World’s top 25 mathematicians raise concerns over AI’s growing role in mathematics

Staff Report | PNN

The rapid advancement of artificial intelligence (AI) has created new possibilities for solving complex and unsolved mathematical problems, but leading mathematicians around the world have expressed concern about its impact. They fear that the growing race among AI laboratories to be the first to solve famous mathematical problems could threaten the traditional culture of mathematical research as well as the intellectual property of researchers.

Twenty-five renowned mathematicians have expressed their concerns in an open letter on the issue. Each of the signatories is a recipient of the Fields Medal, one of the most prestigious international awards in mathematics.

The mathematicians’ concerns have emerged at a time when competition among technology companies over using AI to solve difficult mathematical problems is becoming increasingly intense.

Recently, New York University professor Tristan Buckmaster alleged that OpenAI had pressured one of his collaborators over giving proper credit for solving an important mathematical problem. That collaborator is currently employed by Anthropic.

Buckmaster also questioned whether research conducted using Codex in connection with their work had in any way contributed to OpenAI’s own research. Shortly afterward, the company released an important solution to the Navier–Stokes equations. However, that proof has not yet been independently verified.

Amid the controversy, OpenAI withdrew its sponsorship of a mathematics event at Caltech on Thursday. The decision reportedly came after criticism from several researchers at the university.

In their open letter, the mathematicians said that if AI can solve mathematical problems that have remained unresolved for humanity for a long time, it could undoubtedly represent a major achievement for society. However, an AI-generated solution will have lasting value in the mathematical community only when other mathematicians are able to understand, verify and use it in future research.

They fear that in the race to present solutions to problems quickly through AI, some important stages of research are being overlooked. Insufficient time is being given to properly explain new methods and ideas. At the same time, the risk of failing to adequately acknowledge earlier research or the contributions of researchers involved is also increasing.

They warned that such circumstances could raise serious questions about claims of credit, intellectual property and plagiarism in research.

According to the mathematicians, a new idea does not become fully established in mathematics simply because it has been generated by an AI model. Human mathematicians are needed to verify, explain and develop that idea and pass it on to future generations. If this continuity is disrupted, the process of creating mathematical knowledge as well as transmitting it from one generation to another could be damaged.

Another major concern among mathematicians is the possibility of increased secrecy in research because of AI. Many researchers are worried that there may be uncertainty over whether the information contained in work they conduct using AI coding or mathematics-based tools could somehow be used in the future to develop new models.

On the other hand, major technology companies with enormous financial resources could attempt to use potential research paths developed by an individual researcher or research team and quickly solve the same problem using their own AI systems. If such competition continues, researchers may become more cautious about publishing their work.

As a result, those involved are concerned that the culture of open information sharing and collaboration that has developed in mathematical research over many years could weaken.

The potential changes AI could bring to mathematics have been discussed before. In June this year, a working group of mathematicians published the “Leiden Declaration.” It outlined how the use of large language models, or LLMs, in mathematical research could change research methods, while also presenting various recommendations for mathematicians, educational institutions and policymakers.

Many people are comparing the debate over AI in mathematics with the changes emerging in software engineering and other creative and knowledge-based professions because of AI. In these fields, AI is not merely increasing the speed of work; it is also raising new questions about the nature of work, the concept of credit and the role of humans.

According to the mathematicians, a mathematical proof itself does not represent the entire value of mathematics. It is connected to a much longer process involving the creation of new questions, development of new ideas, teaching students and integrating a discovery into the broader body of knowledge.

Therefore, regardless of how much AI capabilities grow, their central concern is that the intellectual role of humans and the fundamental purpose of research should not be lost in mathematics, science and creative fields.

Experts say this debate is unlikely to remain limited to mathematics. As AI continues to enter one profession and research field after another, similar questions may emerge in science, technology, literature and other creative professions in the future: even if AI makes work faster, how can the purpose, credit and human value of that work be preserved