When mathematicians push back: The Leiden Declaration on AI and Mathematics and why it matters | McDermott Skip to main content

When mathematicians push back: The Leiden Declaration on AI and Mathematics and why it matters

|

Overview


In June 2026, a group of mathematicians, computer scientists, philosophers, and historians published the Leiden Declaration on Artificial Intelligence and Mathematics (the Declaration). It reads as a manifesto for one discipline, yet its concerns – about who can be an author, how results are verified, and what becomes of work fed into AI systems – are precisely the questions now being litigated, legislated, and contracted around in Europe.

For lawyers and businesses, the Declaration is a useful early-warning signal: it shows where professional norms are hardening, often ahead of the law.

In Depth


What the Declaration actually says

Born out of a 2025 conference at the Lorentz Center in Leiden, the Declaration is not a regulation. It is a voluntary code that individuals can sign, and that professional bodies are invited to endorse and adapt. Its force is reputational and normative rather than legal, but that is exactly how many enforceable standards begin.

The Declaration defends five core values of mathematical research, including proof and certainty, attributable authorship, transparent and independently verifiable arguments, shared standards of evaluation, and the autonomy of the field – and warns that current AI use threatens each. The recommendations are concrete: disclose tool use, keep responsibility for correctness with human authors, attribute sources properly, refuse the use of one’s work as training data without consent, and resist results announced by press release before peer review.

Why a maths declaration is really an AI-governance document

Strip away the disciplinary vocabulary and the Declaration tracks the same fault lines as Europe’s AI rulebook, focusing on issues of human accountability, transparency, copyright, and training data, and a refusal to let marketing claims substitute for evidence.

Three threads connect it directly to enforceable obligations:

1. Human authorship and the ‘reserve of humanity’

The Declaration’s insistence that authorship stays human has a striking statutory echo in Italy. Article 25 of Law 132/2025 amended Article 1 of the 1941 Copyright Act so that protected works must be the fruit of human intellectual work, expressly including works created ‘with the aid of’ AI tools, provided that a genuine human creative contribution remains. The practical effect for businesses is evidentiary: where output is essentially machine-generated, protectability becomes hard to prove. The same law channels this principle into the professions (Art. 13: AI as a support tool only, with a duty to inform clients) and the courts (Art. 15: a reserve of human jurisdiction).

2. Attribution, training data and copyright

The Declaration asks that published work not be used to train models without consent, and that authors be able to opt out. Europe has turned a version of this into compliance duties. Under Article 53 of the EU AI Act, Reg. 2024/1689, providers of general-purpose AI models must publish a sufficiently detailed summary of their training content and operate a policy to respect EU copyright law, including the text-and-data-mining opt-out under the 2019 Copyright Directive. Italy’s Law 132/2025 reinforces the point domestically through a new Article 70-septies of the Copyright Act, anchoring AI-training TDM to the existing Articles 70-ter and 70-quater.

For organizations, the gap between norm and law is narrowing fast: what the Declaration frames as an ethical ask (consent and traceable provenance) is increasingly a documented, auditable obligation, with the EU AI Office able to act on complaints from 2 August 2026 onwards.

3. Disclosure, oversight and ‘don’t believe the hype’

The Declaration’s call to disclose tool use and to keep humans responsible for correctness lines up with the AI Act’s transparency duties (Article 50, on labelling AI-generated content) and human-oversight requirements for high-risk systems (Article 14). Its blunt advice to policymakers – to consult experts, not press releases – reads like a plain-language gloss on the Act’s controls against misleading and manipulative practices. Italy’s law adopts the same posture through its anthropocentric, trustworthy-AI framing and sector-specific safeguards in health, public administration, and justice.

Theme Leiden Declaration EU AI Act Italy’s Law 132/2025
Status Voluntary, professional self-governance; signable by individuals via ORCID. Binding regulation, phased application; GPAI duties live since Aug 2025. Binding national law, in force from 10 October 2025; coordinates with the AI Act.
Human authorship Credit and responsibility stay with humans; AI does not replace human labour. No general authorship rule; focus on provider duties and transparency. Art. 25 amends the Copyright Act (L. 633/1941); protection requires human intellectual work.
Disclosure/ transparency Disclose tool use; add a tool & compute disclosure section to papers. Art. 50: label AI-generated content; GPAI technical documentation duties. Anthropocentric, transparency-led; professionals must inform clients of AI use (Art. 13).
Training data & copyright No use as training data without consent; authors should be able to opt out. Art. 53: public training content summary and EU copyright policy (TDM opt-out). New Art. 70-septies LDA frames TDM for AI training via Arts. 70-ter/70-quater.
Human oversight Humans retain responsibility for correctness and adequacy of results. Art. 14: meaningful human oversight of high-risk AI systems. Art. 3 human oversight; judicial reserve (Art. 15); clinical judgment preserved in health.
‘Don’t believe the hype’ Resist publicity-driven claims; insist on peer review over press releases. Curbs misleading practices; AI Office may act on alerts/ complaints. Trustworthy-AI framing; sector controls for high-risk uses and public administration.

What it means in practice

  • For interpretation. Soft instruments like the Leiden Declaration rarely bind a court, but they do shape how open-textured standards are read. Concepts such as ‘human creative contribution’ (Art. 1 Copyright Act), ‘meaningful human oversight’ (AI Act Art. 14) and the professions’ duty of human prevalence (Law 132/2025 Art. 13) will need content, and disciplinary consensus is one place in which judges, regulators, and arbitrators look for it.
  • For publishers and research-intensive businesses. Expect tool-and-compute disclosure sections, attribution diligence, and opt-out handling to move from good practice to contractual and editorial requirements. Licensing of content for training should be treated as a distinct, negotiated right.
  • For regulated professionals in Italy. Article 13 of Law 132/20025 already requires that AI be used only as a support to a predominantly human service, with clear client information a compliance and engagement-letter question, not merely an ethical one.
  • For AI developers and procurers. GPAI transparency and copyright-policy duties under AI Act Art. 53 are live, with enforcement powers from August 2026. Procurement and vendor contracts should test training data provenance, documentation, and opt-out compliance, the areas in which the Declaration urges authors to demand assurances.

Key actions

Treat the Declaration as a leading indicator. Professional norms here foreshadow contractual and regulatory expectations. Align policies now rather than retrofitting later.

Map your AI use to disclosure duties. Adopt a tool, model, and compute disclosure practice across research, content, and professional outputs.

Protect authorship. Document the human creative contribution to safeguard copyright under Italy’s amended Art. 1 of the Copyright Act.

Audit training data provenance. Verify consent, licenses, and TDM opt-outs. Align with AI Act Art. 53 and Italy’s Art. 70-septies.

Keep a human in the loop and on the hook. Assign accountable persons for correctness and oversight (AI Act Art. 14; Law 132/2025 Arts. 3, 13, 15).

Resist hype-driven claims. Require evidence and peer scrutiny before relying on, or publicizing, AI-generated results.

Outlook

The Leiden Declaration will not be enforced in any court. Its significance is that a community defending rigor and human accountability has reached, independently, the same conclusions that EU and Italian law are now codifying.

For business and legal teams, the message is practical: the principles of human authorship, transparency, consent over training data, and human oversight are converging across soft and hard instruments alike. Building them into governance today is cheaper than defending their absence tomorrow.