical arguments underlying the ten results were generated by an internal AI model. Human researchers subsequently prepared the manuscripts, reviewed the results and formalised the proofs in Lean.

AI was therefore used not only to process information or accelerate human work. It directly generated the substantive foundation of the new proofs.

This points towards a new model of scientific activity:

Humans define the research context, organise verification and assume responsibility, while an AI system may identify a new path towards a solution.

What was achieved

The reported results include:

• new upper bounds for sphere-packing density in high-dimensional spaces;

• improved estimates for binary and spherical codes;

• a new construction in group theory;

• results relating to Connes’ rigidity conjecture;

• new lower bounds for arithmetic circuit complexity;

• a quantum parallel repetition theorem;

• new findings concerning the closest vector problem, which is relevant to post-quantum cryptography;

• a solution to Ehrhart’s volume conjecture;

• a new lower bound for multicolour Ramsey numbers;

• results concerning several problems posed by Paul Erdős in extremal graph theory.

The final scientific significance of these results must be assessed by the professional research community.

A publication by the company itself does not replace independent peer review, verification of the proofs or further work by other researchers. Nevertheless, the scale of the reported work is difficult to dismiss as merely another demonstration of improved AI performance.

The central question is changing

Previously, the main question was:

Can AI help a scientist solve a difficult problem?

The question is now becoming:

Can AI systematically create new scientific knowledge that humans subsequently verify, interpret and incorporate into the scientific record?

As AI-driven science develops, attention will increasingly shift away from the model’s ability to produce an answer and towards the ability to demonstrate:

• which system was used;

• how the result was generated;

• which data and tools were involved;

• where the human contribution ended and the machine contribution began;

• how the result was independently verified;

• who assumes responsibility for any potential error.

This is why the next phase of AI-assisted science requires a new infrastructure of trust.

The authorship problem

OpenAI has indicated that it would be inaccurate to attribute authorship of a proof to a human where the proof itself was fully generated by an AI system.

Humans may participate in preparing the manuscript, formalising the proof, interpreting the result and verifying its correctness. However, the core mathematical argument may still have been created by the machine.

This creates a separation between concepts that previously tended to overlap:

• the author of the scientific result;

• the author of the publication;

• the operator of the AI system;

• the researcher who formulated the problem;

• the person who verified the proof;

• the person or organisation assuming responsibility;

• the organisation providing the model and computing infrastructure.

Traditional models of scientific authorship generally assume that an author is a human being who made an intellectual contribution and can take responsibility for the published result.

An AI system, however, has no legal personality, professional reputation or legal responsibility.

Recognising AI as a participant in discovery does not therefore mean automatically recognising it as an author in the legal or academic sense.

What an infrastructure of trust should include

The more independent the role of AI becomes, the more important it is to make the entire research process traceable and verifiable.

Scientific results produced with substantial AI involvement should be supported by records of:

• the precise model and version used;

• the date and conditions of its use;

• the original prompts and research instructions;

• the tools and databases connected to the system;

• the sequence through which the result was generated and reviewed;

• the involvement of human researchers at each stage;

• independent expert assessment;

• formal proof certificates, where available;

• the limitations of the model;

• unsuccessful attempts and alternative conclusions;

• changes made by humans to the AI-generated result.

Such documentation should allow another researcher to understand not only the final conclusion, but also the origin and development of that conclusion.

Formal verification is not sufficient for all scientific disciplines

In mathematics, formal verification systems such as Lean may play an important role. They allow proofs to be expressed in a form that can be checked step by step by a computer.

However, this approach cannot simply be transferred to every scientific field.

In biology, medicine, materials science, engineering and the social sciences, logical consistency alone is not enough. These fields also require:

• laboratory experiments;

• reproducible data;

• sound statistical methodology;

• clinical or technical validation;

• verifiable protocols;

• independent replication;

• institutional and ethical oversight.

AI-driven science is therefore not only a question of building more capable models.

It is also a question of building a new system of scientific governance.

AI is not yet a fully autonomous scientist

The statement that “AI has made a scientific discovery” should be used with caution.

An AI system does not yet operate as an independent scientist in the full institutional and social meaning of the term. It does not autonomously establish a socially significant research programme, obtain research funding, defend its findings before the scientific community or accept professional responsibility for the consequences of applying those findings.

At the same time, describing such a system as merely a tool is becoming increasingly inadequate.

A more accurate description of the current stage may be:

AI is becoming an independent cognitive participant in the scientific process, operating within a human-created framework of problem definition, verification and responsibility.

What universities and research organisations should do

It is no longer sufficient for institutions to maintain a general rule permitting or prohibiting the use of ChatGPT and other AI tools.

They should define:

1. When the involvement of an AI system must be disclosed in a publication.

2. How human and machine intellectual contributions should be distinguished.

3. Which results require independent replication or additional review.

4. Who is responsible for errors in an AI-generated proof or hypothesis.

5. Whether journals, funding bodies or research partners must be notified.

6. How prompts, logs, model versions and research materials should be retained.

7. How confidential data and unpublished results should be protected.

8. Who owns the rights to results created with substantial AI involvement.

9. Which minimum verification standards must be satisfied before publication.

10. How the limitations and uncertainty of AI-generated findings should be documented.

These issues concern more than research ethics.

They also affect intellectual property, contractual obligations, grant funding, research integrity, data protection, liability and the governance of AI systems.

Conclusion

The most important development is not simply that AI may be capable of contributing to the solution of difficult scientific problems.

The structure of scientific discovery itself is changing.

A result may now emerge from a distributed system involving a researcher, an AI model, computing infrastructure, formal verification tools and independent experts.

In such a system, trust can no longer rest solely on the name of an author or the reputation of a research institution.

It must be supported by a verifiable process:

• transparent provenance of the result;

• documented involvement of the AI system;

• independent validation;

• clear allocation of responsibility;

• the ability to reproduce, challenge and review the conclusion.

Complex law. Clear action.

AI is beginning to create new knowledge. The human task is now to build the infrastructure that makes this knowledge verifiable, responsible and worthy of trust.

What matters. What’s next.

This article presents a general scientific, technological and governance perspective. It does not constitute legal advice, a legal opinion or a formal assessment of any specific AI system or research project.