Can AI-generated proofs ever replace human mathematical understanding?

The Leiden Declaration, issued by its working group on 2026-06-02, asks mathematicians to adopt AI only with human responsibility intact. Its central claim is that "Credit and responsibility continue to belong to humans within the mathematical community and should not be given to automated systems." When automated techniques are used, "the responsibility for the correctness and adequacy of the arguments and results" remains "exclusively with the human authors." Authors are asked to disclose tools in a "Tool and computational resource disclosure" section.

The declaration grounds these rules in what it takes proof to be. Proofs give "the highest degree of certainty to their conclusions, as well as imparting understanding of why their conclusions are true." Those are two goods, and the excerpt keeps them apart. The certainty side is under pressure because "Current automated techniques can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs." The problem reaches formalizations too, "where the difficulty lies in the translation between computer-encoded and human presentations of concepts." The understanding side is threatened differently: "broader understanding of the field may be permanently lost in the process of automation." On this account, an argument can pass a correctness check and still fail to show why its conclusion holds.

The declaration's worry about plausible but unreliable output is the form-without-process gap in Does AI separate intellectual form from the thinking behind it?, applied to proofs. Its call for transparency so that arguments can undergo "independent verification" echoes the methodological concern in Does iterative prompt engineering undermine scientific validity?. It is also the normative counterpart to How should AI agents and humans divide research tasks?: that note records humans keeping final decisions in practice, where the declaration makes it a duty. The disclosure rule resembles the permission-style policies in Do university AI policies actually protect what credentials mean?. The declaration ties disclosure to open-science norms (UNESCO, FAIR) rather than to a list of allowed uses, and it leaves the precise form to journals and publishers, who "have already developed guidelines for this."

The excerpt does not establish much empirically. It is a statement of values and recommendations, not a study. It names no case in which an AI argument was checked as correct yet left readers without understanding, and it gives no rate at which "plausible but unreliable" arguments appear. The claim that such arguments are hard to tell from proofs is asserted, and the loss of understanding is a prediction. It also does not show that formal verification alone secures the second good, since it places the difficulty of formalization in translation between machine and human presentations. What follows, at the strength the text supports, is that the declaration is a considered account of what the mathematical community wants to keep. "Correct but not understood" is a risk it names, not a finding it demonstrates.