Mathematicians Hate AI. They Can’t Quit It
Mathematicians express deep concerns about AI's impact on attribution and the future of their field, yet many, including those who accuse AI companies of using their work without credit, continue to use AI tools for research and writing due to their efficiency.
Intelligence analysis by Gemini 2.5 Flash
A growing number of mathematicians are grappling with a paradox: while they fear AI's potential to obscure human contributions, make their work obsolete, and operate without full transparency, they also find AI models like OpenAI's Codex and ChatGPT indispensable for accelerating their research and paper writing, highlighting a complex and unavoidable integration of AI into their disc…
Imagine smart computer programs that are super good at math, like a calculator that can solve really tricky puzzles. Some grown-up mathematicians are a bit grumpy because they think these programs might be using their ideas without saying thank you, or making it hard to tell who solved what first. But even though they're worried, they keep using these programs because they're so fast and helpful, like having a super-speedy assistant for their homework. It's like they can't stop using a cool new toy, even if it sometimes makes them wonder if they'll still be needed to play the game.
Analysis
Tristan Buckmaster
Tristan Buckmaster, a New York University professor, found himself at the center of a controversy after accusing OpenAI of leveraging his work to solve the Navier-Stokes problem, a challenge with a significant bounty. Despite his public claims of uncredited use and the "firestorm" it ignited, Buckmaster continues to utilize OpenAI's coding agent, Codex, for tasks such as tidying research papers. This paradoxical reliance underscores a broader sentiment among mathematicians who, while critical of AI companies' practices, find themselves "stuck" due to the undeniable utility and perceived monopoly of these advanced tools.
Buckmaster's experience highlights the tension between intellectual property rights and the opaque nature of AI model training. He expressed frustration over AI "churning out solutions to long-standing math problems without fully crediting the human work undergirding them," labeling it "irresponsible and childish." His continued use of AI, even as he investigates how OpenAI's agents might have progressed from his earlier work, illustrates the difficult position academics face when powerful, efficient tools become integral to their workflow, regardless of ethical concerns.
Andreas Thom
German mathematician Andreas Thom encountered a similar situation when OpenAI's Astra model claimed to have solved a problem in geometric group theory he had been developing for two decades. Thom was "amazed" and questioned how the AI learned about his specialized techniques, leading OpenAI to amend its press release after he pointed out overlooked prior work. Despite using ChatGPT for his own research, Thom remains skeptical of OpenAI's assurances that his interactions did not influence training data, stating, "AI really kills this entire idea that you could trace back who contributed what."
Thom's perspective emphasizes the erosion of traditional scientific attribution in the age of AI. He concedes that he will "probably never know" if his work fed the AI's result, accepting that the ability to trace contributions "is probably over." This shift represents a significant departure from the established academic practice of peer review and credited collaboration, forcing mathematicians to reconsider the fundamental mechanisms of knowledge creation and sharing in their field.
Navier-Stokes
The Navier-Stokes existence and smoothness problem, a legendary mathematical challenge, became a focal point of the debate when OpenAI announced its solution, allegedly after learning it was close to being solved by human researchers like Buckmaster. This event not only sparked accusations of uncredited work but also ignited a broader discussion about whether AI could render human mathematicians obsolete. OpenAI's subsequent investigation and amendment to its announcement, stating Buckmaster’s prompts "could not have influenced the system," did little to quell the skepticism among the mathematical community.
The controversy surrounding the Navier-Stokes solution underscores the existential questions facing mathematicians. Cornell mathematician Alex Townsend articulated the dual feelings of excitement and nervousness, acknowledging that AI allows for achievements previously impossible while simultaneously questioning "what's my purpose here?" The incident, alongside other AI-driven breakthroughs, has prompted many academics to explore how to integrate these technologies while also advocating for policies, such as those outlined in the Leiden Declaration, to safeguard the integrity and future of human-led mathematical research.
Key points
- Mathematicians are conflicted, finding AI tools like OpenAI's Codex and ChatGPT highly useful despite concerns about attribution and transparency.
- Tristan Buckmaster accused OpenAI of using his work on the Navier-Stokes problem without credit, leading to an OpenAI investigation and amendment.
- Andreas Thom also questioned OpenAI's use of his geometric group theory techniques, highlighting the difficulty in tracing AI's learning sources.
- Concerns include the erosion of traditional scientific attribution, the opaque nature of AI's problem-solving steps, and the existential threat to human mathematicians' purpose.
- Despite these issues, many mathematicians continue to use AI, often with updated privacy settings, due to its efficiency in research and paper writing.
- The mathematical community is advocating for policies and ethical guidelines, as seen in the Leiden Declaration and an open letter from Fields medalists, to ensure AI doesn't "swallow the field."
The integration of AI tools could significantly accelerate mathematical discovery, enabling researchers to tackle problems previously deemed intractable and achieve breakthroughs that expand human knowledge. With proper ethical frameworks and transparent attribution, AI could serve as a powerful collaborator, augmenting human intellect and efficiency in complex research.
The unchecked use of AI in mathematics risks devaluing human intellectual contributions, making it impossible to trace original ideas, and potentially leading to a future where AI companies monopolize mathematical progress without fair credit or understanding of the underlying human work. This could diminish the purpose and motivation for human mathematicians, fundamentally altering the academic landscape.
