A misalignment of AI in mathematics

In recent months, advancements in large language models (LLMs) have significantly enhanced their mathematical capabilities, enabling them to solve major problems in various fields of mathematics. However, the push by AI companies to leverage these models as benchmarks for solving mathematical problems poses a threat to the integrity and essence of the scientific discipline.

The goals of AI companies and the mathematical community have become profoundly misaligned, raising concerns about the impact on the broader scientific, creative, and societal landscape.

Mathematical research focuses on comprehending the fundamental structures of shapes, numbers, and natural phenomena. Over generations, it has developed a rich array of sophisticated concepts, methods, abstractions, and tools to explore the mathematical domain. Famous problems have served as landmarks, against which the progress of mathematical understanding can be measured.

Solving such problems has historically been a testament to new insights and innovative methods, which are subsequently studied and refined by the mathematical community through rigorous discussions and the gradual process of simplification. This process culminates in the creation of textbook presentations suitable for students, who are nurtured with great care to grow into capable researchers.

The mathematical community functions as a microcosm of human society, comprising individuals with diverse approaches, united by core values. Students and ideas are the most precious resources, and the community is responsible for nurturing them until they can flourish independently within the mathematical world. Researchers often suggest challenging problems to develop skills that position students for future advancements in research and other domains.

The dissemination of ideas through talks, private discussions, and careful write-ups, while based on human interaction, takes time and is crucial for the evolution of mathematical knowledge.

However, the recent achievements of AI in solving major mathematical problems have garnered widespread attention, transcending the confines of mathematical circles. The pursuit of solving problems has become a mere tool and proxy for achieving the primary goal of conceptual understanding and insight. When the focus shifts to mass-producing true/false statements at an accelerated pace, it risks undermining the very foundations of mathematical exploration.

The hurried announcements of solutions often lack the necessary write-ups, the isolation of new methods, and proper citation of relevant previous work. This rapid production process raises significant attribution and plagiarism concerns, akin to those faced by other creative professions. Without the involvement of mathematicians to guide and integrate AI-conceived ideas into the mathematical canon, these ideas may never fully materialize, and the critical human transmission chain that fosters mathematical progress would be severed.

This situation represents a broader threat to intellectual work, as the misalignment between AI outcomes and their intended purpose endangers the very essence of productive intellectual endeavors. In numerous fields and activities, traditional training not only facilitates the production of final answers or products but also cultivates understanding, the ability to formulate new questions, and the generation of innovative ideas.

However, AI systems are increasingly capable of directly producing the results of such work, leading to a divergence from the intended goals. The challenges faced by the mathematical community echo similar issues encountered by other scientific and creative professions, signaling potential systemic issues that society at large may confront.

The mathematical community must address these challenges urgently, both within its ranks and with AI companies developing these transformative technologies. Moreover, society as a whole must confront analogous issues arising from the pervasive integration of AI in intellectual work. The primary responsibility lies with the humans who control this new technology, as their decisions will determine whether AI enhances and accelerates genuine mathematical study or, conversely, leads to destructive outcomes.

The fate of mathematics—and by extension, the broader intellectual landscape—rests on the judicious and responsible management of AI's burgeoning influence.