SERIES · As application deadlines approach, Proofs and Prompts is publishing a series of posts from 19 to 23 October for people considering a PhD, doing a PhD or looking for a postdoc: guidelines, discussions and speculation about what to do and what careers in mathematics will look like. This post is one of them. Each is written independently and reflects only its authors’ views. All posts in the series
AI use: ChatGPT was used to improve the exposition of our ideas.
The following is a short summary of a longer text with references, which can be viewed here.
Rapid advances in AI are transforming research, and for the growth of mathematical knowledge, this is thrilling. For our profession, however, this raises critical questions: Will there be a role for human mathematicians to play? How should mathematicians be trained and evaluated? Will there be enough jobs in mathematics? Does it still make sense to pursue a career in mathematics?
We argue that the four main functions of mathematics – discovering truths, being part of human culture and understanding of the world, providing methods for applications, and fostering intellectual growth – will continue to be central in the age of AI. Human mathematicians will still be needed to formulate and prioritize questions, interpret and communicate mathematical results, contribute to AI safety, sustain the social aspects of teaching, and hone analytical and critical thinking skills applicable far beyond academic mathematics.
Given huge uncertainties about the future, nobody can predict which expertise will be in greatest demand. Such expertise cannot be created instantly; it requires years of training, research, and immersion in a professional culture. A strong mathematical community provides a powerful intellectual reserve of such expertise applicable across a wide range of scientific disciplines and industries. This frontier competence can be sustained only by constantly exercising. Just like society needs to maintain fire departments for emergencies, it must support mathematical expertise to preserve and further develop the human capacity to understand and respond to future challenges.
To retain its relevance, however, mathematical culture will need to evolve. For centuries, mathematics relied on the “ownership culture”: competition for priority, with lasting claims to credit for discovering new theorems, enforced through citation and converted into careers, prizes, and reputations via publication lists. This culture is no longer sustainable. If LLMs do most of the heavy lifting, individual credit loses much of its meaning. This may even be healthy: clashing egos have generated much conflict, and mathematics may be better off once egos retreat from “owning” results.
Evaluation criteria based on the ownership culture will have to be revised and rely instead on intellectual agency: broad and deep knowledge, genuine understanding of mathematics and its connections, sound judgment, independent vision, and effective communication skills. Hiring must rely far more on direct mathematical interaction – talks, interviews, sustained conversation – with recommendation letters still important but grounded in substantial personal contact. In the AI era, a theorem proved with heavy AI help should be valued equally to one proved without. Hiring committees should assess mathematicians, not the provenance of their theorems.
The mathematical culture of the future will emphasize a set of new practices. First, it will open a wider mathematical world: instead of focusing on a narrow area, mathematicians will be able to explore a much wider research landscape. Creativity will not disappear; it will simply operate on a frontier moving outward faster than ever. Second, mathematicians will serve as interpreters of massive AI-produced results, helping the wider intellectual community to understand, absorb, connect, and use them. And since the library of available results is always finite while mathematics is infinite, humans will remain contributors, not only readers. Third, mathematicians will use AI to conduct the “big cleanup” of existing mathematical literature, identifying and resolving errors, gaps, obscure arguments, incompatible conventions, and results rediscovered under different names. Mathematicians will use Lean formalization and verification of proofs, but will also complement it with human-readable exposition. The goal is to make the corpus of mathematical literature more reliable and better organized than ever before. Finally, publication formats will evolve to include AI-produced texts, recorded talks, interactive companions, and papers as virtual agents. Publication should become a vibrant infrastructure for navigation, understanding, and further development, rather than a passive record.
Problem solving will decline as professional output but will remain essential as a training tool; discovery-based learning (in the spirit of Alekseev “Abel’s Theorem in Problems and Solutions”) becomes especially valuable. Used well, AI will enable better active and personalized learning: hints rather than solutions, clarifying examples, and diagnostic problems. To test understanding, supervised written tests will need to be supplemented with oral examinations. The aim is to obtain better evidence of subject mastery, not to build a perfect technological defense against dishonesty.
Graduate study will shift emphasis from early specialization and rapid publication toward breadth, depth, communication, and judgment. Faculty-led seminars, reading groups, and advanced courses will grow in importance; as will live mentoring and blackboard exposition. The thesis need not contain the first proof of anything; originality can reside in ideas, methods, questions, connections, or synthesis.
We make a concrete institutional proposal: a small faculty-led lab open to students sharing a background, aiming to combine collaborative research with powerful AI while building the ability to check and understand AI output. The group will meet and brainstorm together, with students taking notes, then the faculty lead will ask AI to respond to the notes, the group will study, check, and discuss the response, with different students focusing on different parts, and the resulting ideas will be written down in a shared document, regularly revised with peer, faculty, and AI comments. The model scales from high-school to graduate research, and success is measured by both the mathematics produced and the growth of the participants.
Finally, we share a few pieces of advice for young mathematicians:
- Accept fundamental uncertainty: build skills robust across many futures rather than organizing life around AI forecasts.
- Learn broadly and deeply; follow your heart: resist early specialization, but achieve genuine mastery in some subjects.
- Put collaboration ahead of competition: find people you enjoy thinking with; help one another understand mathematics.
- Cultivate intellectual agency, with or without AI: whether using powerful models or building understanding by other means, keep solving problems, asking questions, writing explanations, and testing your knowledge.
- Plan around strengths and aspirations, not anxiety: keep multiple career paths open, but do not abandon a beloved subject just because some other occupation looks “safe.” Nothing can provide full security in the age of AI; draw on your talents, skills, and knowledge to build your career.
Rather than trying to salvage the old order, we should preserve what is essential – curiosity, knowledge, understanding, intellectual agency, and the joy of doing and sharing mathematics – as we open our minds to the vast and thrilling mathematical world that we can now explore.
Received 7 October 2026.
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