AI generates mathematical proofs rapidly

In six weeks, artificial intelligence laboratories have published numerous mathematical proofs, including 719 manuscripts by OpenAI, some of which relate to research areas of Hugo Duminil-Copin, a Fields Medal winner. These developments have caused concern among mathematicians, with 25 Fields Medalists criticizing the divergence between AI company goals and those of the mathematical community.

Research structure faces disruption

Mathematicians argue that the validity of these works is not the main issue, but rather the implications for the structure of research, which is typically organized around multi-year projects. According to Matthieu Alfaro, a professor of applied mathematics at the Raphaël Salem Mathematics Laboratory, the situation has disrupted long-term research plans and raises concerns about the role of humans in mathematics.

Exploration versus automation

The AI's approach bypasses the process of exploration, which Alfaro summarizes as "With AI, it's solved, done, go home." This contrasts with the traditional value placed on the journey of discovery, as emphasized by the French rapper Orelsan: "What counts is not the arrival, it's the quest." For mathematicians, the proof itself is crucial, as it is the method of demonstration that is of interest, not just the result.

Opacity and errors in AI-generated proofs

However, the proofs generated by AI can be opaque, even to experts. OpenAI reported that approximately 42% of its main results were formalized in Lean, a software that allows computers to verify each step of a proof. Nevertheless, some manuscripts were retracted the following day after errors were discovered. Alfaro notes that the AI-generated texts are often difficult to understand, even for professionals.

Concerns over intellectual property

The announcement by OpenAI on Navier-Stokes equations sparked controversy, as mathematician Tristan Buckmaster suspected that his unpublished work might have been used by the company, though this was denied. The incident has raised doubts among researchers, some of whom use AI tools themselves. Alfaro admits that this has made some researchers more paranoid, fearing that their ideas might be stolen.

Speed and inequality in research

The use of AI in mathematics has also raised concerns about the speed of progress and the potential for a "research at multiple speeds" scenario. Some researchers are hesitant to use AI intensively, while others are willing to pay for AI licenses for their students. There is also a geopolitical concern that mathematical research may become increasingly dominated by American or Chinese institutions.

Impact on different generations

The impact of these changes varies by generation. For established researchers like Alfaro, the challenge is less immediate, but for young researchers seeking positions, the pressure is significant. Alfaro raises the dilemma of advising students not to use AI when others are using it extensively.

Strain on academic publishing

The academic publishing system is also under strain, with mathematical journals receiving twice as many submissions as before. The evaluation of research, particularly by young researchers, has become more difficult. There are concerns about how to assess candidates when one has significantly more publications than another, and how to quantify the use of AI in submitted papers.

Broader implications for science

The potential impact of AI extends beyond mathematics, with concerns that biology might be the next field affected. However, Alfaro suggests that the situation in biology may differ from that in mathematics, as there are fewer well-defined major problems to solve, and the field is more experimental.

Differential vulnerability in disciplines

Alfaro concludes that while the challenges posed by AI are significant, the role of applied mathematics may be somewhat less vulnerable compared to pure mathematics, particularly when working across disciplines.