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The Dutch city of Leiden has a reputation for hosting conferences on scientific integrity.Credit: Getty
A little more than a decade ago, after a 2014 conference at Leiden University in the Netherlands, researchers published the Leiden Declaration. nature. It requires the responsible use of indicators in research and includes a set of 10 principles that help ensure rigor and fairness in the evaluation of research.1. Along with the San Francisco Declaration on Research Assessment (DORA), the Leiden Principles have been adopted around the world.
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This principle arose in response to a growing body of metric data and innovative computational tools in academia and science that required guardrails for use. Last September, the city of Leiden and its university once again served as a meeting place for scholars concerned about new technology and the integrity of science. This time it was about the role of artificial intelligence in mathematics.
As a result, the Leiden Declaration on Artificial Intelligence and Mathematics published earlier this month2shares some of its namesake’s concerns. The organization recognizes the power and potential of innovative technology and urges researchers and institutions to ensure that human judgment, transparency, and fairness are protected. These principles are the foundation of science and must continue to be maintained. This declaration has received support from researchers across the field, including those who are highly skeptical of AI and those who are more optimistic. nature We wholeheartedly support both the declaration process and its conclusions.
The Leiden Declaration and the workshops that preceded it brought together researchers in mathematics, computer science, philosophy, and history. AI is transforming learning and research in the field, a group of London-based mathematicians write in a paper nature Last week’s comments3. Applications range from automating the checking and verification of mathematical proofs to helping solve (or autonomously solving) unsolved problems in specific areas of mathematics. Just last month, an 80-year-old conundrum in geometry known as the unit distance problem was solved by mathematicians at US technology company OpenAI using just one prompt to a chatbot.
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In the words of Fields Medal medalist Terrence Tao of the University of California, Los Angeles, AI is rapidly changing the job description of mathematicians. But there is no doubt that it is doing more than that. The workshop report says that as AI and commercially available AI software are integrated into mathematical research, “the types of questions pursued and the forms of proofs evaluated will change.”4. The Leiden Declaration warns of the risks this poses to local autonomy. Indeed, across the sciences, evidence is beginning to emerge that the use of AI is correlated with a narrower range of research topics.5. As stated in the declaration, this will disadvantage both researchers who do not have access to the technology and those who do not want to use their own AI tools.
The Leiden Declaration states that mathematical results should continue to be published in a peer-reviewed forum according to the principles of open science, and that “no proprietary knowledge or equipment should be required to understand mathematical results.” Additionally, any material used as training data must have the required attribution and must not be used without consent.
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These recommendations reflect real-world concerns caused by the breakneck pace of development, as highlighted at the workshop. To take the unit distance problem example, OpenAI researchers posted a proof on the publicly accessible company website (see go.nature.com/4epjtkd), and the results were verified by a group of mathematicians independent of the company. However, OpenAI has so far not disclosed the name or details of the software used to solve this conjecture, which was first proposed by Hungarian mathematician Paul Erdos (1913-1996). Additionally, despite several requests, OpenAI, like other technology companies, does not fully disclose on which datasets its models are trained.
The mathematical knowledge that feeds AI models comes from all over the world, with people and institutions from different regions contributing at different points in history. Dirk Jan Struijk, a mathematician and historian who graduated from Leiden, writes in his book: a A concise history of mathematics6First published in 1948, “Mathematics is a vast adventure in ideas. Its history reflects some of the noblest thought of countless generations.”
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The same can be said about AI. The ability of machine learning tools to perform accurately is based on centuries of cataloged, codified, verified, and attributed knowledge. The AI research community must maintain and strengthen this diversity and integrity in mathematics. That means transparency is non-negotiable.
The working group behind the Leiden Declaration and the mathematics community have started an important dialogue on AI in this field. Now is the time for the discussion to expand further and reach other areas.
