Leiden Declaration on Artificial Intelligence and Mathematics

Leiden Declaration on Artificial Intelligence and Mathematics

This declaration calls for action to address the challenges posed by the<br>use of artificial intelligence within mathematics research. It is the<br>result of a community initiative and is endorsed by the International<br>Mathematical Union (IMU).

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Preamble

Technological developments have repeatedly transformed the practice of mathematics. Recent artificial intelligence technologies, including symbolic and neural methods for the generation and formalization of mathematics, may already have initiated a significant chapter in this long history. Among researchers, artificial intelligence has produced a wide range of reactions: enthusiasm for its potential to yield new discoveries; intimidation by the pace of developments; indifference to these rapid changes; and concern for the implications, both for mathematics and in wider society.

Mathematicians have a choice about whether and how to adopt artificial intelligence in the conduct of their research. They also have a responsibility to ensure the continued flourishing of the discipline. This Declaration calls upon mathematicians to exercise this responsibility, and provides recommendations for individuals, institutions, government, and<br>industry.

Although we adopt the perspective of mathematical research, much of what we write applies equally to other aspects of mathematics. This includes work in the broader mathematical sciences, education, mentoring, publishing, funding, science policy, and use of mathematics in the wider world.

The Declaration is conceived in solidarity with other research endeavors and creative professions facing similar challenges, both within and beyond academia. It complements other calls for action such as the<br>Uppsala Code of Ethics for Scientists, the<br>San Francisco Declaration on Research Assessment, the<br>UNESCO Recommendation on Open Science, and the<br>UK Universal Ethical Code for Scientists. The<br>International Mathematical Union Committee on Publishing, the<br>Society for Industrial and Applied Mathematics, and the<br>American Mathematical Society have also produced related material.

About our values

We base our recommendations on what we take to be characteristic values of mathematical research that we have a joint interest in preserving. Among these are the following:

There are many reasons to pursue mathematical research, ranging from intellectual curiosity to a desire to solve practical and societal problems. Underlying much of mathematics is the activity of proof. Mathematical proofs are regarded as conferring the highest degree of certainty to their conclusions, as well as imparting understanding of why their conclusions are true. These characteristics of proof support the scientific integrity of mathematics.

Results are attributable to specific authors who take credit for their discovery and assume responsibility for their correctness. These principles ground the merit-based standards to which we aspire in mathematical research.

Mathematical arguments are regarded as transparent and subject to independent verification. They may be extremely long or difficult, but in principle no proprietary knowledge or equipment should be required to understand them.

Mathematicians share a concern for proper evaluation of mathematical work relative to shared standards of depth, difficulty, and significance.

Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions. A key source of strength of the discipline has long been the autonomous shaping of the direction of research and the methods used to pursue it.

These characteristics of mathematics as a subject matter are also compatible with understanding mathematics as a human practice, and its place in the world. As mathematicians, and also as inhabitants of a shared world, we have a duty to care for other people and our environment.

Potential threats

Recent developments in artificial intelligence threaten each of these values, often in ways that disproportionately affect students and early-career mathematicians, and hence the long term future of the discipline.

Current automated techniques can...