Among mathematicians and theoretical physicists, artificial intelligence provokes a range of reactions. Some see it as irrelevant to their work; others fear it could encroach on the most creative, intellectually rewarding aspects of their fields. Yet, the truth that’s emerging, from the work our team is doing at the London Institute for Mathematical Sciences and elsewhere, is subtler.Rather than displacing human creativity in mathematical sciences, AI is augmenting it. Software can now check proofs line by line and catch errors that would once have taken months of human scrutiny to find. It can search systematically for counterexamples — testing whether a conjecture truly holds or fails in an unexpected way. And it can propose intermediate steps in an argument, suggesting useful auxiliary results that help to bridge the gap between what is known and what still needs to be shown.AI cracks 80-year-old mathematics challenge — researchers are astonishedIn experimental fields, prototype ‘AI scientists’ are beginning to automate parts of the discovery cycle, but they remain constrained by the demands of the physical world: mixing reagents, culturing cells, waiting for reactions and contending with noise in the data. Mathematics and theoretical physics face many fewer bottlenecks. ‘Experiments’ are cheap, fast and digital, and mathematical data — from prime numbers to the properties of abstract structures, such as manifolds — are clean and abundant1.Companies developing AI systems tailored to mathematical reasoning have reported steady progress in the past year. Aristotle, a system from software company Harmonic in Palo Alto, California, has helped to solve several problems posed by the prolific mathematician Paul Erdős — questions that are easy to state but notoriously hard to crack. Axiom Math, a start-up company in Palo Alto, has announced that its AI tool found solutions to many research-level problems that professional mathematicians had not yet solved. Meanwhile, models from technology firms OpenAI in San Francisco, California, and Google DeepMind in London have solved several challenges from the First Proof Project, a set of difficult mathematical problems that test whether AI systems can generate new and verifiable results.Here, we give examples of progress in the past few years in this rapidly evolving area, outline the opportunities that AI presents to scientists and mathematicians in theoretical domains — and invite researchers to lean in to using AI in their work.In theoretical physics and maths, researchers weave together creative insight and rigorous logical reasoning to make discoveries — but this process is only partly understood, and there is no single explanation for how breakthroughs happen. For clarity — without putting forth a definitive model — we break the process into several overlapping phases: setting the agenda, formalizing ideas, proposing conjectures and solving and verifying results. This framework is imperfect, but it provides a useful way to assess where AI is already contributing, where challenges lie and how they might be addressed.Setting the agenda. One of the most distinctly human acts in research is deciding which questions are worth asking in the first place. These might arise from outside the field — through real-world problems or contact with neighbouring disciplines — or from within it, in that theories evolve according to their own internal logic and aesthetic standards2,3. These sources are intertwined: concrete problems can generate new concepts, and abstract theory can reshape and deepen the original question.‘It is incredible’: How AI is transforming mathematicsToday’s AI systems have only limited access to this broader context. As a result, they lack intuition and ‘taste’: a sense of where questions come from, what makes them timely and how they fit into a field’s evolving structure. For instance, physicist Albert Einstein developed his special theory of relativity after noticing a contradiction in how light waves were treated in classical mechanics and in Maxwell’s equations, which describe the interplay of electricity and magnetism.One promising but under-explored direction is to build AI systems that help to sort and prioritize potential problems using criteria selected by researchers. For example, AI could follow those criteria when scanning large mathematical databases, such as the On-Line Encyclopedia of Integer Sequences, or preprint repositories, including arXiv, to identify overlooked connections and structural parallels between fields. Used in this way, AI might sharpen our understanding of how scientists identify fertile directions for discovery.Formalizing ideas. Many important ideas take shape before they can be precisely defined. A classic example is the path integral, introduced by theoretical physicist Richard Feynman, which describes quantum systems by imagining all the ways something could happen and combining them. Although this idea has never been fully pinned down in a strict mathematical sense, it has shaped modern physics and inspired new tools in maths4 — for example, ways to distinguish between different types of knots and methods for counting shapes in complex geometries.‘The job description is changing’: mathematician Terence Tao on the rise of AITurning an informal, prose-style argument into a form that a computer can process often demands substantial effort: reconstructing omitted steps, filling in seemingly obvious gaps and making tacit assumptions explicit. But this process can deepen understanding and expose errors. For example, when mathematician Terence Tao at the University of California, Los Angeles, ran an argument in one of his own papers through a proof assistant (Lean4) to check it, he spotted a subtle gap in the logic. A step that had seemed clear had not been rigorously justified.Even the most accomplished mathematicians can benefit from a system that insists every inference be made explicit. Reducing the human labour involved in formalization would lead to larger, higher-quality bodies of verified maths, which in turn could be used to train better AI models. Fully automating formalization is the long-term goal.Progress has been substantial5, but human input is still required. For example, the Xena project, led by mathematician Kevin Buzzard at Imperial College London, has mobilized university students to systematically digitize all the proofs in the undergraduate maths curriculum.AI is beginning to help scale up such tasks. Computer scientist and mathematician Josef Urban at Chalmers University of Technology in Gothenburg, Sweden, used a large language model to formalize theorems in topology — the study of the properties of shapes when they are stretched or twisted.The deepest advances in maths and physics still require human creativity and judgement.Credit: Roman Rybiansky/London Institute for Mathematical SciencesProposing conjectures. A conjecture is a plausible answer to a well-posed problem—that is, an educated guess that seems likely to be true but has not yet been proven. AI can now generate conjectures, but its role remains tentative and tightly coupled to human oversight.This is not a new area for computational approaches. Early specialized computer programs — such as Graffiti6 and the Ramanujan Machine7 — showed that algorithms can indeed suggest new mathematical ideas, not just check existing ones.Graffiti, for instance, found unexpected patterns in networks — simple diagrams of connected points — that later proved useful in chemistry, in which molecules can be understood in terms of how their atoms are linked. The Ramanujan Machine proposed surprisingly simple formulae for fundamental mathematical constants. Similar approaches are now being applied in theoretical physics, helping researchers to uncover hidden patterns and exact formulae8–10.