You know that uneasy feeling when ChatGPT solves a complex problem, but you can't follow its reasoning? Mathematicians experience something similar—except the very foundation of scientific credibility is at stake. In a new paper called Leiden Declaration on Artificial Intelligence and Mathematics, It is argued that the rapid adoption of AI in mathematical research threatens to undermine the discipline's core values: rigorous proofs, transparent reasoning, and human understanding.
The academic equivalent of a warning shot
Sixteen mathematicians prepared a consensus document, which is now supported by more than 130 researchers и International Mathematical Union .
The statement was the result of a September workshop in the Netherlands, where mathematicians spent months hammering out every detail until they reached a complete consensus. "We got there the hard way," explains Rodrigo Ochigame, an anthropologist who studies artificial intelligence and participated in the process. The endorsement from the International Mathematical Union demonstrates that this is not a fringe concern, but a concern expressed by the mainstream mathematical community.
The black box problem concerns pure mathematics.
AI systems can now generate mathematical proofs that are difficult for humans to verify or understand.
This is where things get alarming: advanced AI models are producing increasingly complex mathematical arguments that are difficult for experts to verify. Unlike a calculator, which displays the calculations being performed, these systems produce complex proofs based on internal processes we don't fully understand. Daniel Litt of the University of Toronto warns of a "rush to announce results" from AI startups whose findings are "mostly correct, but not very interesting"—yet their marketing strategy suggests otherwise.
The attribution problem is much deeper. Artificial intelligence systems are trained on arXiv , an open repository where mathematicians share preprints and then generate results without clear attribution. It's like having a brilliant student who's mastered everyone's homework but can't explain where their ideas came from.
The proposed measures are aimed at the entire pipeline.
Mathematicians advocate for mandatory transparency regarding AI and publicly funded alternatives to corporate tools.
The solutions proposed in the declaration are surprisingly concrete:
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Mandatory disclosure of information about the use of AI in research.
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A more rigorous review system capable of processing work using AI.
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Investments in public computing resources to counter the growing influence of big tech companies on mathematical discoveries.
«"Mathematics is and must always remain a deeply human endeavor," wrote IMU Vice President Ulrike Tillmann. This statement captures the declaration's central contradiction: harnessing the power of AI while preserving human understanding and societal trust.
This isn't mathematical Luddism—it's a recognition that when the foundations of scientific certainty become opaque, everything built on them becomes more precarious. Your smartphone's encryption, your GPS navigation, the algorithms that govern modern finance—all rely on mathematical proofs. If mathematicians can't trust the integrity of their own field, this uncertainty permeates everything.
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