At the London Institute for Mathematical Sciences, researchers are discovering that artificial intelligence doesn't replace human creativity in mathematics and physics—it amplifies it. Rather than rendering mathematicians obsolete, AI has become a tireless collaborator, checking proofs line by line, hunting for counterexamples, and proposing intermediate steps that bridge the gap between what is known and what remains to be discovered.
The capabilities emerging from this partnership are striking. Software can now catch errors in mathematical arguments that would once have consumed months of human scrutiny. It can systematically test whether a conjecture truly holds or fails in unexpected ways. It can suggest auxiliary results—those clever intermediate steps that experienced mathematicians recognize as invaluable scaffolding for a proof. Mathematics and theoretical physics, unlike experimental sciences burdened by the need to mix reagents or wait for reactions, face far fewer bottlenecks. Mathematical experiments are cheap, fast, and digital. The data—from prime numbers to the abstract properties of manifolds—are clean and abundant.
Companies developing AI systems tailored to mathematical reasoning are reporting tangible progress. Harmonic, a software company in Palo Alto, California, developed Aristotle, which has helped solve several problems posed by the prolific mathematician Paul Erdős—questions notorious for being easy to state but brutally hard to crack. Axiom Math, another Palo Alto start-up, announced that its tool found solutions to many research-level problems that professional mathematicians had not yet solved. Meanwhile, models from OpenAI in San Francisco and Google DeepMind in London have solved several challenges from the First Proof Project, a benchmark set of difficult mathematical problems designed to test whether AI can generate genuinely new and verifiable results.
Yet the frontier of how AI shapes discovery extends beyond verification and problem-solving. The research process in mathematics and theoretical physics weaves together creative insight and rigorous logical reasoning in ways that remain only partly understood. Setting the research agenda itself—deciding which questions are worth asking—remains a distinctly human act. These questions arise from real-world problems, contact with neighboring disciplines, or from theories evolving according to their own internal logic and aesthetic standards. Today's AI systems have only limited access to this broader context. They lack the intuition and taste—the sense of where questions come from, what makes them timely, how they fit into a field's evolving structure—that guides human researchers. Albert Einstein, for instance, developed special relativity after noticing a contradiction in how light waves were treated in classical mechanics versus Maxwell's equations describing electricity and magnetism. An AI system would struggle to make that conceptual leap.
One promising direction, still under-explored, is building AI systems that help researchers sort and prioritize potential problems. AI could apply researcher-selected criteria when scanning large mathematical databases like the On-Line Encyclopedia of Integer Sequences or preprint repositories like arXiv, identifying overlooked connections and structural parallels between fields. Used this way, AI might sharpen our understanding of how scientists themselves identify fertile directions for discovery.
The emerging picture suggests neither displacement nor stagnation, but a new rhythm of collaboration—human intuition and aesthetic judgment paired with machine precision and tireless exploration. For mathematics and theoretical physics, where the frontiers of knowledge are bounded more by imagination than by the constraints of the physical world, this partnership may prove transformative.