Artificial Intelligence Guides Mathematicians to Discover New Theorems
Mathematicians from Oxford and Sydney collaborate with DeepMind to use machine learning in discovering and proving new mathematical theorems. The AI uncovers surprising patterns in knot theory and representation theory that human researchers subsequently verify.
Mathematicians partner with artificial intelligence to suggest and prove new mathematical theorems in a groundbreaking collaboration between the University of Oxford, the University of Sydney, and DeepMind. While computers historically generate data for mathematicians, the task of identifying interesting patterns relies mainly on human intuition. However, machine learning now steps in to discern crucial patterns because modern systems generate more data than any mathematician can reasonably study in a lifetime.
The AI system analyzes complex fields like knot theory and representation theory to the surprise of the researchers. Following the machine learning system's suggestions, mathematicians from the University of Oxford discover a surprising connection between algebraic and geometric invariants of knots, which establishes a completely new theorem. Meanwhile, the University of Sydney team uses the AI's connections to move close to proving a 40-year-old conjecture about Kazhdan-Lusztig polynomials.
These results show that machine learning complements mathematical research by guiding human intuition about complex problems. The researchers demonstrate that when mathematical intuition guides machine learning, it provides a powerful framework for uncovering interesting and provable conjectures. This approach proves especially valuable in areas where a large amount of data is available or where mathematical objects are too large to study with classical methods.