‘Like a conversation with a fellow mathematician over coffee’: How AI is reshaping maths research, careers

From brainstorming research questions to generating mathematical proofs, AI is changing how mathematicians approach their work. But researchers say its growing role raises questions about how students learn to think independently, what counts as meaningful research, and which skills future mathematicians will need.

Kaneenika Sinha, an Associate Professor of Mathematics at IISER Pune, told The Indian Express that she uses AI to seek explanations, generate examples, connect ideas and brainstorm research questions. “Talking to a language model feels like having a conversation with an enthusiastic fellow mathematician over coffee!” she said.

Sinha sees potential for students to use AI as a learning aid and sounding board, particularly in a country where gaps in educational infrastructure can limit access to support. “My suggestion to them is to use it to learn, understand and as a sounding board to discuss ideas, but we should not outsource our thinking, cognition and writing powers to it.”

AI as research tool

The possibilities have come into sharper focus following OpenAI’s October 6 release of 722 AI-generated mathematical preprints, grouped into 372 families of results. Three manuscripts were subsequently withdrawn, and the collection has not yet been fully evaluated by the wider mathematical community.

Thomas G Dietterich, Chair of arXiv’s Editorial Advisory Board and Computer Science section, suggested in a post on X that researchers treat the release as though they had discovered “a notebook full of results from a deceased mathematician”. “Our job is to make sense of the notebook,” he wrote.

For mathematicians, that means going beyond establishing whether individual results are correct to understanding how they were obtained, what they establish, and whether they offer new insights.

Sinha said the volume of results makes this assessment particularly important. Beyond mathematical correctness, researchers need to establish whether AI is bringing together existing ideas from different mathematical fields at a scale that people could not previously manage, or developing genuinely new ideas and tools. Given the number of preprints, a proper assessment will take time, she said.

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It is also too early to determine how AI will reshape mathematical research, Sinha said. But if the technology can connect mathematical ideas on a scale beyond what researchers can readily achieve on their own, the community will need to find ways to use that capability to advance the subject.

On the broader research landscape in India, Sinha said researchers in her professional circle were “embracing the new shift with enthusiasm”. She sees AI as a tool for exploring difficult ideas and speeding up their implementation, but said the shift raises questions about how to deepen learning without weakening students’ creative and cognitive abilities, how to assess AI-assisted research, and whether India can develop dedicated AI infrastructure suited to its needs.

Students face excitement and anxiety

For students, the shift is already producing mixed reactions. Sinha said they were excited about AI’s ability to help them learn, while also anxious about what the future holds.

One consequence of OpenAI’s announcement, she noted, was that students with a developing interest in particular areas of mathematics used the release to learn about open problems in those fields.

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But this curiosity sits alongside uncertainty about careers. She said many mathematics students had, in recent years, begun considering options beyond academia. They are now questioning whether their current training will equip them with the skills required in a changing job market. PhD students are also anxious about discussing their ongoing work and the possibility of being “scooped” by AI.

Vamsi Pritham Pingali, a Professor of Mathematics at the Indian Institute of Science (IISc), Bengaluru, is concerned that students could use AI to obtain publishable results without developing the problem-solving skills needed for research. “The student is deprived of valuable training but gains a possible paper. Now must the student do this or not?” he asked.

Vaishnavi Sundararajan, an Assistant Professor in the Department of Computer Science and Engineering at IIT Delhi, raised a similar concern about the value of research training. She questioned the point of a doctorate built around work the researcher might not understand: “What even would be the use of a ‘quick’ PhD where all you have done is churned out proofs that nobody — including you! — might actually understand?”

Sundararajan argued that generative AI is most useful to researchers who already understand the field they are working in. Someone with little logical intuition, she said, may struggle to verify AI-generated Lean proofs thoroughly — a task that could prove as demanding as generating the proof from scratch.

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AI also raises questions about how universities will assess researchers’ abilities when they use AI-generated proofs. Pingali asked: “How can we judge whom to hire if all they did was understand (deeply) AI-written proofs?”

Where mathematicians will still matter

Beyond academia, Pingali sees opportunities for mathematically trained people as AI adoption grows in Indian industries. For privacy reasons, he said, “local open-source models might take the place of ChatGPT or Claude in Indian industries”. He expects people with mathematical training and additional real-world skills to become increasingly important, while cautioning that they must recognise the limitations of mathematical models when applied to complex, real-world problems.

For applications where safety and reliability are critical, he argued, mathematical correctness cannot be replaced by outputs that merely appear to work. “Note that if you want to send a human to the moon, you better be sure that all the algorithms you are using… are mathematically correct. Just empirical heuristics or ‘good enough’ are not enough!” he said.

As mathematical methods are applied to areas such as AI safety and biomedical research, mathematically trained people will be needed not only to develop models, but also to assess their assumptions and limitations in real-world settings. The challenge for future mathematicians, then, may be to learn how to use AI to work more effectively while retaining the judgement needed to understand, question and apply its results.