It has been a tense summer for the global economy, with political uncertainties, skyrocketing energy prices and concerns about the fast-growing use of AI simultaneously dominating the weeks since the UK parliamentary elections. In that context, dozens of world-renowned mathematicians have signed a statement calling for the Institute of Mathematical and Physical Sciences to seriously consider the possible consequences of AI in mathematics, to ensure that the best scientists are used for the good of society.
The statement, known as the Leiden Declaration on Artificial Intelligence and Mathematics, adopts a view that is far from simply a knee-jerk ideological reaction to AI. Rather, this group of signatories is calling into question everything about the commodification of knowledge, the nature of science and the growing need to protect scientific integrity. They are also making a case for the human sense of understanding and meaning, above all else.
That may or may not be an accurate reading, but one thing is clear: each signatory to the statement also stresses a fundamental point that is not simply a pluralism about what constitutes a proof. They are concerned by the difference between being able to produce an answer, versus being able to understand, to reflect and to see meaning.
Whereas industrialists sometimes point out the advances in mathematical problem-solving and proof generation by the most advanced AI models, the Leiden Declaration signatories do a sober assessment that these AI-generated proofs are, in many instances, not simply wrong, but rather untrustworthy. They are not inherently ‘false’ but rather easy for a human reader to be unconsciously convinced by, while actually containing subtle errors that are missed in the rush to completion.
In math, a proof is not simply some verification of a result. Proofs explain why a statement is true. They aim to not only confirm conclusions but to broaden human understanding and knowledge. The tradition is threatened when conclusions can be drawn from black box systems, such that the inputs and/or operation of the system cannot be independently verified.
The point is not that we want to exclude machines assisting mathematicians. It is that we don’t want to be able to rely on seemingly definitive conclusions that could be made by a small number of proprietary computer systems controlled by a few companies. We are concerned that mathematical authority could be corroded by the shift from reason and human judgment to a black box produced by a few corporate entities, thereby undermining the intellectual tradition to which all mathematicians have contributed.
It also encourages discussion about what it calls an unequal relationship between AI companies and the rest of the research community.
We all know that modern AI is trained on a huge corpus of mathematics literature, research papers, worksheets, and preparation materials. The extent to which proper attribution is lost in the process and of the benefit that commercial companies derive from it is worrying.
The announcement notes that the problem mirrors a global “polycrisis.” But mathematicians are also sounding the alarm about funding being diverted from the discipline and universities. As resources become increasingly scarce, “there are concerns from mathematicians and universities that the focus will shift to problems that are easily automated or commercially enticing,” it notes. The implication is a shift from university-based research whose benefits are diffuse and hard to measure. And a growing trend that it points out is for new breakthroughs to be announced on corporate blogs, marketing kicks and investors’ decks, subduing scientific progress under the whims of commercial interests. The declaration also vows to combat what it calls the “misuse of credentials and titles.” But it turns out that there’s a lot of other ways to misappropriate scientific claims, for profits. The declaration states that if current patterns hold true, AI aid will have a huge carbon impact. A report by the United Nations University released this week shows that AI data centres consume more electricity than all but ten countries. It estimates that in the next four years the demand for electricity and water associated with AI systems will double. It also warns that the carbon footprint associated with AI infrastructure is no less than that of Argentina.
These statistics remind supporters of the Leiden Declaration that there is a fundamental paradox. Societal investments in artificial intelligence are immense. But this investment is being made in systems that may ultimately diminish human understanding, rather than augmenting it.
These mathematicians are not calling for AI to be banned. But they are interesting and responsible people, and they are calling for responsibility on the part of the governments, and for public investment in infrastructure that can allow the public to do important IP work.
What makes this warning meaningful is that it comes from a field that has long been associated with the most reliable way to arrive at knowledge: mathematical proof. That is the core concern and interest of people who write about mathematics. The Leiden Declaration is concerned with a factor that is at risk in relations that involve AI: independent verification that a thing works as advertised.
These mathematicians are not saying that we should abandon AI. But they are saying that we should think carefully about what skills and capacities we want to preserve in societies that use such technology. The message of the Leiden Declaration is that, if we are going to use technology to help us find out what is true, we still need transparency and human judgment, and that requires investment in the right tools and infrastructure.
