AI versus mathematicians, who is the winner?

The war between AI and mathematicians has escalated.

Recently, the American company OpenAI disclosed 722 mathematical manuscripts produced by cutting-edge models, classified into 372 sets of mathematical research results, covering difficult problems in many fields such as number theory and geometry, causing huge waves in the global mathematics community.

OpenAI claims that the vast majority of results are obtained using the same process and using an internal model that has not yet been released. On average, each result consumes about 3 hours of calculations for the model.

It was reminiscent of the dispute a month ago. At that time, OpenAI announced that it spent 88 hours using a large model to solve the Navier-Stokes equation, one of the Millennium Prize problems. 25 Fields Medal winners issued a joint open letter "The Serious Misplacement of Artificial Intelligence in Mathematics", warning of the academic risks brought about by AI's "brute force cracking" of mathematical problems.

From "overcoming a century-old problem in 88 hours" to "outputting hundreds of results in batches to smash the market", AI companies are impacting mathematics, the oldest intellectual fortress of mankind, at the pace of industrialization. The game between AI and mathematicians is related to the future direction of the mathematics discipline.

AI can become a powerful tool for mathematical research.

A leap in research efficiency. Traditional mathematical research often relies on mathematicians' personal intuition, experience and long-term accumulation. The verification of a conjecture may take years or even decades. AI can traverse massive possibilities in a very short time, helping mathematicians deal with boring and repetitive calculations, and greatly compressing the research process.

Research boundary expansion. The thinking of human mathematicians is limited by cognitive frameworks and disciplinary inertia, while AI is not bound by existing paradigms. AI has the potential to discover structures and patterns that are difficult for humans to detect. It can also explore multiple proof paths in parallel, quickly eliminate wrong directions, and provide new ideas for anthropologists.

The research threshold is lowered. AI enables researchers in computer science, physics, biology and other fields to more easily use mathematical tools and promote interdisciplinary integration.

However, the hidden worries are equally profound.

AI's "brute force" is essentially a calculation that lacks understanding. It can give answers, but it cannot explain why. Even if a theorem derived by exhaustive calculation is correct, it will hardly bring cognitive enlightenment. When humans overcome mathematical problems, they are often accompanied by the birth of new concepts and new methods. The research process itself will inspire a lot of follow-up work. The research results will be reviewed and digested by peers, ultimately enriching the subject knowledge system.

What is even more serious is the damage to the academic ecology. Mathematical proof requires absolute logical rigor, and the reliability verification of AI-generated content is a big problem.

OpenAI company mass-produces results but does not disclose model details and prompt words, requiring mathematicians to spend a lot of time doing "obligatory verification." This makes mathematicians believe that "releasing more than 700 documents at one time shows not academic research but power." The inversion of "AI announces breakthroughs and humans are free to deal with the aftermath" has eroded the trust of the academic community. Many young scholars are worried that their research directions will be preempted by AI and do not dare to disclose their explorations. This also destroys the normal ecology of the academic community.

There is currently no winner in this war. AI demonstrates the efficiency of industrialized problem-solving, but exposes a profound rupture between “answers” ​​and “understanding.” Mathematicians defend the intrinsic value of the subject, but face the practical dilemma of academic ecology being eroded by commercial logic.

Looking back at history, from the abacus to the computer, every tool revolution in the history of mathematics has reshaped the face of the subject, but it has never ended mathematics itself.

Looking to the future, mathematics in the AI ​​era will most likely bring about the reorganization of the division of labor between humans and machines. The academic community needs to establish academic norms that adapt to the AI ​​era, clarify the release standards and review mechanisms for AI results, and clarify the boundaries of AI participation in scientific research.

The future of mathematics should not be about humans being replaced by AI, but about humans using AI as their assistants to reach distant places that are difficult for any party to reach alone.