Mathematicians Hate AI But Can't Quit It: The Research Dilemma

Artificial intelligence has become an indispensable tool for mathematicians, but it also represents an existential threat to their discipline. Researchers admit they can't stop using it because it saves time and opens new avenues of exploration, even as they fear it may eventually replace their way of thinking.

Context: from calculator to an assistant that questions everything

A decade ago, mathematicians relied on symbolic computation software like Mathematica or SageMath—predictable tools under their control. The arrival of large language models like GPT-4 and Gemini changed the rules: now AI doesn't just calculate, it proposes conjectures, drafts proofs, and even flags errors in formal proofs. That qualitative leap has created a silent dependency across universities and research centers.

Details: proven usefulness and documented risks

A recent Wired report gathers testimonials from mathematicians who use AI daily for tasks that used to take hours: generating test cases, exploring conjectures, or writing first drafts of proofs. According to the publication, tools like Lean combined with generative models have enabled automatic proof verification, but they've also shown that AI can produce plausible yet incorrect reasoning. The debate intensified when several researchers admitted they no longer know how to work without these assistants, while others warn that delegating abstract thinking to a machine erodes mathematical intuition.

Analysis: who wins and who loses from this dependency

The winners are researchers with fewer resources, who gain access to a level of assistance once reserved for elites, and the companies developing these models, which gain data and legitimacy. The losers are traditional mathematicians, whose training based on intuition and manual effort loses relative value. My take: AI won't replace mathematicians, but it will replace those who refuse to use it; the problem is that no one is measuring the cognitive cost of that adoption.

Implications: toward hybrid, regulated mathematics

In the short term, we'll see more journals and conferences requiring disclosure of AI use in proofs, similar to what happened with calculators in exams. In the medium term, mathematical training will have to incorporate AI literacy without sacrificing manual reasoning. And in the long term, the risk is that the discipline splits between those who use AI as a crutch and those who use it as a telescope.

The question isn't whether mathematicians should use AI, but whether they can still call themselves mathematicians when they do.

Source: Wired